Description
In modern economies, prices are generally expressed in units of some form of currency.
ABSTRACT
Title of Document: CONGESTION PRICING FOR THE CAPITAL BELTWAY
Degree Candidate: Joshua Lee Crunkleton
Degree and Year: Master of Science, 2008
Directed By: Dr. Kelly Clifton
Department of Civil and Environmental Engineering
Road users fail to realize their role in congestion. This thesis aims to calculate
the appropriate charges required for users of I-495 – the Capital Beltway surrounding
Washington, D.C. – in order to fulfill their portion of congestion costs. By
developing a model from existing data that showcases traffic characteristics causing
congestion, the user charges necessary to cause drivers to realize the congestion costs
that their vehicles impose on the rest of the traffic stream are determined.
This study concludes that under typical traffic flow conditions for the Capital
Beltway, charges ranging from $0.03 to $0.08 per passenger car equivalent (PCE) per
mile during AM and PM peak periods cause drivers to realize their contribution to
congestion costs. These results are lower than the $0.08 to $0.50 per-mile charges
that previous research has estimated. As vehicles occupy various amounts of road
space, charges on a PCE basis are most equitable.
CONGESTION PRICING FOR THE CAPITAL BELTWAY
By
Joshua Lee Crunkleton
Thesis submitted to the Faculty of the Graduate School of the
University of Maryland, College Park, in partial fulfillment
of the requirements for the degree of
Master of Science
2008
Advisory Committee:
Dr. Kelly Clifton, Chair
Dr. Cinzia Cirillo
Dr. Stanley Young
© Copyright by
Joshua Lee Crunkleton
2008
ii
Dedication
To my grandfather, Joseph A. Crunkleton – this is for you, Pop.
iii
Acknowledgements
I would like to extend my sincere gratitude to the network of people who
helped make this thesis possible.
To my wonderful family and friends: thank you for your perpetual support. It
means more than you know. Without the insight, suggestions, and prior methodology
of Mr. Gabriel Roth, this study would have never existed. Through the guidance of
Dr. Kelly Clifton and my advisory committee – Dr. Cinzia Cirillo and Dr. Stanley
Young – this thesis was able to reach fruition. Last, but definitely not least, Tom
Schinkel, Randy Dittberner, and others with the Virginia Department of
Transportation (VDOT) deserve special thanks in terms of data collection and much-
appreciated feedback.
iv
Table of Contents
Dedication..................................................................................................................... ii
Acknowledgements...................................................................................................... iii
Table of Contents......................................................................................................... iv
List of Tables ............................................................................................................... vi
List of Figures ............................................................................................................. vii
Chapter 1: Introduction................................................................................................. 1
1.1 Background......................................................................................................... 1
1.2 Problem Statement .............................................................................................. 4
1.3 Research Objectives............................................................................................ 6
1.4 Document Organization...................................................................................... 6
Chapter 2: Literature Review........................................................................................ 8
2.1 Congestion Pricing Background/Theory............................................................. 8
2.1.1 Traffic Flow Theory................................................................................... 12
2.2 Implementation ................................................................................................. 14
2.3 Studies............................................................................................................... 17
2.4 Closing Remarks............................................................................................... 21
Chapter 3: Methods and Data ..................................................................................... 22
3.1 Introduction....................................................................................................... 22
3.2 Proposed Method .............................................................................................. 22
3.3 Methodology..................................................................................................... 26
3.3.1 Data............................................................................................................ 27
3.3.2 Speed Analysis........................................................................................... 30
3.3.3 Flow Analysis ............................................................................................ 33
3.3.4 Speed-Flow Relationship........................................................................... 36
3.3.5 Delay Calculations ..................................................................................... 39
3.3.6 Speed Frequency and Probability by Flow Range..................................... 42
3.3.7 Traffic Proportions..................................................................................... 44
3.4 Value of Time Estimation................................................................................. 45
3.5 Model Formulation ........................................................................................... 47
3.6 Assumptions...................................................................................................... 50
Chapter 4: System Evaluation..................................................................................... 52
4.1 Inputs................................................................................................................. 52
4.2 Outputs.............................................................................................................. 53
4.3 Model Demonstration ....................................................................................... 56
4.4 Evaluations........................................................................................................ 59
4.4.1 AM Peak .................................................................................................... 59
4.4.2 PM Peak..................................................................................................... 60
4.4.3 Discussion of Results................................................................................. 62
4.5 Sensitivity Analysis .......................................................................................... 62
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4.5.1 Effect of Elasticity ..................................................................................... 63
4.5.2 Effect of Traffic Proportions...................................................................... 65
4.5.3 Effect of Value of Time and Vehicle Operating Costs.............................. 66
4.6 Summary........................................................................................................... 67
Chapter 5: Implementation ......................................................................................... 68
5.1 Overview........................................................................................................... 68
5.2 Congestion Pricing Strategy ............................................................................. 69
5.2.1 Hours of Operation .................................................................................... 69
5.2.2 Charges ...................................................................................................... 70
5.2.3 Goals .......................................................................................................... 71
5.2.4 Conditions.................................................................................................. 71
5.2.5 Payment Options........................................................................................ 72
5.2.6 Revenue Spending ..................................................................................... 72
5.2.7 Technology ................................................................................................ 73
5.2.7.1 Open Road Tolling.............................................................................. 73
5.2.7.2 Enforcement/Collection...................................................................... 74
5.2.8 Comparisons to Existing Systems.............................................................. 76
5.3 Equity Considerations....................................................................................... 77
5.4 Policy Limitations and Recommendations ....................................................... 79
5.5 Summary........................................................................................................... 82
Chapter 6: Financial Implications............................................................................... 84
6.1 Costs.................................................................................................................. 84
6.1.2 Scenarios Examined................................................................................... 84
6.1.2.1 Gantry Setup on I-495......................................................................... 86
6.1.2.2 Gantry Setup on Entrance and Exit Ramps......................................... 88
6.1.3 Chosen Scenario......................................................................................... 88
6.2 Revenue............................................................................................................. 89
6.3 Break-Even Points/Payoff Calculations............................................................ 91
6.4 Assumptions and Conclusions .......................................................................... 95
Chapter 7: Conclusions and Recommendations ......................................................... 97
7.1 Summary of Results.......................................................................................... 97
7.2 Conclusions....................................................................................................... 98
7.3 Recommendations for Future Research............................................................ 99
Appendix................................................................................................................... 102
References................................................................................................................. 115
vi
List of Tables
Table 2-1: Common Vehicle Charging Options ......................................................... 19
Table 3-1: Vehicle Classification PCE Factors .......................................................... 26
Table 3-2: I-495 Detector Location Information ........................................................ 28
Table 3-3: Delay Calculations Using HCM Equations............................................... 40
Table 3-4: Delay Calculations Using I-495 Regression Equation.............................. 41
Table 3-5: Peak Period Traffic Proportions ................................................................ 45
Table 3-6: FHWA HERS Model – Value of Time ..................................................... 46
Table 3-7: FHWA Vehicle Classifications – Value of Time...................................... 47
Table 4-1: Average AM Peak Hourly Flow for I-495 ................................................ 60
Table 4-2: AM Peak Hourly Congestion Charges for I-495....................................... 60
Table 4-3: AM Peak Traffic Composition Resulting from Congestion Pricing......... 60
Table 4-4: Average PM Peak Hourly Flow for I-495................................................. 61
Table 4-5: PM Peak Hourly Congestion Charges for I-495 ....................................... 61
Table 4-6: PM Peak Traffic Composition Resulting from Congestion Pricing.......... 62
Table 5-1: Hourly Congestion Charges for I-495....................................................... 70
Table 6-1: I-495 System Costs.................................................................................... 87
Table 6-2: Gantry Totals on Entrance and Exit Ramps .............................................. 88
Table 6-3: I-495 System 50-Year Cumulative Costs.................................................. 92
Table 6-4: I-495 System 50-Year Cumulative Revenue............................................. 93
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List of Figures
Figure 1-1: I-495 Region Map...................................................................................... 5
Figure 2-1: Theoretical Congestion Pricing Model .................................................... 12
Figure 2-2: Greenshield’s Model – Speed-Flow Relationship ................................... 13
Figure 2-3: Speed-Flow Curves for Basic Freeway Segments ................................... 14
Figure 3-1: Proposed Method ..................................................................................... 23
Figure 3-2: FHWA Vehicle Classifications................................................................ 25
Figure 3-3: I-495 Data Locations................................................................................ 28
Figure 3-4: Average Hourly Speed – Detector 190064 .............................................. 32
Figure 3-5: Average Hourly Speed by Year – Detector 190064 ................................ 32
Figure 3-6: Average Hourly Flow – Detector 190064................................................ 35
Figure 3-7: Average Hourly Flow by Year – Detector 190064.................................. 35
Figure 3-8: Hourly Volume-to-Capacity Ratio – Detector 190064............................ 36
Figure 3-9: I-495 Speed vs. Flow ............................................................................... 38
Figure 3-10: Speed Probability by Flow Range.......................................................... 43
Figure 3-11: Frequency by Flow Range ..................................................................... 44
Figure 4-1: Model Demonstration .............................................................................. 58
Figure 4-2: Sensitivity of Elasticity Values for Congestion Charges (AM Peak) ...... 64
Figure 4-3: Sensitivity of Elasticity Values for Congestion Charges (PM Peak)....... 64
Figure 5-1: Open Road Tolling Gantry....................................................................... 74
Figure 5-2: License Plate Recognition Software (London) ........................................ 75
Figure 5-3: Typical Gantry Camera Setup (Stockholm)............................................. 76
Figure 6-1: I-495 Gantry Setup (Direct) ..................................................................... 85
Figure 6-2: I-495 Gantry Setup (Entrance and Exit Ramps) ...................................... 85
Figure 6-3: Distribution of Trip Distances.................................................................. 90
Figure 6-4: Yearly I-495 System Payoff..................................................................... 94
Figure A-1: Average Hourly Speed – Detector 90138 ............................................. 102
Figure A-2: Average Hourly Speed by Year – Detector 90138................................ 102
Figure A-3: Average Hourly Flow – Detector 90138............................................... 103
Figure A-4: Average Hourly Flow by Year – Detector 90138 ................................. 103
Figure A-5: Hourly Volume-to-Capacity Ratio – Detector 90138 ........................... 104
Figure A-6: Average Hourly Speed – Detector 90202 ............................................. 104
Figure A-7: Average Hourly Speed by Year – Detector 90202................................ 105
Figure A-8: Average Hourly Flow – Detector 90202............................................... 105
Figure A-9: Average Hourly Flow by Year – Detector 90202 ................................. 106
Figure A-10: Hourly Volume-to-Capacity Ratio – Detector 90202 ......................... 106
Figure A-11: Average Hourly Speed – Detector 90275 ........................................... 107
Figure A-12: Average Hourly Speed by Year – Detector 90275.............................. 107
Figure A-13: Average Hourly Flow – Detector 90275............................................. 108
Figure A-14: Average Hourly Flow by Year – Detector 90275 ............................... 108
Figure A-15: Hourly Volume-to-Capacity Ratio – Detector 90275 ......................... 109
Figure A-16: Average Hourly Speed – Detector 190004 ......................................... 109
Figure A-17: Average Hourly Speed by Year – Detector 190004............................ 110
Figure A-18: Average Hourly Flow – Detector 190004........................................... 110
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Figure A-19: Average Hourly Flow by Year – Detector 190004 ............................. 111
Figure A-20: Hourly Volume-to-Capacity Ratio – Detector 190004 ....................... 111
Figure A-21: Average Hourly Speed – Detector 190057 ......................................... 112
Figure A-22: Average Hourly Speed by Year – Detector 190057............................ 112
Figure A-23: Average Hourly Flow – Detector 190057........................................... 113
Figure A-24: Average Hourly Flow by Year – Detector 190057 ............................. 113
Figure A-25: Hourly Volume-to-Capacity Ratio – Detector 190057 ....................... 114
1
Chapter 1: Introduction
1.1 Background
Traffic congestion is the topic of daily news broadcasts, water cooler horror
stories and mounting frustration nationwide. As slower driving speeds, increased
queuing and worsened travel reliability take center stage, we are left wondering what
led to this condition and, more importantly, where we can turn for relief.
Traffic congestion is a familiar problem around the world, especially for those
in urban areas. Congestion affects everyone and is usually defined in terms of excess
vehicles on a portion of roadway at a certain time that results in speeds that are slower
than free-flow conditions. At its most basic level, the consequence of failing to
effectively manage the capacity of a roadway system results in congestion. Road
capacity has not grown as quickly as road use – between 1990 and 2005, for example,
vehicle-miles traveled increased by 44 percent, while highway lane miles only
increased 4 percent (FHWA 2005, 1990). It goes without saying that if vehicle-miles
traveled have increased at a rate much greater than that of the construction of new
highway lanes, congestion has been a direct result.
Among professionals, metropolitan traffic congestion is often deemed the
single most critical issue we face today in the transportation industry – an idea that is
slowly being expressed by government figures across the country. According to the
Texas Transportation Institute’s 2007 Urban Mobility Report, congestion in
America’s urban areas is estimated to cost approximately $78 billion per year in
wasted fuel and delay costs (Schrank 2007). In addition to these commuting costs,
2
Americans see reductions in both quality of life (reduced air quality, less time with
family and friends, etc.) and productivity. Industry costs relating to the movement of
goods by truck are rising. Congestion in the United States is affecting more roads for
more people – it is estimated that the average weekday peak period trip takes almost
40 percent longer than an identical off-peak trip; this compares to only a 13 percent
increase in 1982 (Dodgson 2006). AM and PM peak periods have also expanded. In
larger cities, drivers spend the equivalent of almost 8 work days each year stuck in
traffic (Paniati 2006) and the situation is only escalating – the duration, extent and
intensity of congestion is increasing annually.
It must be noted in this discussion that congestion is not viewed only in
negative light – there are some who consider traffic congestion to be an inherent sign
of success. More or less, people want to be where opportunities are located and,
often, when the automobile is the dominant mode choice, congestion is a result.
While it is true that a different spin can be placed on any situation, the impact of
congestion on urban areas at the local, regional and national level cannot be refuted.
Effective, accessible transportation networks are key instruments in enhancing quality
of life and, for this reason, congestion issues need to be addressed instead of ignored.
Many analysts believe that efficient transportation depends more on managing
existing demand than on adding new supply (Victoria Transport Policy Institute
2007). The fact that vehicle-miles traveled are increasing at a rate far greater than
roadway construction is evidence that we cannot possibly build our way out of
congestion. Studies have shown that 60-90% of new road capacity is anticipated to
be filled within 5 years of construction and that induced demand (i.e. increased
3
traffic) comes with added capacity (Replogle 2007). This is not surprising, as traffic
attempts to flow along the path of least resistance – if new roads or lanes are
constructed, more people will choose to utilize these paths until the level of
congestion returns to its previous state, at which time users will choose alternate
routes.
Travel is mainly a derived demand, meaning it is usually demanded not for its
own sake but as a means of consuming some other good or service or to participate in
economic activities (i.e. work). Because the activities with which transportation is
associated vary over time, the demand for travel is not constant over time. For
example, many towns and cities experience traffic congestion during peak morning
and evening commuting times, and holiday routes experience seasonal congestion
(Button 2004). Traffic demand has to be adjusted in order to make any tangible
difference.
A key tool for such demand management is user charges (i.e. pricing). In
concept, the ideal form of pricing is congestion pricing, which charges highway users
based on their contribution to highway congestion, which means that the charges are
specific to both a place and a time. Transportation is over-consumed as a direct result
of inadequate pricing. If priced properly, fewer miles will be driven per vehicle and
less transportation will be consumed. Congestion pricing is currently the source of
heated political debate regarding potential congestion solutions and aims to adjust
traffic demand in order to alleviate traffic congestion qualms. Further, there is
consensus among economists that congestion pricing represents the single most viable
and sustainable approach to reducing traffic congestion. Free road use ultimately
4
leads to congestion, which is detrimental to all users. Congestion pricing is a way of
ensuring that those using valuable and congested road space make a financial
contribution, encourages the use of other transportation modes and is intended to
ensure that, for those who have (or choose) to use the roadways, trip times are faster
and more reliable.
Critics argue that users pay for their road usage through gas tax revenue –
generated from the levy imposed on the per-gallon sale of motor fuels at both the
state and federal levels. While this idea is not totally discredited, current gas tax
revenue figures are not enough to justify the amount of road usage that is occurring in
our society. In many states, gas taxes have not been raised since the early 1990s and
when they happen to be raised, it is generally not enough to keep up with inflation. In
fact, twenty-eight states have raised their gas tax rates since 1992, but only three have
raised it enough to keep pace with inflation (Brookings Institute 2003). The public
tends to unknowingly think that their annual contribution to the gas tax is much
greater than it actually is. On average, between $500 and $600 is paid per vehicle per
year towards the gas tax – less than most annual cable television bills.
1.2 Problem Statement
Most people fail to consider the adverse effect that their traveling places on
others – it is the aim of this thesis to address and explore this inadequacy. Many road
users have come to believe that they currently own the right to travel freely and
uninterrupted and that roadways are provided exclusively in order for them to achieve
this goal. Only by attaching a usage-based price to travel habits will drivers
understand, and curb, their role in congestion. Roadways should be viewed as a
5
commodity, in the same light as public utilities (telephone and electric services),
movie tickets or airline pricing, where the price of the services are usage-based and
increase as the demand increases over a certain threshold. Companies in these fields
have used peak period pricing for years – why shouldn’t transportation agencies do
the same?
In this region, traffic congestion is a daily concern on I-495, surrounding
Washington, D.C. Figure 1-1 shows this roadway in context of the region. Correct
user pricing for all lanes of I-495 would ultimately be beneficial to society. It is
important that the optimal price is determined, as incorrect pricing can have an
adverse effect on the economy and inadequate pricing will fail to curb demand.
Figure 1-1: I-495 Region Map
Source: MapQuest
6
1.3 Research Objectives
Due to the aforementioned fact that travelers fail to realize their role in
congestion, the goal of this thesis is to calculate the appropriate charges required for
users of I-495 – the Capital Beltway surrounding Washington, D.C. – in order to
fulfill their portion of congestion costs. The first objective is to develop a model from
existing data that showcases traffic characteristics that cause congestion, in addition
to the results of such interactions. Secondly, the charges necessary to cause vehicle
users to realize the congestion costs that their vehicles impose on the rest of the traffic
stream will be determined. This will be accomplished using prior methodology set
forth by Gabriel Roth and Olegario Villoria (2001). The contribution of this thesis
lies not in the method itself, but by examining the model in the context of a freeway
(I-495) instead of city streets. The third objective of this thesis is to examine the
potential financial implications (costs and revenue) that would be associated with the
proposed congestion pricing system on I-495.
1.4 Document Organization
This thesis is organized into seven chapters and one ancillary appendix. The
previous sections of Chapter 1 contained introductory information regarding traffic
congestion and described the purpose and scope of this work. Chapter 2 serves as a
review of existing literature applicable to this thesis, including information on
congestion/road pricing theory, implementation, and studies. Chapter 3 introduces
the proposed method behind this thesis and the entire model formulation is set forth in
detail – the methodology, from obtaining initial data through creating a functional
7
model, is also discussed. Drawing upon the aforementioned work by Roth and
Villoria, data from detector locations on the Capital Beltway, dating back to 2002, are
examined. Chapter 4 provides an evaluation of the proposed system, along with a
demonstration of the model. Based on this evaluation, optimal pricing ranging from
$0.03 to $0.08 per mile for each passenger car is obtained. Results of applicable
sensitivity analysis are also set forth in this chapter. Chapter 5 outlines potential
implementation of the proposed congestion pricing strategy and includes information
on current technology, equity considerations, and policy limitations. The financial
implications of such a system are provided in Chapter 6, with multiple setup scenarios
being examined and corresponding costs and revenue examined. The benefits and
challenges associated with the system are discussed and system payoff and break-
even points are addressed. Chapter 7 summarizes the results of the thesis and
addresses recommendations for areas of future research.
8
Chapter 2: Literature Review
In terms of summarizing existing literature applicable to this thesis, there are
numerous aspects of congestion/road pricing that are deserving of discussion. The
following sections touch on a varied selection of topics, including congestion pricing
theory, implementation, and studies.
2.1 Congestion Pricing Background/Theory
“An Inquiry into the Nature and Causes of the Wealth of Nations,” written by
Adam Smith in 1776, is widely considered to be the first modern work in the field of
economics. Included is the following passage which deduces that road users should
pay in accordance with their usage (i.e. the magnitude of the road damage they
cause):
“When the carriages which pass over a highway or a bridge (...) pay toll in
proportion to their weight or their tonnage, they pay for the maintenance of
those public works exactly in proportion to the wear and tear which they
occasion of them. It seems scarce possible to invent a more equitable way of
maintaining such works. This tax or toll too, though it is advanced by the
carrier, is finally paid by the consumer, to whom it must always be charged in
the price of the goods. (...) His payment is exactly in proportion to his gain. It
is in reality no more than a part of that gain which he is obliged to give up in
order to get the rest. It seems impossible to imagine a more equitable method
(Smith 307).”
Following Smith’s idea of charging road users appropriately leads to the idea of
congestion pricing. Lindsey and Verhoef (2000) contend that the insight for
congestion pricing comes from the observation that people tend to make socially
efficient choices when they are faced with all the social benefits and costs of their
actions. Congestion pricing is widely viewed by economists as the most efficient
9
means of alleviating traffic congestion, because it employs the price mechanism, with
all its advantages of clarity, universality, and efficiency.
Based on writings such as those by Lindsey and Verhoef (2000), an early
history of congestion pricing can be determined. In the 1920s, Arthur Cecil Pigou
and Frank Knight were the first advocates of theoretical congestion pricing. It was
William Vickrey in the 1960s, however, who wholeheartedly promoted congestion
pricing and was the most influential in making the case on both theoretical and
practical grounds. Vickrey identified the potential for road pricing to influence
travelers’ choice of route and travel mode and his work makes clear that true
congestion pricing entails setting tolls that match the severity of congestion, which
requires that tolls vary according to time, location, type of vehicle, and current
circumstances. Additionally, Vickrey was the first to put forward an operational plan
for road pricing in a specific city (Washington, D.C.) and was steadfast in promoting
the idea of congestion pricing to non-economists. Since this time, several strategies
for the implementation of congestion pricing have emerged.
The four main types of congestion pricing strategies are as follows (FHWA
2001):
• Variably priced / managed lanes – involve variable tolls on separated
lanes within a highway, such as Express Toll Lanes or High Occupancy or
Toll (HOT) Lanes. HOT lanes allow low-occupancy vehicles to pay a
variable toll to use the lanes, while high-occupancy vehicles are allowed to
use the lanes for free.
10
• Variable tolls on entire roadways or smaller sections – both on toll roads
and bridges, as well as on existing toll-free facilities during rush hours.
This strategy raises existing tolls in peak periods and possibly reduces
them in off-peak periods.
• Cordon charges – either variable or fixed charges to drive within or into a
congested area within a city
• Area-wide charges – per-mile charges on all roads within an area that may
vary by level of congestion
In all of these cases, to truly merit the title of congestion pricing, an implementation
strategy must contain a time-of-day element due to the fact that usage varies with
peak periods. This thesis provides area-wide pricing for an entire facility.
Historically, it is possible to identify at least three periods in which policy
measures to curb congestion have emerged (Salomon and Mokhtarian 1997).
Through the mid-1960s, the principal tool was expansion of infrastructure (i.e.
building more roads to accommodate demand). In the 1970s, there was a shift toward
improved management of the available infrastructure – Transportation Systems
Management (TSM). In the early 1980s, there was an increasing realization that
altering human behavior was the next necessary step. This led to the development
and implementation of Transportation Demand Management (TDM) strategies,
involving a wide range of policies to reduce dependence on the single-occupant
automobile. The first two periods can be characterized as emphasizing supply-side
measures, while the third is designed to affect demand. Congestion pricing is a
demand-side measure, as it specifically used to manage demand. Salomon and
11
Mokhtarian (1997) also note that with a growing concern for environmental costs, the
focus on congestion mitigation is also growing as congestion traffic produces more
air pollutants than smooth traffic flow, involves more noise production, and consumes
more energy. Thus, both the individual and society coincide in their perception of the
presence of a problem but not so, however, in assessing the means for solution.
Additionally, trends over the last two decades have demonstrated that little is
accomplished by the variety of measures devised to reduce congestion.
Figure 2-1 shows a theoretical congestion pricing model, as exhibited by
McMullen (1993). The uncongested road pricing situation is shown as demand curve
D
1
, the distance OA represents vehicle costs such as fuel, oil, vehicle wear and tear,
and the driver’s value of time, and the costs incurred by the road operation agency
(road maintenance, policing, etc.) are shown as the distance AB. The horizontal line
BH represents both average total cost (AC) and marginal cost (MC) up to road
volume C – the roadway is not congested between O and C and, therefore, each
additional vehicle trip incurs the same marginal cost as the previous one.
When demand is at D
1
, the optimal user charge is AB, which results in an
optimal traffic level of Q
0
. After encountering congestion at traffic volume C,
additional vehicle trip imposes a cost (i.e. increased travel time) on other vehicles –
for this reason, the average total and marginal costs diverge at greater volumes. At
demand level D
2
, the roadway is congested and the optimal user charge would be
GD+DE, where DE is the congestion fee.
This theoretical model infers that the main reason for excessive congestion is
the fact that users are not required to pay the full social costs of driving during peak
12
hours (McMullen 1993). This model is simplistic in that it ignores the numerous
different vehicle types that utilize the same road space – this would suggest higher
peak hour congest fees for trucks and other large vehicles.
Figure 2-1: Theoretical Congestion Pricing Model
Lastly, elasticity is a term often used in the economics world, but likely to be
misunderstood in the transportation realm. In simplest terms, elasticity refers to the
amount of change in a dependent variable as a result of changes in an independent
variable. For the purpose of this study, changes in road use as a result of increased
costs (i.e. charging) are the focus.
2.1.1 Traffic Flow Theory
While discussing congestion pricing theory, it is important to mention some
aspects of traffic flow theory that relate to this thesis. In regards to traffic flow
13
theory, the topic most closely related to this specific study is the relationship between
traffic flow and traffic speed. Greenshield (1935) developed a linear model of speed
and density, which can be interpreted into the speed-flow relationship shown in
Figure 2-2.
Figure 2-2: Greenshield’s Model – Speed-Flow Relationship
The Highway Capacity Manual (Transportation Research Board 2000) does
not portray the region of unstable/uncertain flow where the above curve wraps back
around itself. This unpredictable area is referred to as hypercongestion (shown in
Figure 2-2) and results in a loss of capacity due to the breakdown of traffic flow. The
HCM speed-flow curves for basic freeway segments are exhibited as Figure 2-3.
When comparing Greenshield’s model to the HCM representation, a few differences
are evident. The area of unstable flow (hypercongestion) is removed and due to the
fact that speeds remain relatively constant at low volumes, the HCM shows the top of
the curve as perfectly horizontal before the effects of higher flow levels begin to
reduce speeds. In sum, the current HCM speed-flow relationship can be broken down
into two sections: an unchanging constant portion at low flows (represented by the
horizontal line) and a slowly downward-curving portion at higher flows.
14
Figure 2-3: Speed-Flow Curves for Basic Freeway Segments
Source: HCM 2000 – Exhibit 23-3
2.2 Implementation
Congestion pricing is more prominent abroad than in the United States.
Systems of varying technological levels have been operating since 1975 in Singapore
and automated systems have been operating full-time in London and Stockholm since
2003 and 2007, respectively, in addition to various other examples in other areas.
In London, a charge is collected when a vehicle enters the central city area on
weekdays between 7:00AM and 6:00PM – no per-mile charges are assessed. The
standard daily charge is £8 ($16 US) if paid by midnight on the day of travel. The
charge is increased to £10 ($20 US) if paid by midnight the following day. The initial
charge for the strategy was £5 ($10 US), but increased to £8 ($16 US) in July 2005
(Transport for London). Based on results provided by Mayor Ken Livingstone
(2007), after London put its initial congestion charging zone into place, it led to an
immediate drop of 70,000 cars per day in the affected zone. Traffic congestion fell
by almost 20 percent and emissions of the greenhouse gas carbon dioxide were cut by
15
more than 15 percent. The retail sector in the zone has seen increases in sales that
have significantly exceeded the national average. People are still traveling in London
– they are simply doing so in more efficient and less polluting ways. There has been
a marked shift away from cars and into public transport and environmentally friendly
modes of travel. There has been a 4 percent modal shift into use of public transport
from private cars since 2000. Simultaneously, the number of bicycle journeys on
London's major roads has risen by 83 percent, to almost half a million per day.
London's pricing scheme has been estimated to produce savings of about 0.7 minutes
per kilometer, or 1.13 minutes per mile (Transport for London 2007).
In Stockholm, a congestion charge is imposed on Swedish registered vehicles
driving into and out of the Stockholm inner city zone on weekdays between 6:30AM
and 6:29PM and each passage into or out of the inner city zone costs SEK 10, 15 or
20 ($1.58 – $3.15 US), depending on the time of day. The accumulated passages
made by any vehicle during a particular day are aggregated and the maximum amount
charged per day and vehicle is SEK 60 ($9.45 US). As the Stockholm scheme was
only implemented in mid-2007, not much actual data has become available.
Therefore, the effectiveness of the scheme has been based on the Stockholm trial
period that occurred before actual implementation commenced. As a result of
congestion charging in Stockholm (Stockholmsförsöket 2006):
• Motor traffic decreased 22% over 24 hours
• Access improved and travel times fell as a result of the reduction in motor
traffic
16
• Traffic reductions lead to less environmental impact and better health, as
emissions from motor vehicles account for a large proportion of the total
pollution in the city
• Public transport usage increased
• Road safety improved as a result of reduced traffic
Focus will shift now to implementations in the United States, as the political climate
for congestion pricing differs greatly from the aforementioned regions.
The USDOT has entered into Urban Partnership Agreements with five cities,
in accordance with their commitment to, among other things, implement broad
congestion pricing. The five cities are: Miami, Minneapolis/St. Paul, New York City,
San Francisco, and Seattle (Lake Washington). These agreements represent the
future of congestion pricing in the United States, as future strategies will be based on
the actual implementation and success of these proposed systems. At the time of this
study, much debate is currently centered on the proposed congestion pricing strategy
in New York City that has recently been voted down.
While the Washington, D.C. area is not one of the USDOT pilot areas, the
first of a network of HOT lanes in Virginia could potentially open in just two years,
and the variably-tolled intercounty connector in Maryland is scheduled for
completion by 2012. Additionally, the state of Oregon is in the process of developing
GPS-based distance measurements to replace the fuel taxes it now uses to pay for
road usage. At the onset, Oregon would not require all vehicles to have the GPS
system – road users would initially have the choice of paying either fuel taxes or
mileage-based charges.
17
Sullivan (2003) notes that in the mid-1970s, the federal government offered
funds to U.S. cities willing to try a pricing scheme to reduce congestion. Although
some implementation studies that produced findings favorable to the concept were
conducted, all of these early initiatives failed, largely due to local community
opposition. In 1991, the U.S. Congress passed a surface transportation act called the
“Intermodal Surface Transportation Efficiency Act (ISTEA).” This act created the
U.S. Congestion Pricing Pilot program, which directed the USDOT to help develop
and fund congestion pricing pilot projects. In 1998, this program was renamed the
“Value Pricing Pilot Program.”
A common feature of value pricing projects is that pricing (i.e. the toll) varies
with the time of day, in an effort to encourage traffic to shift away from peak periods.
Tolls on value pricing facilities are generally determined by the responsible operating
authorities, which include private companies, state DOTs, and regional government
agencies – toll-setting by government agencies involves due process, including public
comment. At the national level, it was recognized that using the rather academic title
“Congestion Pricing” elicited negative emotions. Switching to “Value Pricing”
provided a more positive way to identify the same notion – additionally, toll
collection technologies are usually identified using positive labels, such as “Fastrak,”
“QuickRide,” or “E-ZPass (Sullivan).”
2.3 Studies
Many studies have taken place involving the numerous facets of congestion
and congestion pricing. Salomon and Mokhtarian (1997) identified and classified
18
user responses relating to congestion, which showcase the various options that
travelers have in regards to potential congestion pricing:
1) Accommodate congestion costs/do nothing
2) Reduce congestion costs
3) Change departure time
4) Change route
5) Buy time
6) Invest in productivity-enhancing technology at home
7) Adopt flextime
8) Adopt compressed work week
9) Change mode of travel
10) Telecommute from home
11) Telecommute from a telecenter
12) Change workplace
13) Relocate home
14) Change from full-time to part-time work
15) Start a home-based business
16) Quit work
A system of “first-best” pricing sets tolls to completely match the external
costs generated by each traveler. This is accomplished by having variable charges
that change in real-time with existing conditions. Although useful in a theoretical
sense, “first-best” pricing has limited practicality. “Second-best” congestion pricing
is more realistic and denotes a more static strategy where drivers are aware of
19
applicable charges in advance. This includes the use of step-tolls instead of smoothly
time-varying tolls or tolling according to a fixed daily schedule rather than day-
specific traffic conditions (Lindsey and Verhoef 2000). Table 2-1 ranks common
vehicle charging options in terms of how well they represent the costs imposed by a
particular vehicle trip (Victoria Transport Policy Institute 2007).
Table 2-1: Common Vehicle Charging Options
Rank General Category Examples
Best
Time- and location-specific
road and parking pricing
Variable road pricing, location-specific parking
management, location-specific emission charges
Second
Best
Mileage-pricing
Weight-distance charges, mileage-based vehicle
insurance, prorated motor vehicle excise tax,
mileage based emission charges
Third Best Fuel charges
Increase fuel tax, apply general sales tax to fuel,
pay-at-the-pump insurance, carbon tax, increase
hazardous substance tax
Bad Fixed vehicle charges
Current motor vehicle excise tax, vehicle
purchase and ownership fees
Worst
External costs (not charged
to motorists)
General taxes paying for roads and traffic
services, parking subsidies, uncompensated
external costs
As congestion pricing is quite controversial, Jones (1998) outlined potential
reasons for opposing congestion pricing:
• Drivers find it difficult to accept the idea of being charged for something
they wish to avoid (congestion) and also feel that congestion is not their
fault, but rather something that is imposed on them by others
• Road pricing is not needed, either because congestion is not bad enough or
because other measures are superior
• Pricing will not get people out of their cars
• The technology will not work
• Privacy concerns
• Diversion of traffic outside the charged area
20
• Road pricing is just another form of taxation
• Perceived unfairness
Two critical questions generated by the idea of congestion pricing focus on
the optimal user charge amount and the effectiveness of the system. In terms of
actual per-mile charge estimates, McMullen (1993) shares that previous research has
estimated that, in 2007 amounts, efficient peak-period tolls in the range of $0.08 to
$0.50 per mile are appropriate. The effectiveness question is answered by the
aforementioned idea of elasticity. Based on studies by Oum et al. (1992), changes in
road use as a result of increased costs are consistent with elasticities of -0.5 or less.
Additionally, results from strategies in locations such as Stockholm are more
consistent with an approximate elasticity of -0.2 (Victoria Transport Policy Institute
2007). A negative elasticity indicates that an increase in road pricing is associated
with a decrease in demand/usage. Unfortunately, this value cannot be determined in
advance of actual congestion pricing imposition. For this thesis specifically, the
elasticity estimate shows how well a pricing strategy actually works. As an example,
a price elasticity of -0.2 means that for every 10% increase in road user charges, a 2%
reduction in road usage occurs.
Sullivan (2003) concludes that forward momentum has been established for
innovative road pricing, but future progress toward more widespread use of
congestion-based pricing is likely to take advantage of local opportunities which
present themselves, and will proceed cautiously. Considerable emphasis will be
placed on marketing strategies in order to win consumer acceptance. By preventing
the loss of vehicle throughput that results from a breakdown of traffic flow,
21
congestion pricing maximizes the return on the public’s investment in highway
facilities. Society as a whole also benefits by reducing fuel consumption and vehicle
emissions and allowing more efficient land use decisions (FWHA 2001).
2.4 Closing Remarks
The provided information in this chapter helps to set the framework for this
Capital Beltway study. Area-wide congestion pricing has been shown as a successful
strategy in various parts of the world, but few implementations are operating or being
discussed in the United States. This thesis fills a practical gap in the Washington,
D.C. area – especially as congestion pricing is being considered on the horizon. As
there is limited experience to draw upon, this study attempts to provide meaningful
information.
22
Chapter 3: Methods and Data
3.1 Introduction
This study proposes a method to calculate the appropriate charges required for
users of the Capital Beltway in order to fulfill their portion of congestion costs and is
based upon previous methodology developed by Roth and Villoria (2001). These
charges are calculated through the use of an optimization model. The method is
based primarily on the relationship between traffic speed and traffic flow, from which
delay calculations are determined.
3.2 Proposed Method
This study aims to determine the charge necessary to cause drivers to realize
their congestion costs. The proposed method is illustrated, in the form of a flowchart,
in Figure 3-1 and each step is discussed in-depth.
The first step in this method is to define the study area. I-495, the Capital
Beltway that surrounds Washington, D.C., is an ideal candidate due to the fact that it
exhibits recurring AM and PM peak period congestion problems. This area was
shown in context of the region in Figure 1-1. As the only circumferential roadway in
the area, many key routes connect to the Capital Beltway along its 64 mile length,
providing a critical highway link to other transportation services, including three
regional airports, transit and rail facilities, and port terminals. Due to this
connectivity with other transportation facilities in the area, traffic congestion on I-495
has severe effects on regional mobility, even though it generally consists of 4-lane
23
travel in both directions. In accordance with other locations that have implemented
congestion pricing, the Washington, D.C. area exhibits severe traffic congestion. Key
interchanges are consistently acknowledged as areas of overwhelming congestion and
even though some travel alternatives exist, the automobile is the dominant mode.
1. Choose study area
2. Examine traffic congestion
using a speed-flow relationship
3. Convert congestion
data into monetary amounts
4. Determine basis
for calculating charges
5. Create an
optimization model
6. Analyze financial
implications
Figure 3-1: Proposed Method
Secondly, traffic congestion is examined using the relationship between traffic
flow and traffic speed – this approach is utilized within the Highway Capacity
Manual (Transportation Research Board 2000). In a strictly hypothetical sense, as
flow increases towards roadway capacity, speed should decrease accordingly. The
24
relationship between traffic flow and traffic speed enables the calculation of delay
imposed by users on other vehicles on the roadway. Specific details on developing
and expanding on this speed-flow relationship will be discussed as part of the model
formation later in this chapter.
Next, any applicable congestion data, such as delay imposed, should be
converted into dollar values. This is done by estimating user value of time and
operating costs for the vehicles on the Capital Beltway.
The fourth step in this method is to determine the basis for calculating user
charges. As different vehicles consume varying amounts of road space, it would be
unjust to impose equal charges to every user. Using the Federal Highway
Administration’s (FHWA) vehicle classification system (shown below as Figure 3-2)
and average vehicle lengths, estimates of passenger car equivalents (PCE) for each
vehicle classification can be determined. This table of information is included as
Table 3-1 and allows for extrapolation after calculating optimal charges per PCE.
25
Figure 3-2: FHWA Vehicle Classifications (FHWA 2001)
26
Table 3-1: Vehicle Classification PCE Factors
Vehicle
Class
Vehicle Description
Average
Length (feet)
PCE
Factor
1 Motorcycle 6 0.38
2 Passenger Cars 16 1.00
3 Other Two-Axle, Four-Tire single Unit Vehicles 18 1.13
4 Buses 38 2.38
5 Two-Axle, Six-Tire, Single-Unit Trucks 26 1.63
6 Three-Axle Single-Unit Trucks 25 1.56
7 Four or More Axle Single-Unit Trucks 32 2.00
8 Four or Fewer Axle Single-Trailer Trucks 44 2.75
9 Five-Axle Single-Trailer Trucks 64 4.00
10 Six or More Axle Single-Trailer Trucks 63 3.94
11 Five or Fewer Axle Multi-Trailer Trucks 68 4.25
12 Six-Axle Multi-Trailer Trucks 73 4.56
13 Seven or More Axle Multi-Trailer Trucks 69 4.31
The fifth step in this method is to create an optimization model. For the
purposes of this study, the model will be created using the Solver tool in Microsoft
Excel. In a nutshell, Excel Solver generates specific values (i.e. charges) to optimize
a certain objective. In the case of this study, the optimized variable is the dollar
amount that users of I-495 should be charged per-mile.
Lastly, the financial implications of user-based charging on the Capital
Beltway will be analyzed. Estimates of potential costs and revenue will be examined
in order to provide information on this feasibility aspect.
3.3 Methodology
This section focuses on formulating the model used in this thesis. The
following main points will be addressed:
• The process of obtaining usable data for this study
• Preparing the data for speed and flow analysis
27
• Using the relationship between traffic speed and traffic flow to perform
delay calculations
• Applying relevant user value of time and vehicle operating cost
estimations to setup the model to optimize congestion charges for the
Capital Beltway
3.3.1 Data
The first stage of this thesis involved obtaining I-495 detector data for use in
the study. When contacting the Maryland State Highway Administration (MD SHA)
and the Virginia Department of Transportation (VDOT), the following main
components of desired data were expressed:
• Detector locations on I-495 in Maryland or Virginia
• Permanent detection stations reporting data in intervals less than or equal
to one hour for all hours of the day
• Volume count information (both total counts and counts broken down by
FHWA vehicle classification)
• Vehicle speed information
• Data archived for multiple years
In-road detectors (i.e. loop detectors) are the most commonly used technology
for collecting traffic data and agencies often have permanent detection locations
reporting data. Temporary tubes are sometimes used for specific purposes, but in
general, agencies rely on loop detection for their traffic data. To this extent, Tom
Schinkel of the VDOT Mobility Management Division was able to provide study data
from six permanent detection locations within the Virginia section of I-495. As these
28
detection locations are split directionally, they encompass three general locations.
The following table provides general detector location details and these locations are
also shown graphically in Figure 3-3.
Table 3-2: I-495 Detector Location Information
Detector ID Direction Start Location End Location
90202 North Eisenhower Ave Connector SR 241/Telegraph Rd
190004 South Eisenhower Ave Connector SR 241/Telegraph Rd
90138 North I-95/I-395 29-620/Braddock Rd
190057 South I-95/I-395 29-620/Braddock Rd
90275 North Dulles Access Rd; SR 267/Dulles Toll Rd SR 193/Georgetown Pike
190064 South Dulles Access Rd; SR 267/Dulles Toll Rd SR 193/Georgetown Pike
It should be noted that the detectors are physically located between the given
landmarks, which are easier to decipher while looking at a map than the actual
latitude and longitude coordinates.
Figure 3-3: I-495 Data Locations
Source: Google Maps
29
For this study, it is assumed that the available VDOT detector data is
representative of the entire Virginia portion of I-495. The data was collected on a
per-lane basis and in 15 minute intervals, and was provided in aggregate form with all
lanes combined by direction and data based hourly.
Unfortunately, MD SHA was unable to provide data for this study, as no
functioning permanent detection stations that collected all of the required information
were available. This was based on the fact that this data was not available from any
of the five automatic traffic recorder (ATR) stations located on the Maryland section
of I-495. As such, the data provided by VDOT was used as representative for all of
the Capital Beltway.
The hourly speed and volume data, ranging from as far back as 2002, were
cleansed and laid out in spreadsheet form by detector ID and year in order to provide
consistency for analysis purposes. Due to the fact that detection equipment
sometimes reports false data (i.e. zero volumes, exorbitant speeds, etc.), “cleansing”
of such data is required. This process, in its most basic form, consisted of the
following:
• Separate and organize data from all detectors into individual years
• Determine the day of week that each data point was collected and delete
all weekend data
• Delete any speed and volume outlier data (significant errors in data
collection)
• Assign an hour code (0-23) to each data point
30
• Spreadsheets were setup to contain Detector ID, Hour Code, Volume By
Vehicle Classifications (split from 1-13), and Average Speed For All
Vehicles on each row
As expected with any research, data limitations exist in this study. Since there
was no Maryland data available for use, Virginia data is assumed representative
across the entire Capital Beltway. Although this may not be an entirely valid
assumption, it can be used for information purposes and to calculate pricing for the
Virginia portion of I-495. Also of note, some of the detectors, whether it is based on
their location or specific direction, don’t provide particularly exciting data at all
times. Whether that means certain detectors show consistent speeds throughout the
day or only one pronounced peak period, all data is considered meaningful. Not all
locations on I-495 experience severe AM and PM peak period congestion and this
data tends to make the model more representative instead of over-inflating it to the
side of congestion. If only data from congested locations were used, it would be
inferred that traffic is uniform along the entire Capital Beltway, which is not the case.
3.3.2 Speed Analysis
The provided speed data were broken down by each vehicle classification.
Using weighted averages based on the number of vehicles in each associated
category, average hourly speeds for the entire traffic stream were calculated. For
each of the 24 hours in a day, average speed tables were created for each detector.
With data existing from previous years, the hourly speeds were overlaid to view
yearly changes. An example of these hourly speed plots is shown as Figure 3-4 and
the additional plots from the remaining detectors can be viewed in the Appendix.
31
Based on this plot, two peak periods are evident – one in the morning and one in the
evening. The apparent extent of the evening peak spreads across more hours than the
morning peak. For this thesis, peak periods are visually defined based on the hourly
speed plots from the detectors. From Figure 3-4, these peaks are estimated to occur
from 6AM-10AM and 2PM-7PM.
Speed data can also provide insight from another perspective. By plotting
average hourly speed by year, periods of decreased speed become easily visible. An
example of these hourly speed plots is shown as Figure 3-5 and the additional plots
from the remaining detectors can be viewed in the Appendix. Based on this plot,
decreases in speed are evident from 8AM-10AM and from 3PM-7PM. Coupled with
the previous plot, this information paints a clear picture of peak periods at each
detector location.
For the purpose of this thesis, free-flow speed is said to equal the uncongested
traffic speed – as determined by the average of the 85th percentile speeds for each
detector between 1AM and 4AM for all of 2007. Free-flow speed is therefore found
to equal 63.8 miles per hour (mph) on the Capital Beltway, even though the posted
speed limit is 55 mph.
32
Avg. Hourly Speed - Link 190064
0.00
10.00
20.00
30.00
40.00
50.00
60.00
70.00
80.00
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
Hour of Day
S
p
e
e
d
(
m
p
h
)
2003
2004
2005
2006
2007
Figure 3-4: Average Hourly Speed – Detector 190064
Avg. Hourly Speed by Year - Link 190064
0.00
10.00
20.00
30.00
40.00
50.00
60.00
70.00
80.00
2003 2004 2005 2006 2007
Year
S
p
e
e
d
(
m
p
h
)
12AM 1AM 2AM 3AM 4AM 5AM 6AM 7AM 8AM 9AM 10AM 11AM
12PM 1PM 2PM 3PM 4PM 5PM 6PM 7PM 8PM 9PM 10PM 11PM
Figure 3-5: Average Hourly Speed by Year – Detector 190064
33
3.3.3 Flow Analysis
In a similar fashion to the speed analysis, flow analysis was conducted on the
data. The provided volume data were broken down by each vehicle classification and
multiplied by corresponding PCE factors to represent hourly PCE flow. For each of
the 24 hours in a day, average flow tables were created for each detector. With data
existing from previous years, the hourly flows were overlaid to view yearly changes.
An example of these hourly speed plots is shown as Figure 3-6 and the additional
plots from the remaining detectors can be viewed in the Appendix. As with the
hourly speed plot presented in the previous section, two peak periods are seen – one
in the morning and one in the evening. The apparent extent of the evening peak once
again spreads across more hours than the morning peak – in this case, about two extra
hours.
Across multiple years, changes in flow are evident. This is expected, as traffic
volumes generally increase every year. In addition to higher flow rates, expanded
peak periods start to occur, as traffic shifts to the hours before and after the peak
periods of previous years. The flow data can also be visualized by plotting average
hourly flow by year, making periods of increased flow more visible. An example of
these hourly flow plots is shown as Figure 3-7 and the additional plots from the
remaining detectors can be viewed in the Appendix. Based on this plot, the greatest
flow occurs between the hours of 6AM-11AM and from 12PM-8PM – these are not
necessarily the true peak periods at this location. These are just the times of day
when there is an increase of flow at off-peak hours. Coupled with the previous plot
34
and the speed plots from the previous section, this information provides insight to
peak periods at each detector location.
From the speed analysis, it was determined that the average uncongested
(free-flow) speed on I-495 was 63.8 mph. Using the 2000 edition of the Highway
Capacity Manual and this given free-flow speed, the per-lane capacity of I-495 is
determined to be 2,350 passenger cars per lane per hour (pc/ln/hr). For the purposes
of this thesis, data will be examined on a per-lane basis instead of in terms of the total
facility (i.e. four lanes). By limiting the study to a per-lane basis, uniform traffic
activity across each lane is assumed, even though this is probably not the case on I-
495.
Volume-to-capacity (v/c) ratio is a common statistic used by traffic engineers
to gauge the health or level of service of a certain roadway. Using the flow data and
the capacity figure from the Highway Capacity Manual, the hourly v/c ratio can be
plotted for each detector, with data from previous years included, as well. Volume-
to-capacity ratio plots are another tool used to view peak period conditions on the
roadway. An example of a v/c ratio plot is shown below, with the additional plots
from the remaining detectors available in the Appendix. Based on this plot, the AM
and PM peaks are once again evident – the plot mimics the previous average hourly
flow plot, as the observed flow is an input, along with the capacity, which stays
constant.
35
Avg. Hourly PCE Flow - Link 190064
0
500
1000
1500
2000
2500
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
Hour of Day
P
C
E
F
l
o
w
2002
2003
2004
2005
2006
2007
Figure 3-6: Average Hourly Flow – Detector 190064
Avg. Hourly PCE Flow by Year - Link 190064
0
500
1000
1500
2000
2500
2002 2003 2004 2005 2006 2007
Year
P
C
E
F
l
o
w
12AM 1AM 2AM 3AM 4AM 5AM 6AM 7AM 8AM 9AM 10AM 11AM
12PM 1PM 2PM 3PM 4PM 5PM 6PM 7PM 8PM 9PM 10PM 11PM
Figure 3-7: Average Hourly Flow by Year – Detector 190064
36
v/c Ratio - Link 190064
I-495 Capacity = 2,350 pc/ln/hr
0.00
0.10
0.20
0.30
0.40
0.50
0.60
0.70
0.80
0.90
1.00
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
Hour of Day
v
/
c
R
a
t
i
o
2002
2003
2004
2005
2006
2007
Figure 3-8: Hourly Volume-to-Capacity Ratio – Detector 190064
3.3.4 Speed-Flow Relationship
As the speed and flow data have been looked at separately up to this point,
they are now combined in order to develop the relationship that is the backbone of
this study. Traffic speed and traffic flow data is plotted to see the effect that flow has
on speed – hypothetically, speed decreases as flow increases. While attempting to
approximate the data with a straightforward linear relationship would be easy, it is far
too simplistic and not realistic for this complex phenomenon.
37
The Highway Capacity Manual provides equations that determine speeds
based on a given free-flow speed (FFS) and available flow data (flow rate v
p
). As the
free-flow speed was calculated to be 63.8 mph for I-495, the following equations, as
set forth in Exhibit 23-3 of the Highway Capacity Manual, will be utilized:
For 55 ? FFS ? 70 and for flow rate (v
p
)
(3400 – 30FFS) < v
p
? (1700 + 10FFS),
( )
2.6
1 30 3400
7 340
9 40 1700
p v FFS
S FFS FFS
FFS
(
+ ? | |
= ? ?
(
|
?
\ ¹
(
¸ ¸
Eq. 1
For 55 ? FFS ? 75 and v
p
? (3400 – 30FFS),
S FFS = Eq. 2
The HCM equations are broken down into two sections, due to the fact that at
low volumes, speed remains fairly constant and then starts to decrease at higher flow
rates. As such, the current HCM speed-flow relationship is shown as an unchanging
constant portion at low flows and a slowly downward-curving portion at higher flows.
Based on the above equations, the ranges are 1,486 pc/ln/hr to 2,338 pc/ln/hr for the
first equation and less than 1,486 pc/ln/hr for the second. By entering flow values
from I-495 data and obtaining the corresponding speed values, a speed-flow plot can
be created to show the effect that flow has on speed.
By plotting the HCM equations over the I-495 data points, along with the
fourth-order polynomial regression equation calculated from the data, the speed-flow
relationship is visualized. Within the regression equation, the constant is equal to the
free-flow (uncongested) speed that was determined earlier. The lane capacity of I-
495 (2,350 pc/ln/hr) is shown as the vertical dashed line in the plot.
38
I-495 Speed vs. Flow
y = -2E-12x
4
+ 6E-09x
3
- 7E-06x
2
+ 0.0021x + 63.8
0.00
10.00
20.00
30.00
40.00
50.00
60.00
70.00
80.00
0 250 500 750 1000 1250 1500 1750 2000 2250 2500
Flow (PCE/hour/lane)
S
p
e
e
d
(
m
p
h
)
I-495 Data HCM Calculation Capacity I-495 Data Trendline
Figure 3-9: I-495 Speed vs. Flow
While the HCM calculations may look approximately appropriate to the data,
the regression equation from the I-495 data decreases at a greater rate. The HCM
calculations are based on national averages and I-495 data could vary for a number of
reasons (year built, geometry, etc.). It goes without saying that the general HCM
calculations do not represent I-495 in this case, but would be quite helpful for
situations where actual data for calculations is not available. As discussed in chapter
2, the HCM does not address hypercongestion – the area of unstable flow that occurs
as flow reaches capacity and the curve turns inward on itself. This area is the not
within the scope of this thesis and will not be discussed. While this may seem to be a
limitation, congestion pricing can improve traffic flow to the point where this
scenario does not occur.
39
3.3.5 Delay Calculations
Based on the speed-flow relationship equation derived from the data, the
amount of delay imposed on the traffic stream by an additional PCE/lane/hour (in
minutes per mile) can be calculated. These calculations can be compared to those
generated using the equations from the HCM in order to showcase differences and re-
validate the knowledge that the HCM equations are not appropriate as a
generalization in the case where actual data is present to examine. The delay
calculation process is as follows:
• For possible traffic flows, calculate the corresponding travel speed
• Calculate time to travel one mile at given flow (based on speed)
• Calculate time to travel one mile at one less PCE/lane/hour (based on
speed)
• Multiply the total flow by the difference in the previous two calculations
to obtain the total delay imposed on traffic by an additional PCE/lane/hour
40
Table 3-3: Delay Calculations Using HCM Equations
Traffic Flow
(PCE/lane/hour)
Travel
Speed
(mph)
Time to
travel one
mile at given
volume
(min./mile)
Time to travel one
mile at one less
PCE/lane/hour
(min./mile)
Delay imposed on traffic
stream by an additional
PCE/lane/hour (min./mile)
50 63.80 0.94044 0.94044 0.00000
100 63.80 0.94044 0.94044 0.00000
150 63.80 0.94044 0.94044 0.00000
200 63.80 0.94044 0.94044 0.00000
250 63.80 0.94044 0.94044 0.00000
300 63.80 0.94044 0.94044 0.00000
350 63.80 0.94044 0.94044 0.00000
400 63.80 0.94044 0.94044 0.00000
450 63.80 0.94044 0.94044 0.00000
500 63.80 0.94044 0.94044 0.00000
550 63.80 0.94044 0.94044 0.00000
600 63.80 0.94044 0.94044 0.00000
650 63.80 0.94044 0.94044 0.00000
700 63.80 0.94044 0.94044 0.00000
750 63.80 0.94044 0.94044 0.00000
800 63.80 0.94044 0.94044 0.00000
850 63.80 0.94044 0.94044 0.00000
900 63.80 0.94044 0.94044 0.00000
950 63.80 0.94044 0.94044 0.00000
1000 63.80 0.94044 0.94044 0.00000
1050 63.80 0.94044 0.94044 0.00000
1100 63.80 0.94044 0.94044 0.00000
1150 63.80 0.94044 0.94044 0.00000
1200 63.80 0.94044 0.94044 0.00000
1250 63.80 0.94044 0.94044 0.00000
1300 63.80 0.94044 0.94044 0.00000
1350 63.80 0.94044 0.94044 0.00000
1400 63.80 0.94044 0.94044 0.00000
1450 63.80 0.94044 0.94044 0.00000
1500 63.80 0.94044 0.94044 0.00105
1550 63.79 0.94065 0.94064 0.01297
1600 63.74 0.94137 0.94135 0.03395
1650 63.64 0.94285 0.94281 0.06298
1700 63.47 0.94527 0.94521 0.09995
1750 63.24 0.94881 0.94873 0.14515
1800 62.92 0.95365 0.95354 0.19915
1850 62.50 0.95997 0.95983 0.26280
1900 61.99 0.96796 0.96778 0.33724
1950 61.36 0.97783 0.97761 0.42397
2000 60.62 0.98983 0.98956 0.52492
2050 59.75 1.00422 1.00391 0.64254
2100 58.75 1.02134 1.02097 0.78001
2150 57.61 1.04157 1.04113 0.94139
2200 56.32 1.06537 1.06485 1.13198
2250 54.88 1.09331 1.09271 1.35869
2300 53.28 1.12612 1.12541 1.63075
2338 51.96 1.15483 1.15403 1.87530
2500 not included in HCM equations
41
Table 3-4: Delay Calculations Using I-495 Regression Equation
Traffic Flow
(PCE/lane/hour)
Travel
Speed
(mph)
Time to
travel one
mile at given
volume
(min./mile)
Time to travel one
mile at one less
PCE/lane/hour
(min./mile)
Delay imposed on traffic
stream by an additional
PCE/lane/hour (min./mile)
50 63.89 0.93914 0.93914 0.00000
100 63.95 0.93829 0.93829 0.00000
150 63.98 0.93784 0.93784 0.00000
200 63.98 0.93772 0.93772 0.00012
250 63.97 0.93789 0.93788 0.00145
300 63.95 0.93829 0.93828 0.00305
350 63.90 0.93890 0.93888 0.00481
400 63.85 0.93966 0.93964 0.00665
450 63.79 0.94055 0.94053 0.00851
500 63.73 0.94155 0.94153 0.01033
550 63.65 0.94261 0.94259 0.01210
600 63.58 0.94374 0.94372 0.01378
650 63.50 0.94491 0.94488 0.01539
700 63.42 0.94611 0.94608 0.01696
750 63.34 0.94733 0.94730 0.01851
800 63.25 0.94857 0.94855 0.02010
850 63.17 0.94984 0.94982 0.02183
900 63.08 0.95115 0.95112 0.02377
950 62.99 0.95249 0.95246 0.02605
1000 62.90 0.95390 0.95387 0.02880
1050 62.80 0.95538 0.95535 0.03218
1100 62.70 0.95697 0.95694 0.03637
1150 62.58 0.95870 0.95866 0.04157
1200 62.46 0.96060 0.96056 0.04801
1250 62.32 0.96272 0.96267 0.05593
1300 62.17 0.96510 0.96505 0.06563
1350 62.00 0.96779 0.96774 0.07741
1400 61.80 0.97086 0.97080 0.09163
1450 61.58 0.97437 0.97430 0.10870
1500 61.33 0.97839 0.97831 0.12905
1550 61.04 0.98301 0.98292 0.15321
1600 60.71 0.98832 0.98821 0.18177
1650 60.34 0.99443 0.99430 0.21541
1700 59.91 1.00144 1.00129 0.25493
1750 59.44 1.00949 1.00932 0.30127
1800 58.90 1.01873 1.01853 0.35556
1850 58.29 1.02933 1.02911 0.41915
1900 57.61 1.04149 1.04123 0.49367
1950 56.85 1.05543 1.05513 0.58113
2000 56.00 1.07143 1.07109 0.68400
2050 55.06 1.08979 1.08940 0.80541
2100 54.01 1.11091 1.11046 0.94928
2150 52.85 1.13523 1.13471 1.12066
2200 51.58 1.16331 1.16271 1.32610
2250 50.17 1.19585 1.19515 1.57426
2300 48.63 1.23371 1.23289 1.87670
2338 47.37 1.26671 1.26579 2.15236
2350 46.95 1.27799 1.27703 2.24920
42
3.3.6 Speed Frequency and Probability by Flow Range
The frequency of data points that fall in a certain flow range, along with the
speed probabilities within a certain flow range, are interesting aspects to explore.
Data existing under flow conditions less than 1,200 pc/ln/hr can be grouped together,
as these low-flow areas are less interesting than periods of higher flow.
Using all of the data points, along with three speed ranges (41-50 mph, 51-60
mph, and 61-70 mph), the probability of a data point falling in each speed range can
be calculated for increasing flow rates. This will show the probability of being in
each speed range as a function of flow. This information is displayed in Figure 4-8
and provides a sample probability density function (PDF) for each flow range. The
speed probability graph is not terribly surprising, as the probability of higher speeds
decreases as flow increases. A few strange overlap areas exist, and the 1,901-2,000
pc/ln/hr flow range is particularly interesting since it is a merge point where all three
speed ranges have an equal probability of occurring. Curiosity arises when that sort
of uncertainty exists.
Moving forward, the frequency of data in each flow range is plotted as Figure
4-9 – the relative frequency of the various flow ranges assists with critiquing the data.
When looking at the frequency of data points across different flow ranges, the vast
majority of data is from periods of lower demand that exhibit low-flow conditions
(i.e. off-peak hours). Although regular users of the Capital Beltway may choose to
disagree, this observation makes sense, as there are more uncongested hours than
congested hours in the day. Flows greater than 1,200 pc/ln/hr, are characterized by a
small bell-shaped curve, with a small likelihood of encountering lower volumes at
43
either end of the range. Whenever these situations occur, the onset of some
congestion in these locations may be the result. The frequency of data greater than
2,000 pc/ln/hr is low – possibly due to the fact that traffic is unable to exhibit the
steady flow conditions that enable flows at this rate or higher.
Speed Probability by Flow Range
0.000
0.100
0.200
0.300
0.400
0.500
0.600
0.700
0.800
0.900
1.000
0-1200 1201-1300 1301-1400 1401-1500 1501-1600 1601-1700 1701-1800 1801-1900 1901-2000 >2000
Flow Range (PCE/lane/hour)
P
r
o
b
a
b
i
l
i
t
y
P(41-50) P(51-60) P(61-70)
Figure 3-10: Speed Probability by Flow Range
44
Frequency by Flow Range
0.000
0.100
0.200
0.300
0.400
0.500
0.600
0.700
0.800
0.900
1.000
0-1200 1201-1300 1301-1400 1401-1500 1501-1600 1601-1700 1701-1800 1801-1900 1901-2000 >2000
Flow Range (PCE/lane/hour)
F
r
e
q
u
e
n
c
y
%
Figure 3-11: Frequency by Flow Range
3.3.7 Traffic Proportions
Traffic proportions for each of the 13 FHWA vehicle classifications are
components of the optimization model and will be applied across varying flow levels.
As traffic stream characteristics differ between AM and PM peak periods, analysis is
completed using both periods in order to determine appropriate traffic proportion
percentages. As part of the Federal Highway Administration’s Highway Performance
Monitoring System (HPMS), Maryland collects vehicle classification information on
I-495. For this reason, data from Maryland is able to be included at this stage of the
study. Although this data does not contain speed information and, therefore, cannot
be used throughout the remainder of this study, traffic proportion percentages can be
obtained and compared with the Virginia data that have been utilized up to this point.
45
Based on general knowledge and the aforementioned flow and speed graphs
that showcased evident peak period times, the AM peak period is defined as 6AM-
10AM and the PM peak period is defined as 3PM-7PM. After combining all relevant
data for these time periods and averaging Virginia and Maryland data together, the
following percentages were obtained for each of the 13 FHWA vehicle
classifications:
Table 3-5: Peak Period Traffic Proportions
AM Peak (%) PM Peak (%)
Class 1 0.16 0.16
Class 2 83.18 86.78
Class 3 12.39 10.35
Class 4 0.68 0.42
Class 5 0.90 0.60
Class 6 0.58 0.24
Class 7 0.24 0.07
Class 8 0.22 0.16
Class 9 1.55 1.17
Class 10 0.06 0.02
Class 11 0.03 0.02
Class 12 0.01 0.01
Class 13 0.00 0.00
Although the AM and PM peak period traffic proportion percentages seem rather
similar, they will be used separately when calculating the associated peak period
charges.
3.4 Value of Time Estimation
In order to devise a pricing strategy, dollar amounts must be attributed to the
time spent in congestion (i.e. the delay calculations set forth previously). In order to
do this, user value of time estimates must first be obtained. As no studies have been
undertaken in the Washington, D.C. area to associate value of time estimates to each
of the 13 FHWA vehicle classifications, estimates are extrapolated from the Highway
Economic Requirements System (HERS), a FHWA model designed to simulate
46
improvement selection decisions based on the relative benefit-cost merits of
alternative improvement options (FHWA 2002). The HERS model provides
combined user value of time and vehicle operating costs for seven vehicle classes
which differ from the 13 vehicle classifications used in this study. As the amounts
provided in the model’s documentation are not current, they are converted to
equivalent 2007 dollars. Prevailing wage data is the general basis for user value of
time and costs are compensated by the fact that operating costs differ from vehicle-to-
vehicle. These values include both aspects.
Table 3-6: FHWA HERS Model – Value of Time
Vehicle Class Value (in 2007 $/hour)
Small Auto 21.37
Med. Auto 21.43
4-Tire Truck 24.27
6-Tire Truck 27.18
3-4 Axle Truck 32.19
4-Axle Combo. 34.68
5-Axle Combo. 34.34
Based on the HERS model estimates and general assumptions about vehicle
classifications, value of time and operating costs estimates are calculated for each of
the 13 FHWA vehicle classifications. Table 4-6 showcases these estimates. It should
be noted that operating costs for motorcycles are estimated to be half of those
associated with passenger cars and user value of time is chosen to be represented by
the $11.56 per hour value provided for personal, not business, travel. Additionally,
since no actual occupancy data were available, standard bus occupancy is assumed to
be 30 passengers, all traveling under personal user value of time estimates. While
this estimate may not be precise, it will provide a rough approximation, at the very
least.
47
Table 3-7: FHWA Vehicle Classifications – Value of Time
Vehicle Class Value (in 2007 $/hour)
1 12.31
2 21.40
3 24.27
4 346.93
5 27.18
6 32.19
7 32.19
8 34.68
9 34.34
10 34.34
11 34.34
12 34.34
13 34.34
In this study, the distribution of trip purposes is not taken into account. Value
of time is inherently laden with a trip purpose (i.e. personal use, business use, etc.)
and, for this thesis, the assumption is made that value of time estimates are not
reflecting varying trip purposes.
3.5 Model Formulation
As previously stated, one of the research objectives of this thesis is to develop
a model that optimizes the pricing necessary to cause vehicle users on the Capital
Beltway to realize the congestion costs that their vehicles impose on the rest of the
traffic stream. To this extent, congestion pricing will serve as a demand management
tool. While the model process will be outlined in this section, a visual demonstration
will be provided in the next chapter.
Based on a model developed by Roth and Villoria (2001), the algorithm is as
follows:
48
1. Using a provided initial flow condition and traffic proportions calculated
previously, calculate the initial number of vehicles in each classification
category
2. Using the aforementioned equation that relates speed and flow and the given
flow condition, calculate the initial speed of the traffic system
3. Initial cost (per vehicle) to travel one mile can be calculated by dividing the
total costs for each vehicle classification by the initial speed
4. A variable congestion charge is introduced at this point and the cost for each
vehicle to travel one mile, including the congestion charge, is calculated - this
charge will be varied by the model
5. The percent change in cost after adding the congestion charge is calculated
6. Based on the assumed negative elasticity, the initial number of vehicles, and
the percent change in cost, the change in flow after imposing the congestion
charge is calculated
7. The new flow for each vehicle classification is calculated by subtracting the
change in flow from the initial flow
8. Using the updated total flow in the traffic system, new traffic composition
proportions and speed values can be calculated
9. Calculate the average vehicle speed at one less PCE/lane/hour than the
updated flow condition
10. Calculate costs per vehicle at both the current speed and the speed at one less
PCE/lane/hour in order to determine the cost imposed on the entire traffic
49
stream by one extra PCE (this concept is similar to the delay calculation that
was explained previously)
11. The total cost due to one extra PCE is the cost imposed on the entire traffic
stream by the additional PCE added to the average cost per vehicle under
current conditions
12. A variable percent change is introduced at this point - this is used to calculate
theoretical flow and cost information which is used by the optimization model
13. Using the initial cost per vehicle to travel one mile under initial flow
conditions, calculate a weighted cost average based on the new traffic
proportions
14. The resulting theoretical flow is found by multiplying the initial flow by one
minus the percent change times the elasticity
15. The resulting theoretical cost (i.e. the equilibrium demand price) is found by
adding the weighted cost average based on the new traffic proportions to one
plus the percent change
16. At this point, the model is instructed to force the resulting theoretical cost
minus the total cost due to one extra PCE to equal zero and to minimize the
resulting theoretical flow minus the flow after the imposing the congestion
charge
17. The model runs until an optimal congestion charge solution is reached – this
charge is the amount that equals the congestion cost under the conditions
existing after it is inflicted
50
3.6 Assumptions
Throughout the model formulation process of this study, various assumptions
needed to be made:
• Due to the fact that no comprehensive Maryland data was available for I-
495, the obtained data from Virginia was assumed to be representative of
the entire Capital Beltway. As there are varying levels of traffic collected
at each of the Virginia detector locations, this assumption seems valid.
While the results of this Washington, D.C.-area study may not be entirely
transferable to other regions, the methodology will remain valid.
• When calculating AM and PM peak traffic proportions, it was assumed
that the distribution of vehicle types across all travel lanes remained at the
average values throughout the peaks (instead of changing hourly, etc.).
While some changes might have occurred if the traffic proportions were
analyzed on a per-hour basis, the changes would seemingly be small
enough to merit using overall average values instead.
• As no user value of time or vehicle operating cost data existed that was
broken down into the 13 FHWA vehicle classifications, the estimated
values used in the FHWA HERS model were assumed in this study.
These values were not entirely specific for each vehicle classification, but
are assumed valid due to the lack of more exhaustive data. As stated
previously, the distribution of trip purposes was not taken into account for
the value of time estimation. The assumption is made that value of time
estimates are not reflecting varying trip purposes.
51
• In calculating total vehicle costs, no clear estimates were found on average
bus occupancy on the Capital Beltway. An average occupancy of 30
passengers was assumed, due to the lack of sufficient ridership data. As
this value may seem high, it provides an approximation, although the total
value of bus traffic may potentially be inflated.
• Speed and flow distributions are assumed uniformly equal across all lanes
of I-495 in this study. In actuality, this is not the case. Since the user
charges are calculated at the PCE level, however, this does not seem to
affect the results. Regardless of the per-lane statistics, user charges are
assigned to each PCE.
• User value of time estimates may actually be different than calculated.
User responses to congestion charges vary and people will express varying
elasticity levels. This being said, the value of time estimates set forth in
this study should be taken as approximations.
Due to the various assumptions set forth in this study, it is likely that the
results of this study may be artificially low. In this light, the results can be considered
to be conservative estimations.
The following chapter discusses the system evaluation, along with a
demonstration of the model utilized in this study. Applicable user charges and
sensitivity analysis will also be presented.
52
Chapter 4: System Evaluation
4.1 Inputs
The input parameters for this model have been previously touched on, at least
briefly, as they were obtained or calculated from available I-495 data. To summarize:
• Flow – measured in passenger cars per lane per hour (pc/ln/hr); obtained
from I-495 data
• Speed-flow relationship – regression equation calculated from I-495 data
obtained for this study in order to show the impact of traffic flow on traffic
speed; this equation can be used to estimate speeds under various flow
conditions
• Total vehicle costs – measured in dollars per hour ($/hr); calculated by
summing user value of time and vehicle operating costs for each of the 13
FHWA vehicle classifications
• Traffic proportions – measured as a percentage (%); traffic proportions for
each of the 13 FHWA vehicle classifications were calculated in the AM
and PM peak periods based on the total traffic volume data obtained from
I-495
• Elasticity – unitless number; a negative elasticity indicates the changes
that occur in road use as a result of increased costs; the assumed elasticity
of -0.2 for this model is based on a general literature search, estimates
from the existing charging system in Stockholm, Sweden, and the
knowledge that sufficient transit options do not exist on I-495; elasticity
53
must be estimated, as the true value cannot be determined unless pricing is
actually implemented and travel behavior is observed
While all of these parameters are vital for a functional model, they are not all direct
inputs from the user. The speed-flow regression equation and all applicable constants
are programmed into the model. All other inputs are controlled by the user.
4.2 Outputs
The outputs produced by this model can be placed into two categories: process
outputs and final outputs. Process outputs consist of calculations that occur
throughout the iterative process of the model that lead to the final outputs – the
optimized variables.
Process outputs:
• Initial number of vehicles – measured in passenger car equivalents (PCEs);
calculated based on initial flow and traffic proportion conditions
• Initial speed – measured in miles per hour (mph); calculated from the
speed-flow regression equation using initial flow conditions
• Initial cost (per vehicle) to travel one mile – measured in $/mile;
calculated based on total vehicle costs and initial speed
• Cost to travel one mile (with congestion charge) – measured in $/mile;
calculated using the initial cost (per vehicle) to travel one mile and the
varying congestion charge
• Percent change in cost (after congestion charge) – measured as a
percentage; calculated based on the initial cost (per vehicle) to travel one
mile and the cost to travel one mile (with congestion charge)
54
• Change in flow (after congestion charge) – measured in pc/ln/hr;
calculated using the initial number of vehicles, the assumed elasticity and
the percent change in cost (after congestion charge)
• Percent change in flow (after congestion charge) – measured as a
percentage; calculated using the initial number of vehicles and the change
in flow (after congestion charge)
• New flow (after congestion charge) – measured in pc/ln/hr; calculated
from the initial flow and the change in flow (after congestion charge)
• New proportion of traffic (after congestion charge) – measured as a
percentage; calculated using the new flow (after congestion charge) for
each vehicle classification and the total new flow (after congestion charge)
• New speed (after congestion charge) – measured in mph; calculated from
the speed-flow regression equation using new flow conditions (after
congestion charge)
• Vehicle speed at one PCE/lane/hour less (after congestion charge) –
measured in mph; calculated from the speed-flow regression equation
using one PCE less than new flow conditions (after congestion charge)
• Average cost per vehicle (after congestion charge) – measured in $/mile;
calculated based on the new speed (after congestion charge) and the total
vehicle costs
• Average cost per vehicle at one PCE/lane/hour less (after congestion
charge) – measured in $/mile; calculated based on the vehicle speed at one
PCE/lane/hour less (after congestion charge) and the total vehicle costs
55
• Cost imposed on the entire traffic stream by one extra PCE – measured in
$/mile; calculated using the average cost per vehicle (after congestion
charge), average cost per vehicle at one PCE/lane/hour less (after
congestion charge), and new flow (after congestion charge); this
calculation is similar to the delay calculation process explained previously
• Total cost due to one extra PCE – measured in $/mile; calculated using the
weighted average cost per vehicle at one PCE/lane/hour less (after
congestion charge) and the cost imposed on the entire traffic stream by
one extra PCE
• Resulting theoretical flow (i.e. equilibrium demand flow) – measured in
PCE/ln/hr; calculated using the initial flow conditions, assumed elasticity,
and varying percent change
• Resulting theoretical cost (i.e. equilibrium demand price) – measured in
$/PCE/mile; calculated using the weighted cost (per vehicle) to travel one
mile under initial flow conditions and varying percent change
Final outputs:
• Optimized congestion pricing – measured in $/PCE/mile; obtained from
the optimization model; the objective function is setup as follows:
Minimize: equilibrium demand flow - calculated flow with the congestion
charge
Subject to the constraint: equilibrium demand price = calculated total
cost due to one extra PCE
Variables: percent change; congestion charge
56
• Percent change – measured as a percentage; obtained from the
optimization model, where it is used to equate the equilibrium demand
price and equilibrium demand flow; this percentage corresponds to the
marginal cost of the system – the difference between the weighted cost
(per vehicle) to travel one mile under initial flow conditions and the
equilibrium demand price
4.3 Model Demonstration
In order to summarize accomplishments, this model utilizes the Solver tool in
Excel to find the congestion charge which equates the total cost due to one extra PCE
and the equilibrium demand price. The total cost due to one extra PCE varies with
the congestion charge and the consequent changes in traffic volumes and speeds,
taking into account changes in traffic composition by vehicle classification. The
equilibrium demand price varies in accordance with the assumed elasticity, with the
change in traffic conditions from the initial to the final condition determined by the
Excel model (Roth 2001). The objective function of this model forces the calculated
total cost due to one extra PCE to equal the equilibrium demand price; as a result,
users will pay the marginal cost of the system. This results in a system-optimized
network, where costs imposed by drivers are realized.
Figure 4-1 shows the model spreadsheet layout for an assumed elasticity of -
0.2 and an initial flow condition of 2,000 PCE/lane/hour. From the model’s
standpoint, a positive elasticity input of 0.2 actually corresponds to -0.2. From
Chapter 3, the initial proportion of traffic (based on the AM peak calculations) and
the total vehicle costs are obtained. All calculations are displayed, including optimal
57
congestion price ($0.14 per PCE per mile) and new anticipated flow (1,856
PCE/lane/hour). The yellow highlights denote variable inputs from the user and the
green highlights indicate variables utilized by the Solver tool in Excel.
58
FHWA Vehicle Classes
Description Units
Class 1 Class 2 Class 3 Class 4 Class 5 Class 6 Class 7 Class 8 Class 9 Class 10 Class 11 Class 12 Class 13
Total
speed = (a * flow^4) + (b * flow^3) –
(c * flow^2) + (d * flow) + 63.8
a = -0.000000000002
b = 0.000000006
c = 0.000007
d = 0.0021
average uncongested speed = 63.8 mph
user value of time + vehicle operating costs
$/hour 12.31 21.4 24.27 346.93 27.18 32.19 32.19 34.68 34.34 34.34 34.34 34.34 34.34
Initial flow PCE/lane/hour 2000
Initial proportion of traffic percentage 0.159% 83.177% 12.385% 0.683% 0.898% 0.582% 0.245% 0.224% 1.551% 0.058% 0.030% 0.006% 0.002% 100%
Initial number of vehicles PCEs 3 1664 248 14 18 12 5 4 31 1 1 0 0 2000
Initial speed mph 56.00 56.00 56.00 56.00 56.00 56.00 56.00 56.00 56.00 56.00 56.00 56.00 56.00
Initial cost (per vehicle) to travel 1 mile $/mile 0.21982 0.38214 0.43339 6.19518 0.48536 0.57482 0.57482 0.61929 0.61321 0.61321 0.61321 0.61321 0.61321
Congestion charge $/PCE/mile 0.14
Cost to travel 1 mile (with congestion charge) $/mile 0.36212 0.52445 0.57570 6.33748 0.62766 0.71712 0.71712 0.76159 0.75552 0.75552 0.75552 0.75552 0.75552
Elasticity 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2
Percent change in cost (after congestion
charge) percentage 64.74% 37.24% 32.83% 2.30% 29.32% 24.76% 24.76% 22.98% 23.21% 23.21% 23.21% 23.21% 23.21%
Percent change in flow (after congestion
charge) percentage 12.95% 7.45% 6.57% 0.46% 5.86% 4.95% 4.95% 4.60% 4.64% 4.64% 4.64% 4.64% 4.64%
Change in flow (after congestion charge) PCE/lane/hour 0 124 16 0 1 1 0 0 1 0 0 0 0
New flow (after congestion charge) PCE/lane/hour 3 1540 231 14 17 11 5 4 30 1 1 0 0 1856
New proportion of traffic (after congestion
charge) percentage 0.149% 82.966% 12.471% 0.733% 0.911% 0.596% 0.251% 0.230% 1.594% 0.060% 0.031% 0.006% 0.002%
New speed (after congestion charge) mph 58.22 58.22 58.22 58.22 58.22 58.22 58.22 58.22 58.22 58.22 58.22 58.22 58.22
Flow (with congestion charge) PCE/lane/hour 1856
Vehicle speed (with congestion charge) mph 58.22 58.22 58.22 58.22 58.22 58.22 58.22 58.22 58.22 58.22 58.22 58.22 58.22
Vehicle speed at one PCE/lane/hour less mph 58.23 58.23 58.23 58.23 58.23 58.23 58.23 58.23 58.23 58.23 58.23 58.23 58.23
Average cost per vehicle (at new vehicle
speed) $/mile 0.21145 0.36760 0.41690 5.95938 0.46688 0.55294 0.55294 0.59571 0.58987 0.58987 0.58987 0.58987 0.58987 0.42125
Average cost per vehicle at one PCE/lane/hour
less $/mile 0.21141 0.36752 0.41680 5.95805 0.46678 0.55282 0.55282 0.59558 0.58974 0.58974 0.58974 0.58974 0.58974 0.42115
Cost imposed on the entire traffic stream by
one extra PCE $/mile 0.17458
Total cost due to one extra PCE $/mile 0.59583
Percent change percentage 36.1
Elasticity 0.2
Initial flow PCE/lane/hour 2000
Speed under initial flow conditions mph 56.00 56.00 56.00 56.00 56.00 56.00 56.00 56.00 56.00 56.00 56.00 56.00 56.00
Cost (per vehicle) to travel 1 mile under initial
flow conditions $/PCE/mile 0.21982 0.38214 0.43339 6.19518 0.48536 0.57482 0.57482 0.61929 0.61321 0.61321 0.61321 0.61321 0.61321 0.43791
Resulting theoretical flow (based on elasticity
and % change) PCE/lane/hour 1856
Resulting theoretical cost (based on elasticity
and % change) $/PCE/mile 0.59583
(Resulting theoretical cost - Total cost due to
one extra PCE) $/PCE/mile 0.0
(Resulting theoretical flow - Flow with
congestion charge) PCE/lane/hour 0.0
Figure 4-1: Model Demonstration
59
4.4 Evaluations
As the observed traffic composition differs between AM and PM peaks on the
Capital Beltway, the two periods are examined as separate entities. Initial hourly
volumes are calculated based on averages obtained from all detector data across that
specific hour in 2007. For both the AM and PM peak periods, the average hourly
volumes are provided and optimal congestion charges for an assumed -0.2 elasticity
are displayed for each of the 13 FHWA vehicle classifications on a per-hour basis.
Additionally, the anticipated traffic composition as a result of congestion charging is
offered.
4.4.1 AM Peak
Table 4-1 and Table 4-2 show the average hourly flow and applicable
congestion charges, respectively, for the AM peak period on the Capital Beltway.
Table 4-3 presents the anticipated hourly traffic composition as a result of congestion
charging. Most notably, it is seen that for the AM peak, the optimal congestion
charge ranges from $0.05 to $0.08 per PCE per mile, based on average hourly flow
conditions on I-495. While these figures are applicable to passenger cars, the lowest
possible charges (for class 1 vehicles) range from $0.02 to $0.03 per mile and the
highest possible charges (for class 13 vehicles) range from $0.22 to $0.35 per mile.
The range in charges is directly obtained from the corresponding PCE factors –
vehicles are charged appropriately for the amount of road space that they utilize.
Information on potential charging for roadway sections with greater flow will be
discussed later.
60
Table 4-1: Average AM Peak Hourly Flow for I-495
HOUR OF DAY AVERAGE PCE/LANE/HOUR (2007)
6 (6AM) 1598
7 (7AM) 1743
8 (8AM) 1709
9 (9AM) 1653
Table 4-2: AM Peak Hourly Congestion Charges for I-495
Congestion Charge ($/mile) Vehicle
Classification
Description
PCE
Factor
6AM 7AM 8AM 9AM
1 Motorcycle 0.38 0.02 0.03 0.03 0.02
2 Passenger Cars 1.00 0.05 0.08 0.07 0.06
3 Other Two-Axle, Four-Tire single Unit Vehicles 1.13 0.06 0.09 0.08 0.07
4 Buses 2.38 0.12 0.19 0.17 0.14
5 Two-Axle, Six-Tire, Single-Unit Trucks 1.63 0.08 0.13 0.11 0.10
6 Three-Axle Single-Unit Trucks 1.56 0.08 0.13 0.11 0.09
7 Four or More Axle Single-Unit Trucks 2.00 0.10 0.16 0.14 0.12
8 Four or Fewer Axle Single-Trailer Trucks 2.75 0.14 0.22 0.19 0.17
9 Five-Axle Single-Trailer Trucks 4.00 0.20 0.32 0.28 0.24
10 Six or More Axle Single-Trailer Trucks 3.94 0.20 0.32 0.28 0.24
11 Five or Fewer Axle Multi-Trailer Trucks 4.25 0.21 0.34 0.30 0.26
12 Six-Axle Multi-Trailer Trucks 4.56 0.23 0.37 0.32 0.27
13 Seven or More Axle Multi-Trailer Trucks 4.31 0.22 0.35 0.30 0.26
Table 4-3: AM Peak Traffic Composition Resulting from Congestion Pricing
Traffic Composition (PCE/lane/hour)
6AM 7AM 8AM 9AM
Vehicle
Classification
Initial Final Initial Final Initial Final Initial Final
Total 1598 1550 1743 1668 1709 1641 1653 1596
1 3 2 3 3 3 3 3 2
2 1329 1288 1450 1385 1421 1363 1375 1326
3 198 193 216 207 212 204 205 198
4 11 11 12 12 12 12 11 11
5 14 14 16 15 15 15 15 14
6 9 9 10 10 10 10 10 9
7 4 4 4 4 4 4 4 4
8 4 4 4 4 4 4 4 4
9 25 24 27 26 27 26 26 25
10 1 1 1 1 1 1 1 1
11 0 0 1 1 1 0 0 0
12 0 0 0 0 0 0 0 0
13 0 0 0 0 0 0 0 0
4.4.2 PM Peak
Table 4-4 and Table 4-5 show the average hourly flow and applicable
congestion charges, respectively, for the PM peak period on the Capital Beltway.
61
Table 4-6 presents the anticipated hourly traffic composition as a result of congestion
charging. Most notably, it is seen that for the PM peak, the optimal congestion
charge ranges from $0.03 to $0.08 per PCE per mile, based on average hourly flow
conditions on I-495. While these figures are applicable to passenger cars, the lowest
possible charges (for class 1 vehicles) range from $0.01 to $0.03 per mile and the
highest possible charges (for class 13 vehicles) range from $0.13 to $0.35 per mile.
The range in charges is directly obtained from the corresponding PCE factors –
vehicles are charged appropriately for the amount of road space that they utilize.
Information on potential charging for roadway sections with greater flow will be
discussed later.
Table 4-4: Average PM Peak Hourly Flow for I-495
HOUR OF DAY AVERAGE PCE/LANE/HOUR (2007)
14 (2PM) 1733
15 (3PM) 1674
16 (4PM) 1583
17 (5PM) 1514
18 (6PM) 1439
Table 4-5: PM Peak Hourly Congestion Charges for I-495
Congestion Charge ($/mile) Vehicle
Classification
Description
PCE
Factor
2PM 3PM 4PM 5PM 6PM
1 Motorcycle 0.38 0.03 0.03 0.02 0.02 0.01
2 Passenger Cars 1.00 0.08 0.07 0.05 0.04 0.03
3 Other Two-Axle, Four-Tire single Unit Vehicles 1.13 0.09 0.08 0.06 0.05 0.03
4 Buses 2.38 0.19 0.17 0.12 0.10 0.07
5 Two-Axle, Six-Tire, Single-Unit Trucks 1.63 0.13 0.11 0.08 0.07 0.05
6 Three-Axle Single-Unit Trucks 1.56 0.13 0.11 0.08 0.06 0.05
7 Four or More Axle Single-Unit Trucks 2.00 0.16 0.14 0.10 0.08 0.06
8 Four or Fewer Axle Single-Trailer Trucks 2.75 0.22 0.19 0.14 0.11 0.08
9 Five-Axle Single-Trailer Trucks 4.00 0.32 0.28 0.20 0.16 0.12
10 Six or More Axle Single-Trailer Trucks 3.94 0.32 0.28 0.20 0.16 0.12
11 Five or Fewer Axle Multi-Trailer Trucks 4.25 0.34 0.30 0.21 0.17 0.13
12 Six-Axle Multi-Trailer Trucks 4.56 0.37 0.32 0.23 0.18 0.14
13 Seven or More Axle Multi-Trailer Trucks 4.31 0.35 0.30 0.22 0.17 0.13
62
Table 4-6: PM Peak Traffic Composition Resulting from Congestion Pricing
Traffic Composition (PCE/lane/hour)
2PM 3PM 4PM 5PM 6PM
Vehicle
Classification
Initial Final Initial Final Initial Final Initial Final Initial Final
Total 1733 1660 1674 1613 1583 1537 1514 1478 1439 1411
1 3 3 3 3 3 2 2 2 2 2
2 1504 1439 1453 1398 1374 1333 1314 1282 1249 1224
3 179 173 173 168 164 160 157 153 149 146
4 7 7 7 7 7 7 6 6 6 6
5 10 10 10 10 9 9 9 9 9 8
6 4 4 4 4 4 4 4 4 4 3
7 1 1 1 1 1 1 1 1 1 1
8 3 3 3 3 3 3 2 2 2 2
9 20 20 20 19 19 18 18 17 17 17
10 0 0 0 0 0 0 0 0 0 0
11 0 0 0 0 0 0 0 0 0 0
12 0 0 0 0 0 0 0 0 0 0
13 0 0 0 0 0 0 0 0 0 0
4.4.3 Discussion of Results
As seen in the two previous sections, the optimal AM and PM peak period
charges range from $0.03 to $0.08 per passenger car equivalent per mile. These
estimates are lower than the $0.08 to $0.50 per mile estimates, in 2007 dollars, taken
from existing literature. In terms of the city street methodology on which this study is
based, Roth and Villoria (2001) found optimal pricing in the range of $0.29 to $0.64
per passenger car equivalent per mile, in 2007 dollars. Based on these other figures,
it seems as if there could be other factors that this study did not take into account.
Other estimations may very well have other factors included. For this reason, these
results should be taken as rough approximations.
4.5 Sensitivity Analysis
With any model, it is important to analyze changes in input parameters to
determine the corresponding responses. This section focuses on the effects of direct
inputs into the model – assumed elasticity, traffic proportions, and value of time – on
63
the congestion charges computed. In a way, it is difficult to perform substantial
sensitivity analysis with an optimization model that outputs a single “best” answer.
There are relatively few parameters open for sensitivity analysis since the Solver tool
optimizes the data and the key speed-flow relationship is, more or less, obvious.
Initial flow is another direct input into the model, but is not available for sensitivity
analysis. It goes without saying that speed is a function of flow and that as flow
increases, the optimal congestion charges will increase, as congestion costs are
greater.
4.5.1 Effect of Elasticity
In the previous section, congestion charges were presented based on average
flow conditions in the AM and PM peak periods. This section will take a different
route and present AM and PM peak congestion charge estimates for varying elasticity
levels – flows ranging from 0 to 2,350 PCE/lane/hour (lane capacity) will be
addressed. Figures 4-2 and 4-3 show the sensitivity of AM and PM peak congestion
charges with respect to elasticity, respectively.
64
Flow vs. Congestion Charge - AM Peak
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.40
0 500 1000 1500 2000
Flow (PCE/lane/hour)
C
o
n
g
e
s
t
i
o
n
C
h
a
r
g
e
(
$
/
P
C
E
/
m
i
l
e
)
-0.1 Elasticity
-0.2 Elasticity
-0.3 Elasticity
-0.4 Elasticity
-0.5 Elasticity
-0.6 Elasticity
-0.7 Elasticity
-0.8 Elasticity
-0.9 Elasticity
-1.0 Elasticity
Figure 4-2: Sensitivity of Elasticity Values for Congestion Charges (AM Peak)
Flow vs. Congestion Charge - PM Peak
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.40
0 500 1000 1500 2000
Flow (PCE/lane/hour)
C
o
n
g
e
s
t
i
o
n
C
h
a
r
g
e
(
$
/
P
C
E
/
m
i
l
e
)
-0.1 Elasticity
-0.2 Elasticity
-0.3 Elasticity
-0.4 Elasticity
-0.5 Elasticity
-0.6 Elasticity
-0.7 Elasticity
-0.8 Elasticity
-0.9 Elasticity
-1.0 Elasticity
Figure 4-3: Sensitivity of Elasticity Values for Congestion Charges (PM Peak)
65
Especially interesting about this sensitivity analysis is that a large change in
assumed elasticity does not cause similarly large changes in the congestion charge. In
fact, the optimal charges at lower flow levels (less than about 1,500 PCE/lane/hour)
are very similar across all elasticity levels. It is only at higher flow levels that the
plots fan out from one another. At capacity, the charge varies from $0.09 to $0.38 per
PCE per mile for the AM peak and from $0.09 to $0.37 per PCE per mile for the PM
peak. Even though this is a spread increase of over four times, the total cost is still
not significant enough to claim that assumed elasticity has a large impact on optimal
congestion charges.
From these plots, the effects of elasticity can be easily seen. For an assumed
elasticity value of -1.0, it can be assumed that other transportation (i.e. public transit)
options are readily available. For this reason, there is a larger decrease in road usage
at a lower price. As elasticity go towards -0.1, there is not as much of a decrease in
road usage in the presence of pricing, so charges must be increased in order to cause a
decrease in road usage.
4.5.2 Effect of Traffic Proportions
Traffic proportions have an effect on congestion charges due to the different
total costs incurred per mile for each vehicle classification. For example, in the case
of the I-495 data used in this study, the vast majority of vehicles are passenger cars.
The total cost, per mile, to operate a passenger car is much less than the total cost, per
mile, to operate a seven or more axle multi-trailer truck. For this reason, the weighted
cost of the vehicles in the traffic stream will be lower when there is a greater
percentage of passenger cars rather than large trucks.
66
To illustrate this, assume that the total flow is currently 2,000 PCE/lane/hour.
For simplicity’s sake, there are only two types of vehicles on the roadway: passenger
cars and seven or more axle multi-trailer trucks. Using the same values of time and
elasticity, the optimal congestion charge when the traffic consists of 75% passenger
cars and 25% seven or more axle multi-trailer trucks is $0.15 per PCE per mile.
When the traffic stream consists of 25% passenger cars and 75% seven or more axle
multi-trailer trucks, the optimal congestion charge is $0.19 per PCE per mile. For a
large change in traffic proportion conditions, there is a relatively small change in the
optimal congestion charge.
4.5.3 Effect of Value of Time and Vehicle Operating Costs
It is difficult to address the effect of value of time and vehicle operating costs
due to the fact that traffic proportions interact significantly with these values to
determine the optimal congestion charge. When previously analyzing the effect of
traffic proportions, it was assumed that total costs remained the same as they did
throughout the study. If the total costs for a certain vehicle are incredibly high and
there are none using the roadway, the weighted average of congestion costs across the
traffic stream will be much lower than if there are many of these vehicles on the
roadway. For this reason, the effect of total vehicle costs on optimal congestion
charge is deemed to be worthy of mention, along with the fact that there is a strong
correlation with traffic proportions.
67
4.6 Summary
This chapter has shown that optimal AM and PM peak period charges range
from $0.03 to $0.08 per passenger car equivalent per mile in this study. These
estimates are lower than the $0.08 to $0.50 per mile estimates taken from existing
literature. Based on these figures, it seems as if there could be other factors that this
study did not take into account. Other estimations may very well have other factors
included. For this reason, these results should be taken as rough approximations.
Additionally, lower values infer less congestion – in this case, the congestion pricing
strategy should be examined to see that it is encompassing the hours of the day that
truly merit such pricing, based on the context of this study.
This thesis is limited by the fact that elasticity estimates are assumed
equivalent across the entire traffic population and value of time estimates are assumed
equal across similar vehicle types. In actuality, this would not be the case, as not
everyone is affected in the same way. It is difficult, however, to take these factors
into account and, thus, this study should be viewed under hypothetical pretenses.
Based on the results set forth in this chapter, it is determined that vehicle users
with a lower combined value of time and vehicle operating cost experience the most
change with congestion pricing. Fewer of these users utilize the roadway after
congestion pricing is implemented – this shows that, among other things, these users
either change their driving habits to occur in off-peak hours or they switch to other
forms of transportation. Commercial truck operations and commuters lacking
flexible work schedules are significantly affected by congestion pricing. These users
have a fixed schedule and lack options other than paying the congestion charge.
68
Chapter 5: Implementation
5.1 Overview
While previous chapters have centered on such topics as calculations and data
management, this chapter will focus on the logistics behind implementing a
congestion pricing system for the Capital Beltway. The optimization model
developed in this study can be seen as a “first-best” congestion pricing strategy, as
users realize their full congestion costs and roads are used most efficiently.
Unfortunately, congestion charges that vary in real-time based on actual conditions
are not practical at this point in time. For the sake of feasibility in the Washington,
D.C. area, a “second-best” congestion pricing solution must be examined, where
charges varying on an hourly scale instead of smoothly time-varying charges. When
demonstrating the model in Chapter 4, this was the methodology considered. Without
a system like this, where the general public can be aware of the charges in advance in
order to make an informed decision about their driving habits, acceptance will be
lacking. After a “second-best” system is implemented, more advances can be made
towards a gradual “first-best” solution.
It is important to note that under a congestion pricing scheme, charges should
bear some relationship to congestion costs imposed and vary by time of day and by
location. Ideally, the congestion price they should equal the imposed costs (as
calculated with the optimization model in this study). Instead of paying a flat fee
when passing a cordon, charges should be assessed as vehicles pass pricing points
setup along the roadway and calculated based on miles driven. As described
69
previously, this strategy falls somewhere in the middle of these requirements – hourly
charges enacted on a per-mile basis.
5.2 Congestion Pricing Strategy
This congestion pricing strategy is largely based on a review of other
implemented systems. Obtained data from select locations of I-495 have been
assumed representative across the entire Capital Beltway due to lack of other data. It
should be noted that a more effective approach would be to analyze smaller sections
independently (i.e. split I-495 into a number of predefined zones) based on observed
data in those sections. The congestion charges, therefore, would vary by zone instead
of being assumed representative of the entire roadway. For example, areas exhibiting
traffic flow conditions much greater than calculated averages would be assigned
charges that are higher than those assigned to sections exhibiting lower traffic flow
conditions.
5.2.1 Hours of Operation
The proposed hours of operation for this congestion charging system are
6:00AM – 10:00AM and 2:00PM – 7:00PM. These timeframes encompass the
morning and evening peak periods on the Capital Beltway, as exhibited in Chapter 4.
The hourly extent of the PM peak period is greater than the AM peak, as represented
by the proposed hours of operation. Future iterations of a congestion charging
strategy could add an additional morning hour from 5:00AM – 6:00AM or implement
24-hour charging on I-495. This system will operate only on weekdays, excluding
federal holidays – equating a total of 251 days per year.
70
5.2.2 Charges
Table 5-1 shows the hourly congestion charges for this system, in dollars per
PCE per mile. Corresponding charges for each of the 13 FHWA vehicle
classifications can be obtained by multiplying the charge by the PCE factors that were
presented in Chapter 3.
Table 5-1: Hourly Congestion Charges for I-495
Hour
Charge
($/PCE/mile)
12:00AM - 12:59AM
1:00AM - 1:59AM
2:00AM - 2:59AM
3:00AM - 3:59AM
4:00AM - 4:59AM
5:00AM - 5:59AM
NO CHARGE
6:00AM - 6:59AM 0.05
7:00AM - 7:59AM 0.08
8:00AM - 8:59AM 0.07
9:00AM - 9:59AM 0.06
10:00AM - 10:59AM
11:00AM - 11:59AM
12:00PM - 12:59PM
1:00PM - 1:59PM
NO CHARGE
2:00PM - 2:59PM 0.08
3:00PM - 3:59PM 0.07
4:00PM - 4:59PM 0.05
5:00PM - 5:59PM 0.04
6:00PM - 6:59PM 0.03
7:00PM - 7:59PM
8:00PM - 8:59PM
9:00PM - 9:59PM
10:00PM - 10:59PM
11:00PM - 11:59PM
NO CHARGE
These charges were calculated based on an assumed elasticity estimate of -0.2,
which was discussed previously in Chapter 2 and is based on theoretical studies and
implementation in Stockholm. After implementation, the actual elasticity in regards
to pricing could be obtained and the charges recalculated, accordingly.
71
5.2.3 Goals
The main goal of this congestion pricing strategy is drawn from the research
objectives of this study. As travelers fail to realize their role in congestion, these
charges attempt to equal their contributed congestion costs to the traffic stream.
Secondary goals are operating a system that pays for itself and does not require
subsidies and improved traffic conditions, among others. These are not focal points
of the congestion pricing system, but are worth mentioning as potential positive
outcomes.
5.2.4 Conditions
As evident with other pricing systems that are in-place, special conditions
under the system must be addressed. Pricing systems are typically bogged down with
numerous exemptions and this proposed system attempts to stray away from that
scenario.
For this system, transit and emergency vehicles will be granted free access.
While this is not specifically addressed in this study, the costs of these vehicles would
be subsidized in some way. Additionally, low-income motorists may be eligible for
toll credits that could be used as assistance. Prerequisites for these credits would
need to be determined before implementation. Hybrid vehicle owners will not
receive any discounts, although more stringent charges for vehicles exerting higher
levels of pollution could be considered.
System shut-off conditions must also be in-place to accommodate unforeseen
scenarios. Examples of this have not been found in existing literature and could be
brought on by severe weather or traffic incidents, as examples. Under these special
72
circumstances, the system would be shifted into “no-charge” mode and operated
accordingly until the roadway network regains normal operating conditions. A full
outline of potential system shut-off scenarios would be created before
implementation.
5.2.5 Payment Options
Multiple payment options will exist for users of the Capital Beltway. The
most efficient method, by far, will be a direct withdrawal from a user account, which
travelers stock with funds in advance via the Internet, mail, or telephone. This
method would be comparable to the E-ZPass toll system that exists in the northeast
United States. Other post-travel options will also include Internet, mail, and
telephone-based payments.
Charges accrued that are not tied to a user account will be required monthly,
with users receiving a bill. In this light, congestion charges could be likened to a
monthly cable or telephone bill. Although a monthly billing system would be in-
place, payments would be accepted at any point in time. For example, a user could
pay their total charge on a daily basis instead of waiting until the end of the month to
pay all of the charges that have accumulated. If timely payments are not made, the
user could be assessed a penalty amounting to 20% of the total owed.
5.2.6 Revenue Spending
Revenue spending is a key concern for any congestion pricing system. For the
purposes of this system, revenue will be first utilized to cover start-up and ongoing
costs – these costs are evaluated in the next chapter. After system costs are met,
73
excess revenue can be applied to supporting public transit and road improvements,
with public transit being a priority. By utilizing the revenue in this manner, the
public will know that they are benefiting from the congestion charging in a tangible
way.
5.2.7 Technology
Until recently, technology was not readily available to operate the proposed
congestion pricing system. As the cost of equipment has decreased, complex and
efficient systems are now quite possible. With the technological advances that have
been made since the idea of congestion pricing originated, implementation of a
pricing system is now easier than ever before. The following two sections address the
technology proposed for the I-495 congestion pricing system.
5.2.7.1 Open Road Tolling
Open road tolling refers to the process of collecting tolls on a roadway
without the use of toll plazas, where drivers are charged appropriately without having
to stop or slow down. The major advantage to open road tolling is just that - users are
not required to slow down and are able to maintain their highway travel speed. Tolls
are typically collected using radio frequency identification (RFID) systems – the E-
ZPass system utilized in the northeastern United States is an example of this. Figure
5-1 shows a typical open road tolling gantry setup.
74
Figure 5-1: Open Road Tolling Gantry
The slight disadvantage to open road tolling is the small possibility of equipment not
correctly identifying vehicles. More research is required in this area, but it is not
expected to severely impact systems utilizing this technology.
5.2.7.2 Enforcement/Collection
The enforcement and collection of applicable congestion charges will be
overseen by a system of electronic toll collectors and cameras running to video
recognition software. Open road tolling technology goes hand-in-hand with
electronic toll collection (ETC). ETC systems generally use transponders to
automatically debit pre-paid accounts of registered cars without having them stop or
slow down – this method is, by far, most efficient. Electronic toll collection systems
are based on four key components, all of which are automated. These are:
• Vehicle identification
• Vehicle classification
• Transaction processing
• Violation enforcement
75
As an added incentive for drivers to obtain transponders, 10,000 of them will
be given away before implementation.
In the circumstances where drivers do not have a registered transponder,
enforcement cameras will photograph the vehicle's license plate. Optical recognition
software will be utilized to translate the images into text, which can then be searched
for in the database maintained by the Department of Motor Vehicles. An example of
such software, as used in London, is shown in Figure 5-2. Figure 5-3 shows a typical
camera setup for the charging system implemented in Stockholm.
Figure 5-2: License Plate Recognition Software (London)
Source: Murray-Clark
76
Figure 5-3: Typical Gantry Camera Setup (Stockholm)
(Source: Vägverket)
5.2.8 Comparisons to Existing Systems
Two of the most notable pricing schemes in existence are located in London
and Stockholm. This section aims to briefly compare key components of these
systems to the proposed implementation.
The main difference is that this study’s charging strategy is based per-mile. In
both Stockholm and London, charges are collected at cordons around the city and no
charging is based on actual miles driven. The essence of congestion pricing is based
on location, time, and amount driven. Out of the three, only the proposed Capital
Beltway strategy takes all of these components into account.
In terms of operating hours, both London and Stockholm operate from the
beginning of the morning peak until the end of the evening peak, including the time
between. For I-495, only the peak period hours are part of the charging strategy, as
77
traffic flows throughout the day are not yet great enough to merit charging as a means
to relieve congestion. As the system progresses, however, this is a natural expansion.
Both London and Stockholm utilize cameras with license plate recognition
systems in order to charge drivers. The I-495 system will primarily use electronic toll
collection through transponders, with cameras as a backup option for vehicles that are
not equipped with the necessary transponder.
Revenue spending is a key concern for any pricing strategy. London spends
most of the revenue gained from the system (after ongoing and operating costs are
deducted) on improved bus services within the city. Stockholm, on the other hand,
uses all revenue solely for road construction. It is generally regarded that public
transportation and roadway improvements should be obtained from excess revenue,
as the public can then see, first-hand, how the collected money is being spent. For
this reason, all revenue collected on I-495 after start-up and operating costs are
obtained will be dedicated to these sources.
As a final point, both the London and Stockholm systems are full of
exemptions and discount options for various types of vehicles and residents. The
strategy proposed in this study aimed to avoid this scenario and have as few
exemptions as possible.
5.3 Equity Considerations
A major concern of congestion pricing is that it is unfair to certain groups of
people. This argument stems from the belief that congestion pricing favors the rich,
as the poor are unable to afford the charges. This is actually not the case, as low-
income users of public transportation may benefit greatly from transit improvements
78
brought about by collected revenue and the fact that public transit vehicles are
sanctioned for use within congestion pricing areas, so greater reliability and decreased
travel times could be expected. A well-designed pricing plan can be less burdensome
to low-income citizens than current systems that are based on regressive taxes, such
as car registration fees, sales taxes and the gas tax (FHWA 2001). Hypothetically,
congestion pricing can easily be shown to increase social welfare by making travelers
pay an amount closer to the full social costs resulting from their driving decisions
(Harrington 1998).
Most equity arguments are assuaged though proper revenue recycling, that is,
by creating a focused public benefit instead of what appears to just be a tax. The true
equity impact of any roadway pricing scheme depends heavily on how the revenues
are reused in the transportation system. Equity concerns can be offset by filtering
revenue into programs that benefit lower-income people, such as public transit or
potential pricing credits.
Paying directly for road usage is actually more equitable and efficient, since
users pay in proportion to the costs they impose. Uncharged facilities force everyone
to pay (through congestion), including motorists who reduce their vehicle use. Paying
directly gives individual consumers the savings that result when they drive less,
providing a new opportunity to save money. From a public welfare standpoint, under
congestion conditions, everyone is worse off, whereas under an efficient system,
society as a whole is better off. Congestion is a public “bad” that the government has
the ability to increase the cost of in order to discourage (Department of Legislative
79
Services 2005). Moreover, everyone wins with better air quality and increased
mobility.
As with any situation, there will be perceived winners and losers in regards to
congestion pricing on the Capital Beltway. Before implementation, these potential
conditions must be considered and evaluated in order to possibly mitigate less-than-
positive scenarios. Furthermore, significant public transit options must be improved
before any such system can be implemented. Without acceptable public
transportation options for drivers, a congestion pricing system lacks true equity.
5.4 Policy Limitations and Recommendations
Politics can be the downfall of any congestion pricing initiative. Without
political support, no system can see the light of day. As for the Capital Beltway, an
entire-roadway congestion pricing system is far more feasible than, say, a cordon area
surrounding Washington, D.C. Due to the amount of travelers that enter the city for
employment, a move like this would be seen as a commuter tax and fought hard by all
suburban centers. Unlike London or Stockholm, the Capital Beltway region is
encompassed by three jurisdictions (Maryland, Virginia, and the District of
Columbia), in addition to the federal government. While politics may be a hurdle, it
is one worth handling for the long-term societal good.
In terms of policy suggestions specifically for this study, opinions were
gathered from Patrick DeCorla-Souza, the Team Leader for Highway Pricing and
System Analysis in the Office of Transportation Policy Studies and the Program
Manager for the Urban Partnership Program at the Federal Highway Administration
(FHWA) in Washington, D.C. Although it is out of the scope of this study, it was
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suggested that it would probably make more sense to start pricing the entire freeway
system in the area – not just the Capital Beltway; a key to success with congestion
pricing systems is the comprehensiveness of the pricing network. To make the
system truly work, other taxation should be eliminated, as the system revenue would
hopefully be enough to cover these costs – this way, the public would be far more
accepting of road pricing. Additionally, finding funding sources for expanded transit
options, telecommuting programs, and things of that nature are critical steps towards
congestion pricing. Finally, there are a few political selling points that should be
addressed. These are as follows:
• The congestion pricing system is a replacement of the current taxation
system
• The system is fair – drivers who use more pay more
• The system is efficient – travel delay is decreased or eliminated, the
economy is boosted, and freeway productivity loss is avoided
• The system is good for the environment – lowered emissions through less
idling, positive global warming effect, etc.
Martin Richards, an expert on the London pricing scheme, addressed some
key issues at the Transportation Research Board (TRB) 2008 Annual Meeting. For a
successful system, the media and general public must be well-informed in advance of
any implementation. If this aspect is lacking, the public and media will come to
incorrect conclusions about the system and it then becomes easier for those opposed
to propagate misleading information – thus, rational discussion about the topic is
difficult. The success of system implementation is based on creating a clear vision,
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providing a clear execution pathway, strong leadership that won’t back down or
retract, and total and consistent commitment to the cause.
Lastly, there are multiple perspectives that should be reflected in any
congestion pricing system to ensure effectiveness and fairness – those of the users,
traffic authority, and society. The proposed system in this study addresses these
perspectives, but further examination should be done for each. An outline of
recommended principles for each perspective is as follows (Victoria Transport Policy
Institute 2007):
From the perspective of the user, a congestion pricing system should be easy
to understand, convenient (i.e. does not require vehicles to stop at toll booths), viable
transportation options should exist (i.e. alternative modes, travel times, routes, and
destinations), multiple easy-to-use payment options should exist (i.e. cash, prepaid
card, credit card, etc.), charges should be evident before a trip is undertaken, and the
privacy of users should be assured.
From the perspective of the traffic authority, a congestion pricing system
should consider traffic impacts (vehicles should not be required to stop at toll booths
or delay traffic in other ways), efficient and equitable charges should reflect true user
costs, the system should be effective in reducing traffic congestion and other
transportation problems by changing travel behavior, occasional users and different
vehicle types should be easily accommodated, minimal incorrect charges should
occur, minimal fraud or non-compliance should occur, there should be a positive
return on the system investment (i.e. cost effectiveness), there should be minimal
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disruption during any development phase, and the implementation should be available
for expansion, as needed.
From the perspective of society, a congestion pricing system should have
positive net benefits when all impacts are considered, political acceptability (i.e.
public perception of fairness and value), positive environmental impacts, and the
same integrated charging system should be able to be used to pay other public service
fees (i.e. parking, public transit, etc.).
5.5 Summary
In this chapter, the logistics behind implementing a congestion pricing system
for the Capital Beltway were presented. Effective between weekday hours of 6AM
and 10AM and 2PM and 7PM, the morning and evening peak periods on I-495 are
included. As noted, potential future iterations of a pricing system could expand the
hours of operation or switch to 24-hour pricing. In this study, the charges attempt to
cause roadway users to equal their contributed congestion costs to the traffic stream.
While other implementations are bogged down with exemptions and
discounts, the conditions of this study were relatively straightforward. Transit and
emergency vehicles will be granted free access and low-income users may be eligible
for travel credits. Multiple payment options via the Internet, mail, and telephone will
be available to travelers. System revenue will be first utilized to cover start-up and
ongoing costs. Afterward, excess revenue will be applied to supporting public transit
and road improvements, with public transit being a priority.
Equity considerations must be taken extremely seriously (through revenue
spending, etc.) and it must be realized that policy limitations exist. In order for a
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congestion pricing system to be taken seriously, citizens must believe that the system
is a replacement of the current taxation system, the system is fair (i.e. drivers who use
more pay more), the system is efficient (i.e. travel delay is decreased or eliminated,
the economy is boosted, and freeway productivity loss is avoided), and that the
system is good for the environment. Additionally, pricing on only I-495 is not a
likely option. If pricing were to exist on roadways in the Washington, D.C. area, it
should be implemented on all major roadways (I-495, I-270, I-70, I-95, etc.).
The financial implications for the proposed I-459 congestion pricing system
are presented in the next chapter.
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Chapter 6: Financial Implications
6.1 Costs
In the following sections, estimated cost information for the proposed Capital
Beltway congestion pricing system is provided.
6.1.2 Scenarios Examined
Two potential open road tolling/electronic toll collection setups were
considered in this study. Both involved overhead gantry systems, but differed in cost
due to the layout of the gantries. The premise of this system is that vehicles are
“tracked” at each gantry and if they don’t reach the next gantry within a certain time
(i.e. they exit I-495), their charge is calculated – this amount of time will have to
reflect possible congestion or other occurrences and is not the focus of this thesis.
The two strategies were as follows:
• Gantry setup directly on I-495 – across all four lanes in each direction
• Gantry setup on entrance and exit ramps to/from I-495 – gantries ranging
from 1- to 3-lanes for each entrance and exit ramp
Figures 6-1 and 6-2 show each of these layouts overlaid on the same I-495
interchange.
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Figure 6-1: I-495 Gantry Setup (Direct)
Figure 6-2: I-495 Gantry Setup (Entrance and Exit Ramps)
Using these two layout scenarios, cost information was estimated. The
Research and Innovative Technology Administration of USDOT operates a cost-
estimate database. The fairly recent study of I-75 and I-575 in Atlanta provided some
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cost estimates of not only gantries, but also all facets of project implementation for
HOT lanes – the cost estimate aspects of design, construction, maintenance, and
operation were extrapolated from their estimates for the components necessary for the
proposed congestion pricing system on I-495. Table 6-1 presents the system cost
breakdown for I-495 extrapolated from the USDOT database. Also factored into this
table are the yearly operating costs, which will be discussed later. These categories
are used for both potential scenarios.
6.1.2.1 Gantry Setup on I-495
Using a gantry setup directly on I-495 entails, on average, four 4-lane gantries
at each interchange. The reasoning behind this is that gantries cannot be placed only
before or after entrances and exits – they must be placed both before and after these
points in order to account for all vehicles. Using roadmaps, satellite imagery, and
general knowledge of the region, it is estimated that a total of 166 4-lane gantries
would be required for this scenario – 106 in Maryland and 60 in Virginia. As some
calculations deal with a per-lane basis, this equates to 664 total lanes – 424 in
Maryland and 240 in Virginia.
Using these costs, the proposed system setup on I-495 with gantries directly
on I-495 would be estimated at $58,066,275 – $35,730,075 in Maryland and
$22,336,200 in Virginia.
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Table 6-1: I-495 System Costs
Category Description Notes Cost ($)
Gantry structure - 4 lanes - 75000
Gantry structure - 3 lanes - 65000
Gantry structure - 2 lanes - 60000
Gantry structure - 1 lane - 30000
Toll & communication equipment building 1 per exit 30000
Electronic toll collection (ETC) reader 1 per gantry 4000
Transceiver 1 per gantry 3500
ETC reader controller 1 per gantry 4000
ETC power supply 1 per gantry 250
Camera 1 per gantry 3500
Camera power supply 1 per gantry 250
Image processor per state 6500
Optical character recognition (OCR) server per state 7000
OCR software/interface per state 60000
Vehicle detection sensor 1 per lane/per gantry 4500
Software, interface support, engineering support, and
documentation per state 12000
Lane controller 1 per gantry 12500
Lane cabinet and electronics 1 per gantry 6500
Lane software per state 200000
Variable message sign (approximately one per exit) 1 per exit 60000
Fixed overhead signs on gantry 1 per gantry 10000
Network equipment/connections per state 200000
Power - breaker panel 1 per exit 2000
Power - UPS & battery cabinet 1 per exit 5000
Power - conduit/wiring 1 per exit 20000
Power - disconnect & bypass switch 1 per gantry 3500
Power - generator unit 1 per exit 6500
Power - generator wiring 1 per exit 2000
Contingencies 25% of above total
Mobilization 10% of subtotal
Construction
Construction total All of the above
Design Engineering
and Administration
Design engineering and admin 20% of construction total
Host server and data storage per state 150000
Database software and licenses per state 50000
Host software per state 200000
System applications software per state 400000
Maintenance management per state 200000
Various other computer equipment per state 200000
Installation and configuration support per state 20000
Transponders (100,000 free units to commuters) split 50% 2500000
Customer service center per state 2000000
Capital Cost for
Operations
Capital cost for operations total All of the above
Maintenance costs (per year) 10% of capital costs
Transaction processing charge ($0.12 per transaction) -
85,000,000 transactions per year
split 50% 10200000 Yearly Costs
Yearly total All of the above
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6.1.2.2 Gantry Setup on Entrance and Exit Ramps
Using a gantry setup on I-495 entrance and exit ramps entails gantries ranging
from 1- to 3-lanes on each entrance and exit ramp to account for all vehicles entering
or exiting the roadway. Using roadmaps, satellite imagery, and general knowledge of
the region, it is estimated that the following gantries would be required for this
scenario:
Table 6-2: Gantry Totals on Entrance and Exit Ramps
1-lane 226
2-lane 15
Total
3-lane 3
1-lane 139
2-lane 7
Maryland
3-lane 3
1-lane 87
2-lane 8
Virginia
3-lane 0
As some calculations deal with a per-lane basis, this equates to 265 total lanes – 162
in Maryland and 103 in Virginia.
Using these costs, the proposed system setup on I-495 with gantries on I-495
entrance and exit ramps would be estimated at $53,732,550 – $ 31,968,075 in
Maryland and $21,764,475 in Virginia.
6.1.3 Chosen Scenario
Based on the cost estimates provided in the previous sections, a gantry setup
on I-495 entrance and exit ramps is the most cost-effective option. This presents a
significant cost savings of $4,333,725 compared to using a gantry setup directly on I-
495.
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6.2 Revenue
In order to calculate revenue, the assumed flow during each hour of the
congestion pricing strategy is based on average flow across all detectors providing
data for that hour in 2007. The optimization model was run using these average flows
in order to determine the new flows that can be expected during each hour to provide
revenue estimates. Since no I-495 data is collected on average miles driven per
vehicle on I-495 during each peak period, National Household Travel Survey (NHTS)
data were analyzed to obtain estimates. Based on the NHTS 2001 trip information for
the United States, the data were split into 1-mile increments ranging from one mile to
thirty-two miles. This is based on the assumptions of a distance of one mile between
any two exits on the Capital Beltway and the fact that people will hypothetically
travel along one-half of the 64-mile long roadway, at a maximum. Even though this
method is not entirely precise, it is far more realistic in terms of potential revenue
estimation than splitting up mileage level groups evenly based on traffic flow. Figure
6-3 plots the frequency distribution of trip distances that will be applied to I-495.
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Distribution of Trip Distances
0.000
0.020
0.040
0.060
0.080
0.100
0.120
0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32
Miles Driven
F
r
e
q
u
e
n
c
y
Figure 6-3: Distribution of Trip Distances
Source: NHTS 2001
In applying these trip distribution frequencies to the Capital Beltway, many
assumptions were made. First, traffic in the Washington, D.C. area was assumed
similar to the nationwide traffic represented in the NHTS data. Additionally, it was
assumed that one-way trips on I-495 have the same trip distribution frequencies as
full trips (from beginning to end) at the national level. This is a large assumption, due
to the fact that travel on the Capital Beltway is only a portion of the commute
experienced by travelers. Regardless of the number of assumptions, national trip
distribution frequencies provide a much better estimation than uniform frequency
estimates for each distance.
By using the applicable hourly charges presented in this study and the
corresponding hourly flows and frequency estimates, daily revenue can be calculated.
As an example of how this calculation was accomplished, for the 6:00AM - 6:59AM
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hour, the hourly flow on I-495 averages 1,598 PCE/lane/hour. Once congestion
pricing is implemented, the hourly flow is expected to drop to 1,550 PCE/lane/hour
and the associated charge is $0.05 per PCE per mile. The frequency of vehicles
traveling 1.5 miles on I-495 is 0.099. This results in 153 vehicles paying $0.05 per
mile for 1.5 miles – a total of roughly $11.48 for that portion of traffic (traveling in
one direction) during that hour. Similar calculations are then made for each of the 32
mileage ranges for the same hour and then for every operating hour afterwards. Daily
and yearly revenue estimates can then be obtained.
The total revenue per day for I-495 (in both directions) is estimated to be
$60,282.63. A total of 251 charging days per year equates to a yearly revenue
estimate of $15,130,939.61.
6.3 Break-Even Points/Payoff Calculations
In order to determine system break-even points and payoff calculations, the
system costs were examined over a 50-year period. Taking into account the yearly
costs of operation and maintenance, along with a 10-year equipment lifespan, these
yearly amounts were determined. After 10 years, it is assumed that 50% of the initial
system costs will be required to update the system, as some existing structure remains
usable. After 20 years, however, a complete system overhaul is required. Table 6-3
shows the yearly cumulative costs for the I-495 congestion pricing system. Similarly,
cumulative revenue estimates were made over a 50-year period (Table 6-4), assuming
constant yearly revenue. Payoff is equal to cumulative revenue divided by
cumulative cost for a given year and all estimates are kept in 2007 dollars to provide
easy comparison into the future.
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Table 6-3: I-495 System 50-Year Cumulative Costs
Description Year Cumulative Cost (2007 $)
Setup costs - 53732550
After 1 year of operation 1 64826550
After 2 years of operation 2 75920550
After 3 years of operation 3 87014550
After 4 years of operation 4 98108550
After 5 years of operation 5 109202550
After 6 years of operation 6 120296550
After 7 years of operation 7 131390550
After 8 years of operation 8 142484550
After 9 years of operation 9 153578550
After 10 years of operation (equipment lifespan) 10 164672550
After 11 years of operation 11 202632825
After 12 years of operation 12 213726825
After 13 years of operation 13 224820825
After 14 years of operation 14 235914825
After 15 years of operation 15 247008825
After 16 years of operation 16 258102825
After 17 years of operation 17 269196825
After 18 years of operation 18 280290825
After 19 years of operation 19 291384825
After 20 years of operation (2 equipment lifespans) 20 302478825
After 21 years of operation 21 367305375
After 22 years of operation 22 378399375
After 23 years of operation 23 389493375
After 24 years of operation 24 400587375
After 25 years of operation 25 411681375
After 26 years of operation 26 422775375
After 27 years of operation 27 433869375
After 28 years of operation 28 444963375
After 29 years of operation 29 456057375
After 30 years of operation (3 equipment lifespans) 30 467151375
After 31 years of operation 31 505111650
After 32 years of operation 32 516205650
After 33 years of operation 33 527299650
After 34 years of operation 34 538393650
After 35 years of operation 35 549487650
After 36 years of operation 36 560581650
After 37 years of operation 37 571675650
After 38 years of operation 38 582769650
After 39 years of operation 39 593863650
After 40 years of operation (4 equipment lifespans) 40 604957650
After 41 years of operation 41 669784200
After 42 years of operation 42 680878200
After 43 years of operation 43 691972200
After 44 years of operation 44 703066200
After 45 years of operation 45 714160200
After 46 years of operation 46 725254200
After 47 years of operation 47 736348200
After 48 years of operation 48 747442200
After 49 years of operation 49 758536200
After 50 years of operation (5 equipment lifespans) 50 769630200
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Table 6-4: I-495 System 50-Year Cumulative Revenue
Year Annual Revenue (2007 $) Cumulative Revenue (2007 $) Payoff %
1 15130939.61 15130939.61 0.233
2 15130939.61 30261879.23 0.399
3 15130939.61 45392818.84 0.522
4 15130939.61 60523758.46 0.617
5 15130939.61 75654698.07 0.693
6 15130939.61 90785637.68 0.755
7 15130939.61 105916577.30 0.806
8 15130939.61 121047516.91 0.850
9 15130939.61 136178456.53 0.887
10 15130939.61 151309396.14 0.919
11 15130939.61 166440335.76 0.821
12 15130939.61 181571275.37 0.850
13 15130939.61 196702214.98 0.875
14 15130939.61 211833154.60 0.898
15 15130939.61 226964094.21 0.919
16 15130939.61 242095033.83 0.938
17 15130939.61 257225973.44 0.956
18 15130939.61 272356913.05 0.972
19 15130939.61 287487852.67 0.987
20 15130939.61 302618792.28 1.000
21 15130939.61 317749731.90 0.865
22 15130939.61 332880671.51 0.880
23 15130939.61 348011611.13 0.893
24 15130939.61 363142550.74 0.907
25 15130939.61 378273490.35 0.919
26 15130939.61 393404429.97 0.931
27 15130939.61 408535369.58 0.942
28 15130939.61 423666309.20 0.952
29 15130939.61 438797248.81 0.962
30 15130939.61 453928188.42 0.972
31 15130939.61 469059128.04 0.929
32 15130939.61 484190067.65 0.938
33 15130939.61 499321007.27 0.947
34 15130939.61 514451946.88 0.956
35 15130939.61 529582886.50 0.964
36 15130939.61 544713826.11 0.972
37 15130939.61 559844765.72 0.979
38 15130939.61 574975705.34 0.987
39 15130939.61 590106644.95 0.994
40 15130939.61 605237584.57 1.000
41 15130939.61 620368524.18 0.926
42 15130939.61 635499463.79 0.933
43 15130939.61 650630403.41 0.940
44 15130939.61 665761343.02 0.947
45 15130939.61 680892282.64 0.953
46 15130939.61 696023222.25 0.960
47 15130939.61 711154161.87 0.966
48 15130939.61 726285101.48 0.972
49 15130939.61 741416041.09 0.977
50 15130939.61 756546980.71 0.983
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This revenue estimation is used, along with other potential scenarios involving
yearly revenue growth, to plot system payoff potential over time. Figure 6-4
showcases the results.
System Payoff Over Time (Using Average Revenue Estimates)
0.000
0.200
0.400
0.600
0.800
1.000
1.200
1.400
1.600
1.800
2.000
0 5 10 15 20 25 30 35 40 45 50
Years
%
P
a
y
o
f
f
Constant Revenue 0.5% Growth 1.0% Growth 1.5% Growth 2.0% Growth 2.5% Growth Break-Even
Figure 6-4: Yearly I-495 System Payoff
Looking at system payoff time based on different estimates of yearly revenue
growth produces interesting results. The following can be seen:
• Assuming constant revenue, the system pays for itself every 20 years, but
doesn't ever become profitable
• Assuming a 0.5% growth in revenue every year, the system becomes
profitable after 27 years
• Assuming a 1.0% growth in revenue every year, the system becomes
profitable after 24 years
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• Assuming a 1.5% growth in revenue every year, the system becomes
profitable after 15 years
• Assuming a 2.0% growth in revenue every year, the system becomes
profitable after 14 years
• Assuming a 2.5% growth in revenue every year, the system becomes
profitable after 12 years
As the proposed system at least breaks even with no ongoing debt, it is in the
common good.
6.4 Assumptions and Conclusions
As with other sections of this study, certain assumptions were required to
obtain cost and revenue estimates. First, HOT project estimates from the USDOT
Research and Innovative Technology Administration were assumed representative of
cost estimates for this congestion pricing system. Implementing a HOT lane is
different than an entire-facility system, so this fact was taken into account with the
cost estimates. Secondly, for cumulative cost estimates, 50% rebuild costs were
assumed at 10 years and complete system rebuild costs were assumed at 20 years –
this was based on the fact that the system equipment has a projected lifespan of 10
years. Lastly, NHTS trip data was assumed representative of one-way trips on I-495.
This data was utilized assuming a distance of one mile between any two exits on I-
495 and the fact that people will hypothetically travel one-half of the 64-mile long
Beltway, as a maximum. As stated previously, even though this method is not
entirely precise, it is far more realistic in terms of potential revenue estimation than
splitting up mileage level groups evenly based on traffic flow.
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Due to the fact that charges have been estimated to be lower than previous
research indicates, revenue figures have also been underestimated. In light of this
situation, a congestion pricing system in the Washington, D.C. area could potentially
exhibit faster turnaround and pay for itself in fewer years. Excess revenue could then
be spent on public transportation improvements in the area.
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Chapter 7: Conclusions and Recommendations
7.1 Summary of Results
Road users must be held accountable for the true cost of highways. As travel
is free on the Capital Beltway surrounding Washington, D.C., there is no current
financial incentive to utilize public transportation, alter the timing of necessary trips,
reduce unnecessary trips, or increase carpooling. This thesis aimed to hold users of I-
495 accountable for their role in congestion by calculating appropriate congestion
charges on a per-mile basis. The goal of this thesis was to calculate the appropriate
charges required for users of I-495 in order to fulfill their portion of congestion costs.
This goal was reached within the study, as a model was developed from
existing data on the Capital Beltway that showcases traffic characteristics that cause
congestion, necessary charges for vehicle users to realize the congestion costs that
their vehicles impose on the rest of the traffic stream were calculated, and potential
financial implications (costs and revenue) that would be associated with congestion
pricing were examined.
AM peak period charges ranging from $0.05 to $0.08 per PCE per mile cause
drivers to realize their contribution to congestion and charges ranging from $0.03 to
$0.08 per PCE per mile in the PM peak period accomplish the same. Tables breaking
these charges down across FHWA vehicle classifications were shown in Chapter 4,
along with summaries of anticipated traffic composition after implementing a
congestion pricing system on I-495. These estimates are lower than those based on
prior research, where efficient peak-hour congestion charges have been calculated to
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be between $0.08 and $0.50 per mile. This discrepancy in charging amounts can
most likely be associated with additional factors that were not taken into account in
this study. Chapter 6 showed that the proposed system with constant revenue will be
able to pay for itself with no yearly subsidy required. If revenue increases are
obtained, however, the system will both pay for itself and provide excess funds for
use in transit improvements or minor roadway improvements. Additionally, since the
charging estimates set forth in this thesis may be considered conservative
approximations, a congestion pricing system on the Capital Beltway may be more
cost effective than this study shows, with the system paying for itself in less time.
7.2 Conclusions
As mentioned previously, the proposed congestion system for the Capital
Beltway is a "second-best" solution – containing charges varying on an hourly scale
instead of smoothly time-varying charges. We are a long way from a potential "first-
best" solution, with congestion charges varying in real-time based on actual
conditions, as such a system is not practical at this point in time. Based on this fact,
any solution is better than no solution – a Washington, D.C. area congestion pricing
system needs to start somewhere. This study provides a good building block to the
positives of congestion pricing, but there is still much ground to be covered.
Although this study is a, more-or-less, hypothetical scenario, hopefully it can
pave the way for future discussion and research into facility-wide per-mile pricing
systems in the United States. Based on the results of this study, the charges necessary
for people to realize their congestion costs are not exorbitant. Education is key to
enlightenment, however, as most people truly fail to realize how paying for
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something like road usage can be more beneficial for society. Proponents of
congestion pricing must increase their public education efforts in hopes to gain
further support. Through all of this, we must all also realize that there is not one
perfect solution for congestion management – all available options must be
considered, including transit advancements and pricing.
7.3 Recommendations for Future Research
In closing, as there remains much ground for future research, the following
suggestions are made:
1. The entire regional freeway system should be examined in light of this
study, not just the Capital Beltway – network comprehensiveness is a
critical component of a successful congestion pricing strategy
2. Based on the lack of data for this study, more functioning traffic detectors
are needed to collect valid speed, volume, and vehicle classification data –
new sensor installations along with updates to the existing sensor network
are necessary to gather more precise data. Additionally, data collection
standards should exist for comprehensiveness between jurisdictions. In
terms of costs, discussion with various transportation professionals has
provided that installation costs for a fixed sensor network are estimated
between $7,500 and $20,000 per site. The range in cost is due primarily to
the extent to which existing infrastructure can be reused. Reuse of
existing poles, sign trusses, and existing power and communications feeds
reduce cost. Methods and technology that allow for reuse of existing
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infrastructure, though more expensive, may prove to be the more cost
effective option overall.
3. Congestion charging based on smaller time increments (or even real-time)
would require data in much smaller increments instead of the hourly
aggregations utilized in this study – various charging options should be
evaluated.
4. Instead of utilizing NHTS data to estimate one-way trips during AM and
PM peaks on I-495, surveys could be conducted in order to have a more
precise estimate of revenue possibilities.
5. This study focused on gantries, cameras, and license plate reader
technology, as costs were able to be obtained. Different technology may
be cheaper and easier to install – for example, charges related to mileage
driven in a priced region may be assessed by utilizing in-vehicle units
(IVUs), such as those in-place in Singapore, with no need for gantries or
cameras.
6. User value of time and vehicle operating cost estimates could be evaluated
more precisely instead relying on FHWA estimates – future surveys and
experiments could be conducted to gather this data.
7. While this study focuses on charging across all lanes on the Capital
Beltway, a similar analysis could be accomplished using a HOT lane
setup, like those being constructed in the region.
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8. Environmental costs such as air pollution caused by idling vehicles were
not considered in this thesis – special attention should be focused on
various environmental costs for future work.
9. A variation of this study could be focused on finding the number of
vehicles that need to be removed from a traffic stream at a given time in
order to reach a certain level of service (LOS), average speed, or some
other performance metric. Using a revised version of this model,
corresponding pricing can be set in order to reach these traffic volume
goals.
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Appendix
Avg. Hourly Speed - Link 90138
0.00
10.00
20.00
30.00
40.00
50.00
60.00
70.00
80.00
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
Hour of Day
S
p
e
e
d
(
m
p
h
)
2005
2006
2007
Figure A-1: Average Hourly Speed – Detector 90138
Avg. Hourly Speed by Year - Link 90138
0.00
10.00
20.00
30.00
40.00
50.00
60.00
70.00
80.00
2005 2006 2007
Year
S
p
e
e
d
(
m
p
h
)
12AM 1AM 2AM 3AM 4AM 5AM 6AM 7AM 8AM 9AM 10AM 11AM
12PM 1PM 2PM 3PM 4PM 5PM 6PM 7PM 8PM 9PM 10PM 11PM
Figure A-2: Average Hourly Speed by Year – Detector 90138
103
Avg. Hourly PCE Flow - Link 90138
0
500
1000
1500
2000
2500
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
Hour of Day
P
C
E
F
l
o
w
2003
2005
2006
2007
Figure A-3: Average Hourly Flow – Detector 90138
Avg. Hourly PCE Flow by Year - Link 90138
0
500
1000
1500
2000
2500
2003 2005 2006 2007
Year
P
C
E
F
l
o
w
12AM 1AM 2AM 3AM 4AM 5AM 6AM 7AM 8AM 9AM 10AM 11AM
12PM 1PM 2PM 3PM 4PM 5PM 6PM 7PM 8PM 9PM 10PM 11PM
Figure A-4: Average Hourly Flow by Year – Detector 90138
104
V/C Ratio - Link 90138
I-495 Capacity = 2,350 pc/ln/hr
0.00
0.10
0.20
0.30
0.40
0.50
0.60
0.70
0.80
0.90
1.00
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
Hour of Day
V
/
C
R
a
t
i
o
2003
2005
2006
2007
Figure A-5: Hourly Volume-to-Capacity Ratio – Detector 90138
Avg. Hourly Speed - Link 90202
0.00
10.00
20.00
30.00
40.00
50.00
60.00
70.00
80.00
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
Hour of Day
S
p
e
e
d
(
m
p
h
)
2003
2004
2005
2006
2007
Figure A-6: Average Hourly Speed – Detector 90202
105
Avg. Hourly Speed by Year - Link 90202
0.00
10.00
20.00
30.00
40.00
50.00
60.00
70.00
80.00
2003 2004 2005 2006 2007
Year
S
p
e
e
d
(
m
p
h
)
12AM 1AM 2AM 3AM 4AM 5AM 6AM 7AM 8AM 9AM 10AM 11AM
12PM 1PM 2PM 3PM 4PM 5PM 6PM 7PM 8PM 9PM 10PM 11PM
Figure A-7: Average Hourly Speed by Year – Detector 90202
Avg. Hourly PCE Flow - Link 90202
0
500
1000
1500
2000
2500
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
Hour of Day
P
C
E
F
l
o
w
2002
2003
2004
2005
2006
2007
Figure A-8: Average Hourly Flow – Detector 90202
106
Avg. Hourly PCE Flow by Year - Link 90202
0
500
1000
1500
2000
2500
2002 2003 2004 2005 2006 2007
Year
P
C
E
F
l
o
w
12AM 1AM 2AM 3AM 4AM 5AM 6AM 7AM 8AM 9AM 10AM 11AM
12PM 1PM 2PM 3PM 4PM 5PM 6PM 7PM 8PM 9PM 10PM 11PM
Figure A-9: Average Hourly Flow by Year – Detector 90202
V/C Ratio - Link 90202
I-495 Capacity = 2,350 pc/ln/hr
0.00
0.10
0.20
0.30
0.40
0.50
0.60
0.70
0.80
0.90
1.00
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
Hour of Day
V
/
C
R
a
t
i
o
2002
2003
2004
2005
2006
2007
Figure A-10: Hourly Volume-to-Capacity Ratio – Detector 90202
107
Avg. Hourly Speed - Link 90275
0.00
10.00
20.00
30.00
40.00
50.00
60.00
70.00
80.00
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
Hour of Day
S
p
e
e
d
(
m
p
h
)
2003
2005
2006
2007
Figure A-11: Average Hourly Speed – Detector 90275
Avg. Hourly Speed by Year - Link 90275
0.00
10.00
20.00
30.00
40.00
50.00
60.00
70.00
80.00
2003 2005 2006 2007
Year
S
p
e
e
d
(
m
p
h
)
12AM 1AM 2AM 3AM 4AM 5AM 6AM 7AM 8AM 9AM 10AM 11AM
12PM 1PM 2PM 3PM 4PM 5PM 6PM 7PM 8PM 9PM 10PM 11PM
Figure A-12: Average Hourly Speed by Year – Detector 90275
108
Avg. Hourly PCE Flow - Link 90275
0
500
1000
1500
2000
2500
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
Hour of Day
P
C
E
F
l
o
w
2002
2003
2004
2005
2006
2007
Figure A-13: Average Hourly Flow – Detector 90275
Avg. Hourly PCE Flow by Year - Link 90275
0
500
1000
1500
2000
2500
2002 2003 2004 2005 2006 2007
Year
P
C
E
F
l
o
w
12AM 1AM 2AM 3AM 4AM 5AM 6AM 7AM 8AM 9AM 10AM 11AM
12PM 1PM 2PM 3PM 4PM 5PM 6PM 7PM 8PM 9PM 10PM 11PM
Figure A-14: Average Hourly Flow by Year – Detector 90275
109
V/C Ratio - Link 90275
I-495 Capacity = 2,350 pc/ln/hr
0.00
0.10
0.20
0.30
0.40
0.50
0.60
0.70
0.80
0.90
1.00
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
Hour of Day
V
/
C
R
a
t
i
o
2002
2003
2004
2005
2006
2007
Figure A-15: Hourly Volume-to-Capacity Ratio – Detector 90275
Avg. Hourly Speed - Link 190004
0.00
10.00
20.00
30.00
40.00
50.00
60.00
70.00
80.00
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
Hour of Day
S
p
e
e
d
(
m
p
h
)
2003
2004
2005
Figure A-16: Average Hourly Speed – Detector 190004
110
Avg. Hourly Speed by Year - Link 190004
0.00
10.00
20.00
30.00
40.00
50.00
60.00
70.00
80.00
2003 2004 2005
Year
S
p
e
e
d
(
m
p
h
)
12AM 1AM 2AM 3AM 4AM 5AM 6AM 7AM 8AM 9AM 10AM 11AM
12PM 1PM 2PM 3PM 4PM 5PM 6PM 7PM 8PM 9PM 10PM 11PM
Figure A-17: Average Hourly Speed by Year – Detector 190004
Avg. Hourly PCE Flow - Link 190004
0
500
1000
1500
2000
2500
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
Hour of Day
P
C
E
F
l
o
w
2002
2003
2004
2005
Figure A-18: Average Hourly Flow – Detector 190004
111
Avg. Hourly PCE Flow by Year - Link 190004
0
500
1000
1500
2000
2500
2002 2003 2004 2005
Year
P
C
E
F
l
o
w
12AM 1AM 2AM 3AM 4AM 5AM 6AM 7AM 8AM 9AM 10AM 11AM
12PM 1PM 2PM 3PM 4PM 5PM 6PM 7PM 8PM 9PM 10PM 11PM
Figure A-19: Average Hourly Flow by Year – Detector 190004
V/C Ratio - Link 190004
I-495 Capacity = 2,350 pc/ln/hr
0.00
0.10
0.20
0.30
0.40
0.50
0.60
0.70
0.80
0.90
1.00
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
Hour of Day
V
/
C
R
a
t
i
o
2002
2003
2004
2005
Figure A-20: Hourly Volume-to-Capacity Ratio – Detector 190004
112
Avg. Hourly Speed - Link 190057
0.00
10.00
20.00
30.00
40.00
50.00
60.00
70.00
80.00
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
Hour of Day
S
p
e
e
d
(
m
p
h
)
2005
2006
2007
Figure A-21: Average Hourly Speed – Detector 190057
Avg. Hourly Speed by Year - Link 190057
0.00
10.00
20.00
30.00
40.00
50.00
60.00
70.00
80.00
2005 2006 2007
Year
S
p
e
e
d
(
m
p
h
)
12AM 1AM 2AM 3AM 4AM 5AM 6AM 7AM 8AM 9AM 10AM 11AM
12PM 1PM 2PM 3PM 4PM 5PM 6PM 7PM 8PM 9PM 10PM 11PM
Figure A-22: Average Hourly Speed by Year – Detector 190057
113
Avg. Hourly PCE Flow - Link 190057
0
500
1000
1500
2000
2500
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
Hour of Day
P
C
E
F
l
o
w
2003
2005
2006
2007
Figure A-23: Average Hourly Flow – Detector 190057
Avg. Hourly PCE Flow by Year - Link 190057
0
500
1000
1500
2000
2500
2003 2005 2006 2007
Year
P
C
E
F
l
o
w
12AM 1AM 2AM 3AM 4AM 5AM 6AM 7AM 8AM 9AM 10AM 11AM
12PM 1PM 2PM 3PM 4PM 5PM 6PM 7PM 8PM 9PM 10PM 11PM
Figure A-24: Average Hourly Flow by Year – Detector 190057
114
V/C Ratio - Link 190057
I-495 Capacity = 2,350 pc/ln/hr
0.00
0.10
0.20
0.30
0.40
0.50
0.60
0.70
0.80
0.90
1.00
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
Hour of Day
V
/
C
R
a
t
i
o
2003
2005
2006
2007
Figure A-25: Hourly Volume-to-Capacity Ratio – Detector 190057
115
References
Brookings Institution. (2003). “Fueling Transportation Finance: A Primer on the Gas
Tax.” Accessed online:
http://www.brookings.edu/reports/2003/03transportation_puentes.aspx.
Button, Kenneth. (2004). “Road Pricing.” Center for Transportation Policy, Operation
and Logistics, School of Public Policy, George Mason University.
Department of Legislative Services. (2005). “Congestion Pricing: A Potential Tool
for Reducing Congestion on Maryland’s Roadways.” Office of Policy
Analysis, Annapolis.
Dodgson, John, Emily Bulman and Simon Maunder. (2006). “Using Charges to
Tackle Road Congestion in the United States: Lessons from Abroad.” NERA
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Greenshields, B .D. (1935). “A Study in Highway Capacity.” Proceedings of the
Highway Research Board, Vol. 4, 448-477.
Harrington, W., A. Krupnick and A. Alberini. (1998). “Overcoming Public Aversion
to Congestion Pricing.” Resources for the Future.
Jones, P. (1998). "Urban Road Pricing: Public Acceptability and Barriers to
Implementation." Road Pricing, Traffic Congestion and the Environment:
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Lindsey, C. Robin and Erik T. Verhoef. (2000). "Traffic Congestion and Congestion
Pricing." Tinbergen Institute Discussion Papers.
Livingstone, Ken. (2007). "Clear Up the Congestion-Pricing Gridlock." New York
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McMullen, B. Starr. (1993). “Congestion Pricing and Demand Management: A
Discussion of the Issues.” Policy Studies Journal, Vol. 21, No. 2, 285-295.
Murray-Clark, Malcolm. (2007). "Congestion Charging in London: Past, Present and
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Oum, Tae H., W. G. Waters II, and Jong Say Yong. (1992). “Concepts of Price
Elasticities of Transport Demand and Recent Empirical Estimates: An
Interpretive Survey.” Journal of Transport Economics and Policy XXVI, 2.
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Paniati, Jeffrey F. (2006). “Enabling Congestion Pricing in the United States.”
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Systems and Services – October 2006.
Replogle, Michael. (2007). “Does the Rubber meet the Road? Investigating the
Alternatives to Congestion Pricing.” Environmental Defense.
Roth, Gabriel and Olegario G. Villoria, Jr. (2001). “Finances of a Commercialized
Urban Road Network Subject to Congestion Pricing.” Transportation
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Salomon, Ilan and Patricia L. Mokhtarian. (1997). "Coping with Congestion:
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Shrank, D.L. and T.J. Lomax. (2007). The 2007 Urban Mobility Report. Texas
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Smith, Adam. (1776). “An Inquiry into the Nature and Causes of the Wealth of
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Smith, Richard. (2007). "Maintaining the 'Open' in ORT." Presented at Violations
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Stockholmsförsöket - City of Stockholm. (2006). "Facts and Results from the
Stockholm Trials." Accessed online:
http://stockholmsforsoket.episerverhotell.net
Sullivan, Edward. (2003). “Implementing Value Pricing for U.S. Roadways.”
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401-413.
Transport for London. (2007). “Central London Congestion Charging – Impacts
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Transportation Research Board. (2000). Highway Capacity Manual 2000.
U.S. Department of Transportation, Federal Highway Administration. (1990).
“Highway Statistics 1990.” Accessed online:
http://isddc.dot.gov/OLPFiles/FHWA/013263.pdf.
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U.S. Department of Transportation, Federal Highway Administration. (2001). Traffic
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doc_450511192.pdf
In modern economies, prices are generally expressed in units of some form of currency.
ABSTRACT
Title of Document: CONGESTION PRICING FOR THE CAPITAL BELTWAY
Degree Candidate: Joshua Lee Crunkleton
Degree and Year: Master of Science, 2008
Directed By: Dr. Kelly Clifton
Department of Civil and Environmental Engineering
Road users fail to realize their role in congestion. This thesis aims to calculate
the appropriate charges required for users of I-495 – the Capital Beltway surrounding
Washington, D.C. – in order to fulfill their portion of congestion costs. By
developing a model from existing data that showcases traffic characteristics causing
congestion, the user charges necessary to cause drivers to realize the congestion costs
that their vehicles impose on the rest of the traffic stream are determined.
This study concludes that under typical traffic flow conditions for the Capital
Beltway, charges ranging from $0.03 to $0.08 per passenger car equivalent (PCE) per
mile during AM and PM peak periods cause drivers to realize their contribution to
congestion costs. These results are lower than the $0.08 to $0.50 per-mile charges
that previous research has estimated. As vehicles occupy various amounts of road
space, charges on a PCE basis are most equitable.
CONGESTION PRICING FOR THE CAPITAL BELTWAY
By
Joshua Lee Crunkleton
Thesis submitted to the Faculty of the Graduate School of the
University of Maryland, College Park, in partial fulfillment
of the requirements for the degree of
Master of Science
2008
Advisory Committee:
Dr. Kelly Clifton, Chair
Dr. Cinzia Cirillo
Dr. Stanley Young
© Copyright by
Joshua Lee Crunkleton
2008
ii
Dedication
To my grandfather, Joseph A. Crunkleton – this is for you, Pop.
iii
Acknowledgements
I would like to extend my sincere gratitude to the network of people who
helped make this thesis possible.
To my wonderful family and friends: thank you for your perpetual support. It
means more than you know. Without the insight, suggestions, and prior methodology
of Mr. Gabriel Roth, this study would have never existed. Through the guidance of
Dr. Kelly Clifton and my advisory committee – Dr. Cinzia Cirillo and Dr. Stanley
Young – this thesis was able to reach fruition. Last, but definitely not least, Tom
Schinkel, Randy Dittberner, and others with the Virginia Department of
Transportation (VDOT) deserve special thanks in terms of data collection and much-
appreciated feedback.
iv
Table of Contents
Dedication..................................................................................................................... ii
Acknowledgements...................................................................................................... iii
Table of Contents......................................................................................................... iv
List of Tables ............................................................................................................... vi
List of Figures ............................................................................................................. vii
Chapter 1: Introduction................................................................................................. 1
1.1 Background......................................................................................................... 1
1.2 Problem Statement .............................................................................................. 4
1.3 Research Objectives............................................................................................ 6
1.4 Document Organization...................................................................................... 6
Chapter 2: Literature Review........................................................................................ 8
2.1 Congestion Pricing Background/Theory............................................................. 8
2.1.1 Traffic Flow Theory................................................................................... 12
2.2 Implementation ................................................................................................. 14
2.3 Studies............................................................................................................... 17
2.4 Closing Remarks............................................................................................... 21
Chapter 3: Methods and Data ..................................................................................... 22
3.1 Introduction....................................................................................................... 22
3.2 Proposed Method .............................................................................................. 22
3.3 Methodology..................................................................................................... 26
3.3.1 Data............................................................................................................ 27
3.3.2 Speed Analysis........................................................................................... 30
3.3.3 Flow Analysis ............................................................................................ 33
3.3.4 Speed-Flow Relationship........................................................................... 36
3.3.5 Delay Calculations ..................................................................................... 39
3.3.6 Speed Frequency and Probability by Flow Range..................................... 42
3.3.7 Traffic Proportions..................................................................................... 44
3.4 Value of Time Estimation................................................................................. 45
3.5 Model Formulation ........................................................................................... 47
3.6 Assumptions...................................................................................................... 50
Chapter 4: System Evaluation..................................................................................... 52
4.1 Inputs................................................................................................................. 52
4.2 Outputs.............................................................................................................. 53
4.3 Model Demonstration ....................................................................................... 56
4.4 Evaluations........................................................................................................ 59
4.4.1 AM Peak .................................................................................................... 59
4.4.2 PM Peak..................................................................................................... 60
4.4.3 Discussion of Results................................................................................. 62
4.5 Sensitivity Analysis .......................................................................................... 62
v
4.5.1 Effect of Elasticity ..................................................................................... 63
4.5.2 Effect of Traffic Proportions...................................................................... 65
4.5.3 Effect of Value of Time and Vehicle Operating Costs.............................. 66
4.6 Summary........................................................................................................... 67
Chapter 5: Implementation ......................................................................................... 68
5.1 Overview........................................................................................................... 68
5.2 Congestion Pricing Strategy ............................................................................. 69
5.2.1 Hours of Operation .................................................................................... 69
5.2.2 Charges ...................................................................................................... 70
5.2.3 Goals .......................................................................................................... 71
5.2.4 Conditions.................................................................................................. 71
5.2.5 Payment Options........................................................................................ 72
5.2.6 Revenue Spending ..................................................................................... 72
5.2.7 Technology ................................................................................................ 73
5.2.7.1 Open Road Tolling.............................................................................. 73
5.2.7.2 Enforcement/Collection...................................................................... 74
5.2.8 Comparisons to Existing Systems.............................................................. 76
5.3 Equity Considerations....................................................................................... 77
5.4 Policy Limitations and Recommendations ....................................................... 79
5.5 Summary........................................................................................................... 82
Chapter 6: Financial Implications............................................................................... 84
6.1 Costs.................................................................................................................. 84
6.1.2 Scenarios Examined................................................................................... 84
6.1.2.1 Gantry Setup on I-495......................................................................... 86
6.1.2.2 Gantry Setup on Entrance and Exit Ramps......................................... 88
6.1.3 Chosen Scenario......................................................................................... 88
6.2 Revenue............................................................................................................. 89
6.3 Break-Even Points/Payoff Calculations............................................................ 91
6.4 Assumptions and Conclusions .......................................................................... 95
Chapter 7: Conclusions and Recommendations ......................................................... 97
7.1 Summary of Results.......................................................................................... 97
7.2 Conclusions....................................................................................................... 98
7.3 Recommendations for Future Research............................................................ 99
Appendix................................................................................................................... 102
References................................................................................................................. 115
vi
List of Tables
Table 2-1: Common Vehicle Charging Options ......................................................... 19
Table 3-1: Vehicle Classification PCE Factors .......................................................... 26
Table 3-2: I-495 Detector Location Information ........................................................ 28
Table 3-3: Delay Calculations Using HCM Equations............................................... 40
Table 3-4: Delay Calculations Using I-495 Regression Equation.............................. 41
Table 3-5: Peak Period Traffic Proportions ................................................................ 45
Table 3-6: FHWA HERS Model – Value of Time ..................................................... 46
Table 3-7: FHWA Vehicle Classifications – Value of Time...................................... 47
Table 4-1: Average AM Peak Hourly Flow for I-495 ................................................ 60
Table 4-2: AM Peak Hourly Congestion Charges for I-495....................................... 60
Table 4-3: AM Peak Traffic Composition Resulting from Congestion Pricing......... 60
Table 4-4: Average PM Peak Hourly Flow for I-495................................................. 61
Table 4-5: PM Peak Hourly Congestion Charges for I-495 ....................................... 61
Table 4-6: PM Peak Traffic Composition Resulting from Congestion Pricing.......... 62
Table 5-1: Hourly Congestion Charges for I-495....................................................... 70
Table 6-1: I-495 System Costs.................................................................................... 87
Table 6-2: Gantry Totals on Entrance and Exit Ramps .............................................. 88
Table 6-3: I-495 System 50-Year Cumulative Costs.................................................. 92
Table 6-4: I-495 System 50-Year Cumulative Revenue............................................. 93
vii
List of Figures
Figure 1-1: I-495 Region Map...................................................................................... 5
Figure 2-1: Theoretical Congestion Pricing Model .................................................... 12
Figure 2-2: Greenshield’s Model – Speed-Flow Relationship ................................... 13
Figure 2-3: Speed-Flow Curves for Basic Freeway Segments ................................... 14
Figure 3-1: Proposed Method ..................................................................................... 23
Figure 3-2: FHWA Vehicle Classifications................................................................ 25
Figure 3-3: I-495 Data Locations................................................................................ 28
Figure 3-4: Average Hourly Speed – Detector 190064 .............................................. 32
Figure 3-5: Average Hourly Speed by Year – Detector 190064 ................................ 32
Figure 3-6: Average Hourly Flow – Detector 190064................................................ 35
Figure 3-7: Average Hourly Flow by Year – Detector 190064.................................. 35
Figure 3-8: Hourly Volume-to-Capacity Ratio – Detector 190064............................ 36
Figure 3-9: I-495 Speed vs. Flow ............................................................................... 38
Figure 3-10: Speed Probability by Flow Range.......................................................... 43
Figure 3-11: Frequency by Flow Range ..................................................................... 44
Figure 4-1: Model Demonstration .............................................................................. 58
Figure 4-2: Sensitivity of Elasticity Values for Congestion Charges (AM Peak) ...... 64
Figure 4-3: Sensitivity of Elasticity Values for Congestion Charges (PM Peak)....... 64
Figure 5-1: Open Road Tolling Gantry....................................................................... 74
Figure 5-2: License Plate Recognition Software (London) ........................................ 75
Figure 5-3: Typical Gantry Camera Setup (Stockholm)............................................. 76
Figure 6-1: I-495 Gantry Setup (Direct) ..................................................................... 85
Figure 6-2: I-495 Gantry Setup (Entrance and Exit Ramps) ...................................... 85
Figure 6-3: Distribution of Trip Distances.................................................................. 90
Figure 6-4: Yearly I-495 System Payoff..................................................................... 94
Figure A-1: Average Hourly Speed – Detector 90138 ............................................. 102
Figure A-2: Average Hourly Speed by Year – Detector 90138................................ 102
Figure A-3: Average Hourly Flow – Detector 90138............................................... 103
Figure A-4: Average Hourly Flow by Year – Detector 90138 ................................. 103
Figure A-5: Hourly Volume-to-Capacity Ratio – Detector 90138 ........................... 104
Figure A-6: Average Hourly Speed – Detector 90202 ............................................. 104
Figure A-7: Average Hourly Speed by Year – Detector 90202................................ 105
Figure A-8: Average Hourly Flow – Detector 90202............................................... 105
Figure A-9: Average Hourly Flow by Year – Detector 90202 ................................. 106
Figure A-10: Hourly Volume-to-Capacity Ratio – Detector 90202 ......................... 106
Figure A-11: Average Hourly Speed – Detector 90275 ........................................... 107
Figure A-12: Average Hourly Speed by Year – Detector 90275.............................. 107
Figure A-13: Average Hourly Flow – Detector 90275............................................. 108
Figure A-14: Average Hourly Flow by Year – Detector 90275 ............................... 108
Figure A-15: Hourly Volume-to-Capacity Ratio – Detector 90275 ......................... 109
Figure A-16: Average Hourly Speed – Detector 190004 ......................................... 109
Figure A-17: Average Hourly Speed by Year – Detector 190004............................ 110
Figure A-18: Average Hourly Flow – Detector 190004........................................... 110
viii
Figure A-19: Average Hourly Flow by Year – Detector 190004 ............................. 111
Figure A-20: Hourly Volume-to-Capacity Ratio – Detector 190004 ....................... 111
Figure A-21: Average Hourly Speed – Detector 190057 ......................................... 112
Figure A-22: Average Hourly Speed by Year – Detector 190057............................ 112
Figure A-23: Average Hourly Flow – Detector 190057........................................... 113
Figure A-24: Average Hourly Flow by Year – Detector 190057 ............................. 113
Figure A-25: Hourly Volume-to-Capacity Ratio – Detector 190057 ....................... 114
1
Chapter 1: Introduction
1.1 Background
Traffic congestion is the topic of daily news broadcasts, water cooler horror
stories and mounting frustration nationwide. As slower driving speeds, increased
queuing and worsened travel reliability take center stage, we are left wondering what
led to this condition and, more importantly, where we can turn for relief.
Traffic congestion is a familiar problem around the world, especially for those
in urban areas. Congestion affects everyone and is usually defined in terms of excess
vehicles on a portion of roadway at a certain time that results in speeds that are slower
than free-flow conditions. At its most basic level, the consequence of failing to
effectively manage the capacity of a roadway system results in congestion. Road
capacity has not grown as quickly as road use – between 1990 and 2005, for example,
vehicle-miles traveled increased by 44 percent, while highway lane miles only
increased 4 percent (FHWA 2005, 1990). It goes without saying that if vehicle-miles
traveled have increased at a rate much greater than that of the construction of new
highway lanes, congestion has been a direct result.
Among professionals, metropolitan traffic congestion is often deemed the
single most critical issue we face today in the transportation industry – an idea that is
slowly being expressed by government figures across the country. According to the
Texas Transportation Institute’s 2007 Urban Mobility Report, congestion in
America’s urban areas is estimated to cost approximately $78 billion per year in
wasted fuel and delay costs (Schrank 2007). In addition to these commuting costs,
2
Americans see reductions in both quality of life (reduced air quality, less time with
family and friends, etc.) and productivity. Industry costs relating to the movement of
goods by truck are rising. Congestion in the United States is affecting more roads for
more people – it is estimated that the average weekday peak period trip takes almost
40 percent longer than an identical off-peak trip; this compares to only a 13 percent
increase in 1982 (Dodgson 2006). AM and PM peak periods have also expanded. In
larger cities, drivers spend the equivalent of almost 8 work days each year stuck in
traffic (Paniati 2006) and the situation is only escalating – the duration, extent and
intensity of congestion is increasing annually.
It must be noted in this discussion that congestion is not viewed only in
negative light – there are some who consider traffic congestion to be an inherent sign
of success. More or less, people want to be where opportunities are located and,
often, when the automobile is the dominant mode choice, congestion is a result.
While it is true that a different spin can be placed on any situation, the impact of
congestion on urban areas at the local, regional and national level cannot be refuted.
Effective, accessible transportation networks are key instruments in enhancing quality
of life and, for this reason, congestion issues need to be addressed instead of ignored.
Many analysts believe that efficient transportation depends more on managing
existing demand than on adding new supply (Victoria Transport Policy Institute
2007). The fact that vehicle-miles traveled are increasing at a rate far greater than
roadway construction is evidence that we cannot possibly build our way out of
congestion. Studies have shown that 60-90% of new road capacity is anticipated to
be filled within 5 years of construction and that induced demand (i.e. increased
3
traffic) comes with added capacity (Replogle 2007). This is not surprising, as traffic
attempts to flow along the path of least resistance – if new roads or lanes are
constructed, more people will choose to utilize these paths until the level of
congestion returns to its previous state, at which time users will choose alternate
routes.
Travel is mainly a derived demand, meaning it is usually demanded not for its
own sake but as a means of consuming some other good or service or to participate in
economic activities (i.e. work). Because the activities with which transportation is
associated vary over time, the demand for travel is not constant over time. For
example, many towns and cities experience traffic congestion during peak morning
and evening commuting times, and holiday routes experience seasonal congestion
(Button 2004). Traffic demand has to be adjusted in order to make any tangible
difference.
A key tool for such demand management is user charges (i.e. pricing). In
concept, the ideal form of pricing is congestion pricing, which charges highway users
based on their contribution to highway congestion, which means that the charges are
specific to both a place and a time. Transportation is over-consumed as a direct result
of inadequate pricing. If priced properly, fewer miles will be driven per vehicle and
less transportation will be consumed. Congestion pricing is currently the source of
heated political debate regarding potential congestion solutions and aims to adjust
traffic demand in order to alleviate traffic congestion qualms. Further, there is
consensus among economists that congestion pricing represents the single most viable
and sustainable approach to reducing traffic congestion. Free road use ultimately
4
leads to congestion, which is detrimental to all users. Congestion pricing is a way of
ensuring that those using valuable and congested road space make a financial
contribution, encourages the use of other transportation modes and is intended to
ensure that, for those who have (or choose) to use the roadways, trip times are faster
and more reliable.
Critics argue that users pay for their road usage through gas tax revenue –
generated from the levy imposed on the per-gallon sale of motor fuels at both the
state and federal levels. While this idea is not totally discredited, current gas tax
revenue figures are not enough to justify the amount of road usage that is occurring in
our society. In many states, gas taxes have not been raised since the early 1990s and
when they happen to be raised, it is generally not enough to keep up with inflation. In
fact, twenty-eight states have raised their gas tax rates since 1992, but only three have
raised it enough to keep pace with inflation (Brookings Institute 2003). The public
tends to unknowingly think that their annual contribution to the gas tax is much
greater than it actually is. On average, between $500 and $600 is paid per vehicle per
year towards the gas tax – less than most annual cable television bills.
1.2 Problem Statement
Most people fail to consider the adverse effect that their traveling places on
others – it is the aim of this thesis to address and explore this inadequacy. Many road
users have come to believe that they currently own the right to travel freely and
uninterrupted and that roadways are provided exclusively in order for them to achieve
this goal. Only by attaching a usage-based price to travel habits will drivers
understand, and curb, their role in congestion. Roadways should be viewed as a
5
commodity, in the same light as public utilities (telephone and electric services),
movie tickets or airline pricing, where the price of the services are usage-based and
increase as the demand increases over a certain threshold. Companies in these fields
have used peak period pricing for years – why shouldn’t transportation agencies do
the same?
In this region, traffic congestion is a daily concern on I-495, surrounding
Washington, D.C. Figure 1-1 shows this roadway in context of the region. Correct
user pricing for all lanes of I-495 would ultimately be beneficial to society. It is
important that the optimal price is determined, as incorrect pricing can have an
adverse effect on the economy and inadequate pricing will fail to curb demand.
Figure 1-1: I-495 Region Map
Source: MapQuest
6
1.3 Research Objectives
Due to the aforementioned fact that travelers fail to realize their role in
congestion, the goal of this thesis is to calculate the appropriate charges required for
users of I-495 – the Capital Beltway surrounding Washington, D.C. – in order to
fulfill their portion of congestion costs. The first objective is to develop a model from
existing data that showcases traffic characteristics that cause congestion, in addition
to the results of such interactions. Secondly, the charges necessary to cause vehicle
users to realize the congestion costs that their vehicles impose on the rest of the traffic
stream will be determined. This will be accomplished using prior methodology set
forth by Gabriel Roth and Olegario Villoria (2001). The contribution of this thesis
lies not in the method itself, but by examining the model in the context of a freeway
(I-495) instead of city streets. The third objective of this thesis is to examine the
potential financial implications (costs and revenue) that would be associated with the
proposed congestion pricing system on I-495.
1.4 Document Organization
This thesis is organized into seven chapters and one ancillary appendix. The
previous sections of Chapter 1 contained introductory information regarding traffic
congestion and described the purpose and scope of this work. Chapter 2 serves as a
review of existing literature applicable to this thesis, including information on
congestion/road pricing theory, implementation, and studies. Chapter 3 introduces
the proposed method behind this thesis and the entire model formulation is set forth in
detail – the methodology, from obtaining initial data through creating a functional
7
model, is also discussed. Drawing upon the aforementioned work by Roth and
Villoria, data from detector locations on the Capital Beltway, dating back to 2002, are
examined. Chapter 4 provides an evaluation of the proposed system, along with a
demonstration of the model. Based on this evaluation, optimal pricing ranging from
$0.03 to $0.08 per mile for each passenger car is obtained. Results of applicable
sensitivity analysis are also set forth in this chapter. Chapter 5 outlines potential
implementation of the proposed congestion pricing strategy and includes information
on current technology, equity considerations, and policy limitations. The financial
implications of such a system are provided in Chapter 6, with multiple setup scenarios
being examined and corresponding costs and revenue examined. The benefits and
challenges associated with the system are discussed and system payoff and break-
even points are addressed. Chapter 7 summarizes the results of the thesis and
addresses recommendations for areas of future research.
8
Chapter 2: Literature Review
In terms of summarizing existing literature applicable to this thesis, there are
numerous aspects of congestion/road pricing that are deserving of discussion. The
following sections touch on a varied selection of topics, including congestion pricing
theory, implementation, and studies.
2.1 Congestion Pricing Background/Theory
“An Inquiry into the Nature and Causes of the Wealth of Nations,” written by
Adam Smith in 1776, is widely considered to be the first modern work in the field of
economics. Included is the following passage which deduces that road users should
pay in accordance with their usage (i.e. the magnitude of the road damage they
cause):
“When the carriages which pass over a highway or a bridge (...) pay toll in
proportion to their weight or their tonnage, they pay for the maintenance of
those public works exactly in proportion to the wear and tear which they
occasion of them. It seems scarce possible to invent a more equitable way of
maintaining such works. This tax or toll too, though it is advanced by the
carrier, is finally paid by the consumer, to whom it must always be charged in
the price of the goods. (...) His payment is exactly in proportion to his gain. It
is in reality no more than a part of that gain which he is obliged to give up in
order to get the rest. It seems impossible to imagine a more equitable method
(Smith 307).”
Following Smith’s idea of charging road users appropriately leads to the idea of
congestion pricing. Lindsey and Verhoef (2000) contend that the insight for
congestion pricing comes from the observation that people tend to make socially
efficient choices when they are faced with all the social benefits and costs of their
actions. Congestion pricing is widely viewed by economists as the most efficient
9
means of alleviating traffic congestion, because it employs the price mechanism, with
all its advantages of clarity, universality, and efficiency.
Based on writings such as those by Lindsey and Verhoef (2000), an early
history of congestion pricing can be determined. In the 1920s, Arthur Cecil Pigou
and Frank Knight were the first advocates of theoretical congestion pricing. It was
William Vickrey in the 1960s, however, who wholeheartedly promoted congestion
pricing and was the most influential in making the case on both theoretical and
practical grounds. Vickrey identified the potential for road pricing to influence
travelers’ choice of route and travel mode and his work makes clear that true
congestion pricing entails setting tolls that match the severity of congestion, which
requires that tolls vary according to time, location, type of vehicle, and current
circumstances. Additionally, Vickrey was the first to put forward an operational plan
for road pricing in a specific city (Washington, D.C.) and was steadfast in promoting
the idea of congestion pricing to non-economists. Since this time, several strategies
for the implementation of congestion pricing have emerged.
The four main types of congestion pricing strategies are as follows (FHWA
2001):
• Variably priced / managed lanes – involve variable tolls on separated
lanes within a highway, such as Express Toll Lanes or High Occupancy or
Toll (HOT) Lanes. HOT lanes allow low-occupancy vehicles to pay a
variable toll to use the lanes, while high-occupancy vehicles are allowed to
use the lanes for free.
10
• Variable tolls on entire roadways or smaller sections – both on toll roads
and bridges, as well as on existing toll-free facilities during rush hours.
This strategy raises existing tolls in peak periods and possibly reduces
them in off-peak periods.
• Cordon charges – either variable or fixed charges to drive within or into a
congested area within a city
• Area-wide charges – per-mile charges on all roads within an area that may
vary by level of congestion
In all of these cases, to truly merit the title of congestion pricing, an implementation
strategy must contain a time-of-day element due to the fact that usage varies with
peak periods. This thesis provides area-wide pricing for an entire facility.
Historically, it is possible to identify at least three periods in which policy
measures to curb congestion have emerged (Salomon and Mokhtarian 1997).
Through the mid-1960s, the principal tool was expansion of infrastructure (i.e.
building more roads to accommodate demand). In the 1970s, there was a shift toward
improved management of the available infrastructure – Transportation Systems
Management (TSM). In the early 1980s, there was an increasing realization that
altering human behavior was the next necessary step. This led to the development
and implementation of Transportation Demand Management (TDM) strategies,
involving a wide range of policies to reduce dependence on the single-occupant
automobile. The first two periods can be characterized as emphasizing supply-side
measures, while the third is designed to affect demand. Congestion pricing is a
demand-side measure, as it specifically used to manage demand. Salomon and
11
Mokhtarian (1997) also note that with a growing concern for environmental costs, the
focus on congestion mitigation is also growing as congestion traffic produces more
air pollutants than smooth traffic flow, involves more noise production, and consumes
more energy. Thus, both the individual and society coincide in their perception of the
presence of a problem but not so, however, in assessing the means for solution.
Additionally, trends over the last two decades have demonstrated that little is
accomplished by the variety of measures devised to reduce congestion.
Figure 2-1 shows a theoretical congestion pricing model, as exhibited by
McMullen (1993). The uncongested road pricing situation is shown as demand curve
D
1
, the distance OA represents vehicle costs such as fuel, oil, vehicle wear and tear,
and the driver’s value of time, and the costs incurred by the road operation agency
(road maintenance, policing, etc.) are shown as the distance AB. The horizontal line
BH represents both average total cost (AC) and marginal cost (MC) up to road
volume C – the roadway is not congested between O and C and, therefore, each
additional vehicle trip incurs the same marginal cost as the previous one.
When demand is at D
1
, the optimal user charge is AB, which results in an
optimal traffic level of Q
0
. After encountering congestion at traffic volume C,
additional vehicle trip imposes a cost (i.e. increased travel time) on other vehicles –
for this reason, the average total and marginal costs diverge at greater volumes. At
demand level D
2
, the roadway is congested and the optimal user charge would be
GD+DE, where DE is the congestion fee.
This theoretical model infers that the main reason for excessive congestion is
the fact that users are not required to pay the full social costs of driving during peak
12
hours (McMullen 1993). This model is simplistic in that it ignores the numerous
different vehicle types that utilize the same road space – this would suggest higher
peak hour congest fees for trucks and other large vehicles.
Figure 2-1: Theoretical Congestion Pricing Model
Lastly, elasticity is a term often used in the economics world, but likely to be
misunderstood in the transportation realm. In simplest terms, elasticity refers to the
amount of change in a dependent variable as a result of changes in an independent
variable. For the purpose of this study, changes in road use as a result of increased
costs (i.e. charging) are the focus.
2.1.1 Traffic Flow Theory
While discussing congestion pricing theory, it is important to mention some
aspects of traffic flow theory that relate to this thesis. In regards to traffic flow
13
theory, the topic most closely related to this specific study is the relationship between
traffic flow and traffic speed. Greenshield (1935) developed a linear model of speed
and density, which can be interpreted into the speed-flow relationship shown in
Figure 2-2.
Figure 2-2: Greenshield’s Model – Speed-Flow Relationship
The Highway Capacity Manual (Transportation Research Board 2000) does
not portray the region of unstable/uncertain flow where the above curve wraps back
around itself. This unpredictable area is referred to as hypercongestion (shown in
Figure 2-2) and results in a loss of capacity due to the breakdown of traffic flow. The
HCM speed-flow curves for basic freeway segments are exhibited as Figure 2-3.
When comparing Greenshield’s model to the HCM representation, a few differences
are evident. The area of unstable flow (hypercongestion) is removed and due to the
fact that speeds remain relatively constant at low volumes, the HCM shows the top of
the curve as perfectly horizontal before the effects of higher flow levels begin to
reduce speeds. In sum, the current HCM speed-flow relationship can be broken down
into two sections: an unchanging constant portion at low flows (represented by the
horizontal line) and a slowly downward-curving portion at higher flows.
14
Figure 2-3: Speed-Flow Curves for Basic Freeway Segments
Source: HCM 2000 – Exhibit 23-3
2.2 Implementation
Congestion pricing is more prominent abroad than in the United States.
Systems of varying technological levels have been operating since 1975 in Singapore
and automated systems have been operating full-time in London and Stockholm since
2003 and 2007, respectively, in addition to various other examples in other areas.
In London, a charge is collected when a vehicle enters the central city area on
weekdays between 7:00AM and 6:00PM – no per-mile charges are assessed. The
standard daily charge is £8 ($16 US) if paid by midnight on the day of travel. The
charge is increased to £10 ($20 US) if paid by midnight the following day. The initial
charge for the strategy was £5 ($10 US), but increased to £8 ($16 US) in July 2005
(Transport for London). Based on results provided by Mayor Ken Livingstone
(2007), after London put its initial congestion charging zone into place, it led to an
immediate drop of 70,000 cars per day in the affected zone. Traffic congestion fell
by almost 20 percent and emissions of the greenhouse gas carbon dioxide were cut by
15
more than 15 percent. The retail sector in the zone has seen increases in sales that
have significantly exceeded the national average. People are still traveling in London
– they are simply doing so in more efficient and less polluting ways. There has been
a marked shift away from cars and into public transport and environmentally friendly
modes of travel. There has been a 4 percent modal shift into use of public transport
from private cars since 2000. Simultaneously, the number of bicycle journeys on
London's major roads has risen by 83 percent, to almost half a million per day.
London's pricing scheme has been estimated to produce savings of about 0.7 minutes
per kilometer, or 1.13 minutes per mile (Transport for London 2007).
In Stockholm, a congestion charge is imposed on Swedish registered vehicles
driving into and out of the Stockholm inner city zone on weekdays between 6:30AM
and 6:29PM and each passage into or out of the inner city zone costs SEK 10, 15 or
20 ($1.58 – $3.15 US), depending on the time of day. The accumulated passages
made by any vehicle during a particular day are aggregated and the maximum amount
charged per day and vehicle is SEK 60 ($9.45 US). As the Stockholm scheme was
only implemented in mid-2007, not much actual data has become available.
Therefore, the effectiveness of the scheme has been based on the Stockholm trial
period that occurred before actual implementation commenced. As a result of
congestion charging in Stockholm (Stockholmsförsöket 2006):
• Motor traffic decreased 22% over 24 hours
• Access improved and travel times fell as a result of the reduction in motor
traffic
16
• Traffic reductions lead to less environmental impact and better health, as
emissions from motor vehicles account for a large proportion of the total
pollution in the city
• Public transport usage increased
• Road safety improved as a result of reduced traffic
Focus will shift now to implementations in the United States, as the political climate
for congestion pricing differs greatly from the aforementioned regions.
The USDOT has entered into Urban Partnership Agreements with five cities,
in accordance with their commitment to, among other things, implement broad
congestion pricing. The five cities are: Miami, Minneapolis/St. Paul, New York City,
San Francisco, and Seattle (Lake Washington). These agreements represent the
future of congestion pricing in the United States, as future strategies will be based on
the actual implementation and success of these proposed systems. At the time of this
study, much debate is currently centered on the proposed congestion pricing strategy
in New York City that has recently been voted down.
While the Washington, D.C. area is not one of the USDOT pilot areas, the
first of a network of HOT lanes in Virginia could potentially open in just two years,
and the variably-tolled intercounty connector in Maryland is scheduled for
completion by 2012. Additionally, the state of Oregon is in the process of developing
GPS-based distance measurements to replace the fuel taxes it now uses to pay for
road usage. At the onset, Oregon would not require all vehicles to have the GPS
system – road users would initially have the choice of paying either fuel taxes or
mileage-based charges.
17
Sullivan (2003) notes that in the mid-1970s, the federal government offered
funds to U.S. cities willing to try a pricing scheme to reduce congestion. Although
some implementation studies that produced findings favorable to the concept were
conducted, all of these early initiatives failed, largely due to local community
opposition. In 1991, the U.S. Congress passed a surface transportation act called the
“Intermodal Surface Transportation Efficiency Act (ISTEA).” This act created the
U.S. Congestion Pricing Pilot program, which directed the USDOT to help develop
and fund congestion pricing pilot projects. In 1998, this program was renamed the
“Value Pricing Pilot Program.”
A common feature of value pricing projects is that pricing (i.e. the toll) varies
with the time of day, in an effort to encourage traffic to shift away from peak periods.
Tolls on value pricing facilities are generally determined by the responsible operating
authorities, which include private companies, state DOTs, and regional government
agencies – toll-setting by government agencies involves due process, including public
comment. At the national level, it was recognized that using the rather academic title
“Congestion Pricing” elicited negative emotions. Switching to “Value Pricing”
provided a more positive way to identify the same notion – additionally, toll
collection technologies are usually identified using positive labels, such as “Fastrak,”
“QuickRide,” or “E-ZPass (Sullivan).”
2.3 Studies
Many studies have taken place involving the numerous facets of congestion
and congestion pricing. Salomon and Mokhtarian (1997) identified and classified
18
user responses relating to congestion, which showcase the various options that
travelers have in regards to potential congestion pricing:
1) Accommodate congestion costs/do nothing
2) Reduce congestion costs
3) Change departure time
4) Change route
5) Buy time
6) Invest in productivity-enhancing technology at home
7) Adopt flextime
8) Adopt compressed work week
9) Change mode of travel
10) Telecommute from home
11) Telecommute from a telecenter
12) Change workplace
13) Relocate home
14) Change from full-time to part-time work
15) Start a home-based business
16) Quit work
A system of “first-best” pricing sets tolls to completely match the external
costs generated by each traveler. This is accomplished by having variable charges
that change in real-time with existing conditions. Although useful in a theoretical
sense, “first-best” pricing has limited practicality. “Second-best” congestion pricing
is more realistic and denotes a more static strategy where drivers are aware of
19
applicable charges in advance. This includes the use of step-tolls instead of smoothly
time-varying tolls or tolling according to a fixed daily schedule rather than day-
specific traffic conditions (Lindsey and Verhoef 2000). Table 2-1 ranks common
vehicle charging options in terms of how well they represent the costs imposed by a
particular vehicle trip (Victoria Transport Policy Institute 2007).
Table 2-1: Common Vehicle Charging Options
Rank General Category Examples
Best
Time- and location-specific
road and parking pricing
Variable road pricing, location-specific parking
management, location-specific emission charges
Second
Best
Mileage-pricing
Weight-distance charges, mileage-based vehicle
insurance, prorated motor vehicle excise tax,
mileage based emission charges
Third Best Fuel charges
Increase fuel tax, apply general sales tax to fuel,
pay-at-the-pump insurance, carbon tax, increase
hazardous substance tax
Bad Fixed vehicle charges
Current motor vehicle excise tax, vehicle
purchase and ownership fees
Worst
External costs (not charged
to motorists)
General taxes paying for roads and traffic
services, parking subsidies, uncompensated
external costs
As congestion pricing is quite controversial, Jones (1998) outlined potential
reasons for opposing congestion pricing:
• Drivers find it difficult to accept the idea of being charged for something
they wish to avoid (congestion) and also feel that congestion is not their
fault, but rather something that is imposed on them by others
• Road pricing is not needed, either because congestion is not bad enough or
because other measures are superior
• Pricing will not get people out of their cars
• The technology will not work
• Privacy concerns
• Diversion of traffic outside the charged area
20
• Road pricing is just another form of taxation
• Perceived unfairness
Two critical questions generated by the idea of congestion pricing focus on
the optimal user charge amount and the effectiveness of the system. In terms of
actual per-mile charge estimates, McMullen (1993) shares that previous research has
estimated that, in 2007 amounts, efficient peak-period tolls in the range of $0.08 to
$0.50 per mile are appropriate. The effectiveness question is answered by the
aforementioned idea of elasticity. Based on studies by Oum et al. (1992), changes in
road use as a result of increased costs are consistent with elasticities of -0.5 or less.
Additionally, results from strategies in locations such as Stockholm are more
consistent with an approximate elasticity of -0.2 (Victoria Transport Policy Institute
2007). A negative elasticity indicates that an increase in road pricing is associated
with a decrease in demand/usage. Unfortunately, this value cannot be determined in
advance of actual congestion pricing imposition. For this thesis specifically, the
elasticity estimate shows how well a pricing strategy actually works. As an example,
a price elasticity of -0.2 means that for every 10% increase in road user charges, a 2%
reduction in road usage occurs.
Sullivan (2003) concludes that forward momentum has been established for
innovative road pricing, but future progress toward more widespread use of
congestion-based pricing is likely to take advantage of local opportunities which
present themselves, and will proceed cautiously. Considerable emphasis will be
placed on marketing strategies in order to win consumer acceptance. By preventing
the loss of vehicle throughput that results from a breakdown of traffic flow,
21
congestion pricing maximizes the return on the public’s investment in highway
facilities. Society as a whole also benefits by reducing fuel consumption and vehicle
emissions and allowing more efficient land use decisions (FWHA 2001).
2.4 Closing Remarks
The provided information in this chapter helps to set the framework for this
Capital Beltway study. Area-wide congestion pricing has been shown as a successful
strategy in various parts of the world, but few implementations are operating or being
discussed in the United States. This thesis fills a practical gap in the Washington,
D.C. area – especially as congestion pricing is being considered on the horizon. As
there is limited experience to draw upon, this study attempts to provide meaningful
information.
22
Chapter 3: Methods and Data
3.1 Introduction
This study proposes a method to calculate the appropriate charges required for
users of the Capital Beltway in order to fulfill their portion of congestion costs and is
based upon previous methodology developed by Roth and Villoria (2001). These
charges are calculated through the use of an optimization model. The method is
based primarily on the relationship between traffic speed and traffic flow, from which
delay calculations are determined.
3.2 Proposed Method
This study aims to determine the charge necessary to cause drivers to realize
their congestion costs. The proposed method is illustrated, in the form of a flowchart,
in Figure 3-1 and each step is discussed in-depth.
The first step in this method is to define the study area. I-495, the Capital
Beltway that surrounds Washington, D.C., is an ideal candidate due to the fact that it
exhibits recurring AM and PM peak period congestion problems. This area was
shown in context of the region in Figure 1-1. As the only circumferential roadway in
the area, many key routes connect to the Capital Beltway along its 64 mile length,
providing a critical highway link to other transportation services, including three
regional airports, transit and rail facilities, and port terminals. Due to this
connectivity with other transportation facilities in the area, traffic congestion on I-495
has severe effects on regional mobility, even though it generally consists of 4-lane
23
travel in both directions. In accordance with other locations that have implemented
congestion pricing, the Washington, D.C. area exhibits severe traffic congestion. Key
interchanges are consistently acknowledged as areas of overwhelming congestion and
even though some travel alternatives exist, the automobile is the dominant mode.
1. Choose study area
2. Examine traffic congestion
using a speed-flow relationship
3. Convert congestion
data into monetary amounts
4. Determine basis
for calculating charges
5. Create an
optimization model
6. Analyze financial
implications
Figure 3-1: Proposed Method
Secondly, traffic congestion is examined using the relationship between traffic
flow and traffic speed – this approach is utilized within the Highway Capacity
Manual (Transportation Research Board 2000). In a strictly hypothetical sense, as
flow increases towards roadway capacity, speed should decrease accordingly. The
24
relationship between traffic flow and traffic speed enables the calculation of delay
imposed by users on other vehicles on the roadway. Specific details on developing
and expanding on this speed-flow relationship will be discussed as part of the model
formation later in this chapter.
Next, any applicable congestion data, such as delay imposed, should be
converted into dollar values. This is done by estimating user value of time and
operating costs for the vehicles on the Capital Beltway.
The fourth step in this method is to determine the basis for calculating user
charges. As different vehicles consume varying amounts of road space, it would be
unjust to impose equal charges to every user. Using the Federal Highway
Administration’s (FHWA) vehicle classification system (shown below as Figure 3-2)
and average vehicle lengths, estimates of passenger car equivalents (PCE) for each
vehicle classification can be determined. This table of information is included as
Table 3-1 and allows for extrapolation after calculating optimal charges per PCE.
25
Figure 3-2: FHWA Vehicle Classifications (FHWA 2001)
26
Table 3-1: Vehicle Classification PCE Factors
Vehicle
Class
Vehicle Description
Average
Length (feet)
PCE
Factor
1 Motorcycle 6 0.38
2 Passenger Cars 16 1.00
3 Other Two-Axle, Four-Tire single Unit Vehicles 18 1.13
4 Buses 38 2.38
5 Two-Axle, Six-Tire, Single-Unit Trucks 26 1.63
6 Three-Axle Single-Unit Trucks 25 1.56
7 Four or More Axle Single-Unit Trucks 32 2.00
8 Four or Fewer Axle Single-Trailer Trucks 44 2.75
9 Five-Axle Single-Trailer Trucks 64 4.00
10 Six or More Axle Single-Trailer Trucks 63 3.94
11 Five or Fewer Axle Multi-Trailer Trucks 68 4.25
12 Six-Axle Multi-Trailer Trucks 73 4.56
13 Seven or More Axle Multi-Trailer Trucks 69 4.31
The fifth step in this method is to create an optimization model. For the
purposes of this study, the model will be created using the Solver tool in Microsoft
Excel. In a nutshell, Excel Solver generates specific values (i.e. charges) to optimize
a certain objective. In the case of this study, the optimized variable is the dollar
amount that users of I-495 should be charged per-mile.
Lastly, the financial implications of user-based charging on the Capital
Beltway will be analyzed. Estimates of potential costs and revenue will be examined
in order to provide information on this feasibility aspect.
3.3 Methodology
This section focuses on formulating the model used in this thesis. The
following main points will be addressed:
• The process of obtaining usable data for this study
• Preparing the data for speed and flow analysis
27
• Using the relationship between traffic speed and traffic flow to perform
delay calculations
• Applying relevant user value of time and vehicle operating cost
estimations to setup the model to optimize congestion charges for the
Capital Beltway
3.3.1 Data
The first stage of this thesis involved obtaining I-495 detector data for use in
the study. When contacting the Maryland State Highway Administration (MD SHA)
and the Virginia Department of Transportation (VDOT), the following main
components of desired data were expressed:
• Detector locations on I-495 in Maryland or Virginia
• Permanent detection stations reporting data in intervals less than or equal
to one hour for all hours of the day
• Volume count information (both total counts and counts broken down by
FHWA vehicle classification)
• Vehicle speed information
• Data archived for multiple years
In-road detectors (i.e. loop detectors) are the most commonly used technology
for collecting traffic data and agencies often have permanent detection locations
reporting data. Temporary tubes are sometimes used for specific purposes, but in
general, agencies rely on loop detection for their traffic data. To this extent, Tom
Schinkel of the VDOT Mobility Management Division was able to provide study data
from six permanent detection locations within the Virginia section of I-495. As these
28
detection locations are split directionally, they encompass three general locations.
The following table provides general detector location details and these locations are
also shown graphically in Figure 3-3.
Table 3-2: I-495 Detector Location Information
Detector ID Direction Start Location End Location
90202 North Eisenhower Ave Connector SR 241/Telegraph Rd
190004 South Eisenhower Ave Connector SR 241/Telegraph Rd
90138 North I-95/I-395 29-620/Braddock Rd
190057 South I-95/I-395 29-620/Braddock Rd
90275 North Dulles Access Rd; SR 267/Dulles Toll Rd SR 193/Georgetown Pike
190064 South Dulles Access Rd; SR 267/Dulles Toll Rd SR 193/Georgetown Pike
It should be noted that the detectors are physically located between the given
landmarks, which are easier to decipher while looking at a map than the actual
latitude and longitude coordinates.
Figure 3-3: I-495 Data Locations
Source: Google Maps
29
For this study, it is assumed that the available VDOT detector data is
representative of the entire Virginia portion of I-495. The data was collected on a
per-lane basis and in 15 minute intervals, and was provided in aggregate form with all
lanes combined by direction and data based hourly.
Unfortunately, MD SHA was unable to provide data for this study, as no
functioning permanent detection stations that collected all of the required information
were available. This was based on the fact that this data was not available from any
of the five automatic traffic recorder (ATR) stations located on the Maryland section
of I-495. As such, the data provided by VDOT was used as representative for all of
the Capital Beltway.
The hourly speed and volume data, ranging from as far back as 2002, were
cleansed and laid out in spreadsheet form by detector ID and year in order to provide
consistency for analysis purposes. Due to the fact that detection equipment
sometimes reports false data (i.e. zero volumes, exorbitant speeds, etc.), “cleansing”
of such data is required. This process, in its most basic form, consisted of the
following:
• Separate and organize data from all detectors into individual years
• Determine the day of week that each data point was collected and delete
all weekend data
• Delete any speed and volume outlier data (significant errors in data
collection)
• Assign an hour code (0-23) to each data point
30
• Spreadsheets were setup to contain Detector ID, Hour Code, Volume By
Vehicle Classifications (split from 1-13), and Average Speed For All
Vehicles on each row
As expected with any research, data limitations exist in this study. Since there
was no Maryland data available for use, Virginia data is assumed representative
across the entire Capital Beltway. Although this may not be an entirely valid
assumption, it can be used for information purposes and to calculate pricing for the
Virginia portion of I-495. Also of note, some of the detectors, whether it is based on
their location or specific direction, don’t provide particularly exciting data at all
times. Whether that means certain detectors show consistent speeds throughout the
day or only one pronounced peak period, all data is considered meaningful. Not all
locations on I-495 experience severe AM and PM peak period congestion and this
data tends to make the model more representative instead of over-inflating it to the
side of congestion. If only data from congested locations were used, it would be
inferred that traffic is uniform along the entire Capital Beltway, which is not the case.
3.3.2 Speed Analysis
The provided speed data were broken down by each vehicle classification.
Using weighted averages based on the number of vehicles in each associated
category, average hourly speeds for the entire traffic stream were calculated. For
each of the 24 hours in a day, average speed tables were created for each detector.
With data existing from previous years, the hourly speeds were overlaid to view
yearly changes. An example of these hourly speed plots is shown as Figure 3-4 and
the additional plots from the remaining detectors can be viewed in the Appendix.
31
Based on this plot, two peak periods are evident – one in the morning and one in the
evening. The apparent extent of the evening peak spreads across more hours than the
morning peak. For this thesis, peak periods are visually defined based on the hourly
speed plots from the detectors. From Figure 3-4, these peaks are estimated to occur
from 6AM-10AM and 2PM-7PM.
Speed data can also provide insight from another perspective. By plotting
average hourly speed by year, periods of decreased speed become easily visible. An
example of these hourly speed plots is shown as Figure 3-5 and the additional plots
from the remaining detectors can be viewed in the Appendix. Based on this plot,
decreases in speed are evident from 8AM-10AM and from 3PM-7PM. Coupled with
the previous plot, this information paints a clear picture of peak periods at each
detector location.
For the purpose of this thesis, free-flow speed is said to equal the uncongested
traffic speed – as determined by the average of the 85th percentile speeds for each
detector between 1AM and 4AM for all of 2007. Free-flow speed is therefore found
to equal 63.8 miles per hour (mph) on the Capital Beltway, even though the posted
speed limit is 55 mph.
32
Avg. Hourly Speed - Link 190064
0.00
10.00
20.00
30.00
40.00
50.00
60.00
70.00
80.00
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
Hour of Day
S
p
e
e
d
(
m
p
h
)
2003
2004
2005
2006
2007
Figure 3-4: Average Hourly Speed – Detector 190064
Avg. Hourly Speed by Year - Link 190064
0.00
10.00
20.00
30.00
40.00
50.00
60.00
70.00
80.00
2003 2004 2005 2006 2007
Year
S
p
e
e
d
(
m
p
h
)
12AM 1AM 2AM 3AM 4AM 5AM 6AM 7AM 8AM 9AM 10AM 11AM
12PM 1PM 2PM 3PM 4PM 5PM 6PM 7PM 8PM 9PM 10PM 11PM
Figure 3-5: Average Hourly Speed by Year – Detector 190064
33
3.3.3 Flow Analysis
In a similar fashion to the speed analysis, flow analysis was conducted on the
data. The provided volume data were broken down by each vehicle classification and
multiplied by corresponding PCE factors to represent hourly PCE flow. For each of
the 24 hours in a day, average flow tables were created for each detector. With data
existing from previous years, the hourly flows were overlaid to view yearly changes.
An example of these hourly speed plots is shown as Figure 3-6 and the additional
plots from the remaining detectors can be viewed in the Appendix. As with the
hourly speed plot presented in the previous section, two peak periods are seen – one
in the morning and one in the evening. The apparent extent of the evening peak once
again spreads across more hours than the morning peak – in this case, about two extra
hours.
Across multiple years, changes in flow are evident. This is expected, as traffic
volumes generally increase every year. In addition to higher flow rates, expanded
peak periods start to occur, as traffic shifts to the hours before and after the peak
periods of previous years. The flow data can also be visualized by plotting average
hourly flow by year, making periods of increased flow more visible. An example of
these hourly flow plots is shown as Figure 3-7 and the additional plots from the
remaining detectors can be viewed in the Appendix. Based on this plot, the greatest
flow occurs between the hours of 6AM-11AM and from 12PM-8PM – these are not
necessarily the true peak periods at this location. These are just the times of day
when there is an increase of flow at off-peak hours. Coupled with the previous plot
34
and the speed plots from the previous section, this information provides insight to
peak periods at each detector location.
From the speed analysis, it was determined that the average uncongested
(free-flow) speed on I-495 was 63.8 mph. Using the 2000 edition of the Highway
Capacity Manual and this given free-flow speed, the per-lane capacity of I-495 is
determined to be 2,350 passenger cars per lane per hour (pc/ln/hr). For the purposes
of this thesis, data will be examined on a per-lane basis instead of in terms of the total
facility (i.e. four lanes). By limiting the study to a per-lane basis, uniform traffic
activity across each lane is assumed, even though this is probably not the case on I-
495.
Volume-to-capacity (v/c) ratio is a common statistic used by traffic engineers
to gauge the health or level of service of a certain roadway. Using the flow data and
the capacity figure from the Highway Capacity Manual, the hourly v/c ratio can be
plotted for each detector, with data from previous years included, as well. Volume-
to-capacity ratio plots are another tool used to view peak period conditions on the
roadway. An example of a v/c ratio plot is shown below, with the additional plots
from the remaining detectors available in the Appendix. Based on this plot, the AM
and PM peaks are once again evident – the plot mimics the previous average hourly
flow plot, as the observed flow is an input, along with the capacity, which stays
constant.
35
Avg. Hourly PCE Flow - Link 190064
0
500
1000
1500
2000
2500
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
Hour of Day
P
C
E
F
l
o
w
2002
2003
2004
2005
2006
2007
Figure 3-6: Average Hourly Flow – Detector 190064
Avg. Hourly PCE Flow by Year - Link 190064
0
500
1000
1500
2000
2500
2002 2003 2004 2005 2006 2007
Year
P
C
E
F
l
o
w
12AM 1AM 2AM 3AM 4AM 5AM 6AM 7AM 8AM 9AM 10AM 11AM
12PM 1PM 2PM 3PM 4PM 5PM 6PM 7PM 8PM 9PM 10PM 11PM
Figure 3-7: Average Hourly Flow by Year – Detector 190064
36
v/c Ratio - Link 190064
I-495 Capacity = 2,350 pc/ln/hr
0.00
0.10
0.20
0.30
0.40
0.50
0.60
0.70
0.80
0.90
1.00
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
Hour of Day
v
/
c
R
a
t
i
o
2002
2003
2004
2005
2006
2007
Figure 3-8: Hourly Volume-to-Capacity Ratio – Detector 190064
3.3.4 Speed-Flow Relationship
As the speed and flow data have been looked at separately up to this point,
they are now combined in order to develop the relationship that is the backbone of
this study. Traffic speed and traffic flow data is plotted to see the effect that flow has
on speed – hypothetically, speed decreases as flow increases. While attempting to
approximate the data with a straightforward linear relationship would be easy, it is far
too simplistic and not realistic for this complex phenomenon.
37
The Highway Capacity Manual provides equations that determine speeds
based on a given free-flow speed (FFS) and available flow data (flow rate v
p
). As the
free-flow speed was calculated to be 63.8 mph for I-495, the following equations, as
set forth in Exhibit 23-3 of the Highway Capacity Manual, will be utilized:
For 55 ? FFS ? 70 and for flow rate (v
p
)
(3400 – 30FFS) < v
p
? (1700 + 10FFS),
( )
2.6
1 30 3400
7 340
9 40 1700
p v FFS
S FFS FFS
FFS
(
+ ? | |
= ? ?
(
|
?
\ ¹
(
¸ ¸
Eq. 1
For 55 ? FFS ? 75 and v
p
? (3400 – 30FFS),
S FFS = Eq. 2
The HCM equations are broken down into two sections, due to the fact that at
low volumes, speed remains fairly constant and then starts to decrease at higher flow
rates. As such, the current HCM speed-flow relationship is shown as an unchanging
constant portion at low flows and a slowly downward-curving portion at higher flows.
Based on the above equations, the ranges are 1,486 pc/ln/hr to 2,338 pc/ln/hr for the
first equation and less than 1,486 pc/ln/hr for the second. By entering flow values
from I-495 data and obtaining the corresponding speed values, a speed-flow plot can
be created to show the effect that flow has on speed.
By plotting the HCM equations over the I-495 data points, along with the
fourth-order polynomial regression equation calculated from the data, the speed-flow
relationship is visualized. Within the regression equation, the constant is equal to the
free-flow (uncongested) speed that was determined earlier. The lane capacity of I-
495 (2,350 pc/ln/hr) is shown as the vertical dashed line in the plot.
38
I-495 Speed vs. Flow
y = -2E-12x
4
+ 6E-09x
3
- 7E-06x
2
+ 0.0021x + 63.8
0.00
10.00
20.00
30.00
40.00
50.00
60.00
70.00
80.00
0 250 500 750 1000 1250 1500 1750 2000 2250 2500
Flow (PCE/hour/lane)
S
p
e
e
d
(
m
p
h
)
I-495 Data HCM Calculation Capacity I-495 Data Trendline
Figure 3-9: I-495 Speed vs. Flow
While the HCM calculations may look approximately appropriate to the data,
the regression equation from the I-495 data decreases at a greater rate. The HCM
calculations are based on national averages and I-495 data could vary for a number of
reasons (year built, geometry, etc.). It goes without saying that the general HCM
calculations do not represent I-495 in this case, but would be quite helpful for
situations where actual data for calculations is not available. As discussed in chapter
2, the HCM does not address hypercongestion – the area of unstable flow that occurs
as flow reaches capacity and the curve turns inward on itself. This area is the not
within the scope of this thesis and will not be discussed. While this may seem to be a
limitation, congestion pricing can improve traffic flow to the point where this
scenario does not occur.
39
3.3.5 Delay Calculations
Based on the speed-flow relationship equation derived from the data, the
amount of delay imposed on the traffic stream by an additional PCE/lane/hour (in
minutes per mile) can be calculated. These calculations can be compared to those
generated using the equations from the HCM in order to showcase differences and re-
validate the knowledge that the HCM equations are not appropriate as a
generalization in the case where actual data is present to examine. The delay
calculation process is as follows:
• For possible traffic flows, calculate the corresponding travel speed
• Calculate time to travel one mile at given flow (based on speed)
• Calculate time to travel one mile at one less PCE/lane/hour (based on
speed)
• Multiply the total flow by the difference in the previous two calculations
to obtain the total delay imposed on traffic by an additional PCE/lane/hour
40
Table 3-3: Delay Calculations Using HCM Equations
Traffic Flow
(PCE/lane/hour)
Travel
Speed
(mph)
Time to
travel one
mile at given
volume
(min./mile)
Time to travel one
mile at one less
PCE/lane/hour
(min./mile)
Delay imposed on traffic
stream by an additional
PCE/lane/hour (min./mile)
50 63.80 0.94044 0.94044 0.00000
100 63.80 0.94044 0.94044 0.00000
150 63.80 0.94044 0.94044 0.00000
200 63.80 0.94044 0.94044 0.00000
250 63.80 0.94044 0.94044 0.00000
300 63.80 0.94044 0.94044 0.00000
350 63.80 0.94044 0.94044 0.00000
400 63.80 0.94044 0.94044 0.00000
450 63.80 0.94044 0.94044 0.00000
500 63.80 0.94044 0.94044 0.00000
550 63.80 0.94044 0.94044 0.00000
600 63.80 0.94044 0.94044 0.00000
650 63.80 0.94044 0.94044 0.00000
700 63.80 0.94044 0.94044 0.00000
750 63.80 0.94044 0.94044 0.00000
800 63.80 0.94044 0.94044 0.00000
850 63.80 0.94044 0.94044 0.00000
900 63.80 0.94044 0.94044 0.00000
950 63.80 0.94044 0.94044 0.00000
1000 63.80 0.94044 0.94044 0.00000
1050 63.80 0.94044 0.94044 0.00000
1100 63.80 0.94044 0.94044 0.00000
1150 63.80 0.94044 0.94044 0.00000
1200 63.80 0.94044 0.94044 0.00000
1250 63.80 0.94044 0.94044 0.00000
1300 63.80 0.94044 0.94044 0.00000
1350 63.80 0.94044 0.94044 0.00000
1400 63.80 0.94044 0.94044 0.00000
1450 63.80 0.94044 0.94044 0.00000
1500 63.80 0.94044 0.94044 0.00105
1550 63.79 0.94065 0.94064 0.01297
1600 63.74 0.94137 0.94135 0.03395
1650 63.64 0.94285 0.94281 0.06298
1700 63.47 0.94527 0.94521 0.09995
1750 63.24 0.94881 0.94873 0.14515
1800 62.92 0.95365 0.95354 0.19915
1850 62.50 0.95997 0.95983 0.26280
1900 61.99 0.96796 0.96778 0.33724
1950 61.36 0.97783 0.97761 0.42397
2000 60.62 0.98983 0.98956 0.52492
2050 59.75 1.00422 1.00391 0.64254
2100 58.75 1.02134 1.02097 0.78001
2150 57.61 1.04157 1.04113 0.94139
2200 56.32 1.06537 1.06485 1.13198
2250 54.88 1.09331 1.09271 1.35869
2300 53.28 1.12612 1.12541 1.63075
2338 51.96 1.15483 1.15403 1.87530
2500 not included in HCM equations
41
Table 3-4: Delay Calculations Using I-495 Regression Equation
Traffic Flow
(PCE/lane/hour)
Travel
Speed
(mph)
Time to
travel one
mile at given
volume
(min./mile)
Time to travel one
mile at one less
PCE/lane/hour
(min./mile)
Delay imposed on traffic
stream by an additional
PCE/lane/hour (min./mile)
50 63.89 0.93914 0.93914 0.00000
100 63.95 0.93829 0.93829 0.00000
150 63.98 0.93784 0.93784 0.00000
200 63.98 0.93772 0.93772 0.00012
250 63.97 0.93789 0.93788 0.00145
300 63.95 0.93829 0.93828 0.00305
350 63.90 0.93890 0.93888 0.00481
400 63.85 0.93966 0.93964 0.00665
450 63.79 0.94055 0.94053 0.00851
500 63.73 0.94155 0.94153 0.01033
550 63.65 0.94261 0.94259 0.01210
600 63.58 0.94374 0.94372 0.01378
650 63.50 0.94491 0.94488 0.01539
700 63.42 0.94611 0.94608 0.01696
750 63.34 0.94733 0.94730 0.01851
800 63.25 0.94857 0.94855 0.02010
850 63.17 0.94984 0.94982 0.02183
900 63.08 0.95115 0.95112 0.02377
950 62.99 0.95249 0.95246 0.02605
1000 62.90 0.95390 0.95387 0.02880
1050 62.80 0.95538 0.95535 0.03218
1100 62.70 0.95697 0.95694 0.03637
1150 62.58 0.95870 0.95866 0.04157
1200 62.46 0.96060 0.96056 0.04801
1250 62.32 0.96272 0.96267 0.05593
1300 62.17 0.96510 0.96505 0.06563
1350 62.00 0.96779 0.96774 0.07741
1400 61.80 0.97086 0.97080 0.09163
1450 61.58 0.97437 0.97430 0.10870
1500 61.33 0.97839 0.97831 0.12905
1550 61.04 0.98301 0.98292 0.15321
1600 60.71 0.98832 0.98821 0.18177
1650 60.34 0.99443 0.99430 0.21541
1700 59.91 1.00144 1.00129 0.25493
1750 59.44 1.00949 1.00932 0.30127
1800 58.90 1.01873 1.01853 0.35556
1850 58.29 1.02933 1.02911 0.41915
1900 57.61 1.04149 1.04123 0.49367
1950 56.85 1.05543 1.05513 0.58113
2000 56.00 1.07143 1.07109 0.68400
2050 55.06 1.08979 1.08940 0.80541
2100 54.01 1.11091 1.11046 0.94928
2150 52.85 1.13523 1.13471 1.12066
2200 51.58 1.16331 1.16271 1.32610
2250 50.17 1.19585 1.19515 1.57426
2300 48.63 1.23371 1.23289 1.87670
2338 47.37 1.26671 1.26579 2.15236
2350 46.95 1.27799 1.27703 2.24920
42
3.3.6 Speed Frequency and Probability by Flow Range
The frequency of data points that fall in a certain flow range, along with the
speed probabilities within a certain flow range, are interesting aspects to explore.
Data existing under flow conditions less than 1,200 pc/ln/hr can be grouped together,
as these low-flow areas are less interesting than periods of higher flow.
Using all of the data points, along with three speed ranges (41-50 mph, 51-60
mph, and 61-70 mph), the probability of a data point falling in each speed range can
be calculated for increasing flow rates. This will show the probability of being in
each speed range as a function of flow. This information is displayed in Figure 4-8
and provides a sample probability density function (PDF) for each flow range. The
speed probability graph is not terribly surprising, as the probability of higher speeds
decreases as flow increases. A few strange overlap areas exist, and the 1,901-2,000
pc/ln/hr flow range is particularly interesting since it is a merge point where all three
speed ranges have an equal probability of occurring. Curiosity arises when that sort
of uncertainty exists.
Moving forward, the frequency of data in each flow range is plotted as Figure
4-9 – the relative frequency of the various flow ranges assists with critiquing the data.
When looking at the frequency of data points across different flow ranges, the vast
majority of data is from periods of lower demand that exhibit low-flow conditions
(i.e. off-peak hours). Although regular users of the Capital Beltway may choose to
disagree, this observation makes sense, as there are more uncongested hours than
congested hours in the day. Flows greater than 1,200 pc/ln/hr, are characterized by a
small bell-shaped curve, with a small likelihood of encountering lower volumes at
43
either end of the range. Whenever these situations occur, the onset of some
congestion in these locations may be the result. The frequency of data greater than
2,000 pc/ln/hr is low – possibly due to the fact that traffic is unable to exhibit the
steady flow conditions that enable flows at this rate or higher.
Speed Probability by Flow Range
0.000
0.100
0.200
0.300
0.400
0.500
0.600
0.700
0.800
0.900
1.000
0-1200 1201-1300 1301-1400 1401-1500 1501-1600 1601-1700 1701-1800 1801-1900 1901-2000 >2000
Flow Range (PCE/lane/hour)
P
r
o
b
a
b
i
l
i
t
y
P(41-50) P(51-60) P(61-70)
Figure 3-10: Speed Probability by Flow Range
44
Frequency by Flow Range
0.000
0.100
0.200
0.300
0.400
0.500
0.600
0.700
0.800
0.900
1.000
0-1200 1201-1300 1301-1400 1401-1500 1501-1600 1601-1700 1701-1800 1801-1900 1901-2000 >2000
Flow Range (PCE/lane/hour)
F
r
e
q
u
e
n
c
y
%
Figure 3-11: Frequency by Flow Range
3.3.7 Traffic Proportions
Traffic proportions for each of the 13 FHWA vehicle classifications are
components of the optimization model and will be applied across varying flow levels.
As traffic stream characteristics differ between AM and PM peak periods, analysis is
completed using both periods in order to determine appropriate traffic proportion
percentages. As part of the Federal Highway Administration’s Highway Performance
Monitoring System (HPMS), Maryland collects vehicle classification information on
I-495. For this reason, data from Maryland is able to be included at this stage of the
study. Although this data does not contain speed information and, therefore, cannot
be used throughout the remainder of this study, traffic proportion percentages can be
obtained and compared with the Virginia data that have been utilized up to this point.
45
Based on general knowledge and the aforementioned flow and speed graphs
that showcased evident peak period times, the AM peak period is defined as 6AM-
10AM and the PM peak period is defined as 3PM-7PM. After combining all relevant
data for these time periods and averaging Virginia and Maryland data together, the
following percentages were obtained for each of the 13 FHWA vehicle
classifications:
Table 3-5: Peak Period Traffic Proportions
AM Peak (%) PM Peak (%)
Class 1 0.16 0.16
Class 2 83.18 86.78
Class 3 12.39 10.35
Class 4 0.68 0.42
Class 5 0.90 0.60
Class 6 0.58 0.24
Class 7 0.24 0.07
Class 8 0.22 0.16
Class 9 1.55 1.17
Class 10 0.06 0.02
Class 11 0.03 0.02
Class 12 0.01 0.01
Class 13 0.00 0.00
Although the AM and PM peak period traffic proportion percentages seem rather
similar, they will be used separately when calculating the associated peak period
charges.
3.4 Value of Time Estimation
In order to devise a pricing strategy, dollar amounts must be attributed to the
time spent in congestion (i.e. the delay calculations set forth previously). In order to
do this, user value of time estimates must first be obtained. As no studies have been
undertaken in the Washington, D.C. area to associate value of time estimates to each
of the 13 FHWA vehicle classifications, estimates are extrapolated from the Highway
Economic Requirements System (HERS), a FHWA model designed to simulate
46
improvement selection decisions based on the relative benefit-cost merits of
alternative improvement options (FHWA 2002). The HERS model provides
combined user value of time and vehicle operating costs for seven vehicle classes
which differ from the 13 vehicle classifications used in this study. As the amounts
provided in the model’s documentation are not current, they are converted to
equivalent 2007 dollars. Prevailing wage data is the general basis for user value of
time and costs are compensated by the fact that operating costs differ from vehicle-to-
vehicle. These values include both aspects.
Table 3-6: FHWA HERS Model – Value of Time
Vehicle Class Value (in 2007 $/hour)
Small Auto 21.37
Med. Auto 21.43
4-Tire Truck 24.27
6-Tire Truck 27.18
3-4 Axle Truck 32.19
4-Axle Combo. 34.68
5-Axle Combo. 34.34
Based on the HERS model estimates and general assumptions about vehicle
classifications, value of time and operating costs estimates are calculated for each of
the 13 FHWA vehicle classifications. Table 4-6 showcases these estimates. It should
be noted that operating costs for motorcycles are estimated to be half of those
associated with passenger cars and user value of time is chosen to be represented by
the $11.56 per hour value provided for personal, not business, travel. Additionally,
since no actual occupancy data were available, standard bus occupancy is assumed to
be 30 passengers, all traveling under personal user value of time estimates. While
this estimate may not be precise, it will provide a rough approximation, at the very
least.
47
Table 3-7: FHWA Vehicle Classifications – Value of Time
Vehicle Class Value (in 2007 $/hour)
1 12.31
2 21.40
3 24.27
4 346.93
5 27.18
6 32.19
7 32.19
8 34.68
9 34.34
10 34.34
11 34.34
12 34.34
13 34.34
In this study, the distribution of trip purposes is not taken into account. Value
of time is inherently laden with a trip purpose (i.e. personal use, business use, etc.)
and, for this thesis, the assumption is made that value of time estimates are not
reflecting varying trip purposes.
3.5 Model Formulation
As previously stated, one of the research objectives of this thesis is to develop
a model that optimizes the pricing necessary to cause vehicle users on the Capital
Beltway to realize the congestion costs that their vehicles impose on the rest of the
traffic stream. To this extent, congestion pricing will serve as a demand management
tool. While the model process will be outlined in this section, a visual demonstration
will be provided in the next chapter.
Based on a model developed by Roth and Villoria (2001), the algorithm is as
follows:
48
1. Using a provided initial flow condition and traffic proportions calculated
previously, calculate the initial number of vehicles in each classification
category
2. Using the aforementioned equation that relates speed and flow and the given
flow condition, calculate the initial speed of the traffic system
3. Initial cost (per vehicle) to travel one mile can be calculated by dividing the
total costs for each vehicle classification by the initial speed
4. A variable congestion charge is introduced at this point and the cost for each
vehicle to travel one mile, including the congestion charge, is calculated - this
charge will be varied by the model
5. The percent change in cost after adding the congestion charge is calculated
6. Based on the assumed negative elasticity, the initial number of vehicles, and
the percent change in cost, the change in flow after imposing the congestion
charge is calculated
7. The new flow for each vehicle classification is calculated by subtracting the
change in flow from the initial flow
8. Using the updated total flow in the traffic system, new traffic composition
proportions and speed values can be calculated
9. Calculate the average vehicle speed at one less PCE/lane/hour than the
updated flow condition
10. Calculate costs per vehicle at both the current speed and the speed at one less
PCE/lane/hour in order to determine the cost imposed on the entire traffic
49
stream by one extra PCE (this concept is similar to the delay calculation that
was explained previously)
11. The total cost due to one extra PCE is the cost imposed on the entire traffic
stream by the additional PCE added to the average cost per vehicle under
current conditions
12. A variable percent change is introduced at this point - this is used to calculate
theoretical flow and cost information which is used by the optimization model
13. Using the initial cost per vehicle to travel one mile under initial flow
conditions, calculate a weighted cost average based on the new traffic
proportions
14. The resulting theoretical flow is found by multiplying the initial flow by one
minus the percent change times the elasticity
15. The resulting theoretical cost (i.e. the equilibrium demand price) is found by
adding the weighted cost average based on the new traffic proportions to one
plus the percent change
16. At this point, the model is instructed to force the resulting theoretical cost
minus the total cost due to one extra PCE to equal zero and to minimize the
resulting theoretical flow minus the flow after the imposing the congestion
charge
17. The model runs until an optimal congestion charge solution is reached – this
charge is the amount that equals the congestion cost under the conditions
existing after it is inflicted
50
3.6 Assumptions
Throughout the model formulation process of this study, various assumptions
needed to be made:
• Due to the fact that no comprehensive Maryland data was available for I-
495, the obtained data from Virginia was assumed to be representative of
the entire Capital Beltway. As there are varying levels of traffic collected
at each of the Virginia detector locations, this assumption seems valid.
While the results of this Washington, D.C.-area study may not be entirely
transferable to other regions, the methodology will remain valid.
• When calculating AM and PM peak traffic proportions, it was assumed
that the distribution of vehicle types across all travel lanes remained at the
average values throughout the peaks (instead of changing hourly, etc.).
While some changes might have occurred if the traffic proportions were
analyzed on a per-hour basis, the changes would seemingly be small
enough to merit using overall average values instead.
• As no user value of time or vehicle operating cost data existed that was
broken down into the 13 FHWA vehicle classifications, the estimated
values used in the FHWA HERS model were assumed in this study.
These values were not entirely specific for each vehicle classification, but
are assumed valid due to the lack of more exhaustive data. As stated
previously, the distribution of trip purposes was not taken into account for
the value of time estimation. The assumption is made that value of time
estimates are not reflecting varying trip purposes.
51
• In calculating total vehicle costs, no clear estimates were found on average
bus occupancy on the Capital Beltway. An average occupancy of 30
passengers was assumed, due to the lack of sufficient ridership data. As
this value may seem high, it provides an approximation, although the total
value of bus traffic may potentially be inflated.
• Speed and flow distributions are assumed uniformly equal across all lanes
of I-495 in this study. In actuality, this is not the case. Since the user
charges are calculated at the PCE level, however, this does not seem to
affect the results. Regardless of the per-lane statistics, user charges are
assigned to each PCE.
• User value of time estimates may actually be different than calculated.
User responses to congestion charges vary and people will express varying
elasticity levels. This being said, the value of time estimates set forth in
this study should be taken as approximations.
Due to the various assumptions set forth in this study, it is likely that the
results of this study may be artificially low. In this light, the results can be considered
to be conservative estimations.
The following chapter discusses the system evaluation, along with a
demonstration of the model utilized in this study. Applicable user charges and
sensitivity analysis will also be presented.
52
Chapter 4: System Evaluation
4.1 Inputs
The input parameters for this model have been previously touched on, at least
briefly, as they were obtained or calculated from available I-495 data. To summarize:
• Flow – measured in passenger cars per lane per hour (pc/ln/hr); obtained
from I-495 data
• Speed-flow relationship – regression equation calculated from I-495 data
obtained for this study in order to show the impact of traffic flow on traffic
speed; this equation can be used to estimate speeds under various flow
conditions
• Total vehicle costs – measured in dollars per hour ($/hr); calculated by
summing user value of time and vehicle operating costs for each of the 13
FHWA vehicle classifications
• Traffic proportions – measured as a percentage (%); traffic proportions for
each of the 13 FHWA vehicle classifications were calculated in the AM
and PM peak periods based on the total traffic volume data obtained from
I-495
• Elasticity – unitless number; a negative elasticity indicates the changes
that occur in road use as a result of increased costs; the assumed elasticity
of -0.2 for this model is based on a general literature search, estimates
from the existing charging system in Stockholm, Sweden, and the
knowledge that sufficient transit options do not exist on I-495; elasticity
53
must be estimated, as the true value cannot be determined unless pricing is
actually implemented and travel behavior is observed
While all of these parameters are vital for a functional model, they are not all direct
inputs from the user. The speed-flow regression equation and all applicable constants
are programmed into the model. All other inputs are controlled by the user.
4.2 Outputs
The outputs produced by this model can be placed into two categories: process
outputs and final outputs. Process outputs consist of calculations that occur
throughout the iterative process of the model that lead to the final outputs – the
optimized variables.
Process outputs:
• Initial number of vehicles – measured in passenger car equivalents (PCEs);
calculated based on initial flow and traffic proportion conditions
• Initial speed – measured in miles per hour (mph); calculated from the
speed-flow regression equation using initial flow conditions
• Initial cost (per vehicle) to travel one mile – measured in $/mile;
calculated based on total vehicle costs and initial speed
• Cost to travel one mile (with congestion charge) – measured in $/mile;
calculated using the initial cost (per vehicle) to travel one mile and the
varying congestion charge
• Percent change in cost (after congestion charge) – measured as a
percentage; calculated based on the initial cost (per vehicle) to travel one
mile and the cost to travel one mile (with congestion charge)
54
• Change in flow (after congestion charge) – measured in pc/ln/hr;
calculated using the initial number of vehicles, the assumed elasticity and
the percent change in cost (after congestion charge)
• Percent change in flow (after congestion charge) – measured as a
percentage; calculated using the initial number of vehicles and the change
in flow (after congestion charge)
• New flow (after congestion charge) – measured in pc/ln/hr; calculated
from the initial flow and the change in flow (after congestion charge)
• New proportion of traffic (after congestion charge) – measured as a
percentage; calculated using the new flow (after congestion charge) for
each vehicle classification and the total new flow (after congestion charge)
• New speed (after congestion charge) – measured in mph; calculated from
the speed-flow regression equation using new flow conditions (after
congestion charge)
• Vehicle speed at one PCE/lane/hour less (after congestion charge) –
measured in mph; calculated from the speed-flow regression equation
using one PCE less than new flow conditions (after congestion charge)
• Average cost per vehicle (after congestion charge) – measured in $/mile;
calculated based on the new speed (after congestion charge) and the total
vehicle costs
• Average cost per vehicle at one PCE/lane/hour less (after congestion
charge) – measured in $/mile; calculated based on the vehicle speed at one
PCE/lane/hour less (after congestion charge) and the total vehicle costs
55
• Cost imposed on the entire traffic stream by one extra PCE – measured in
$/mile; calculated using the average cost per vehicle (after congestion
charge), average cost per vehicle at one PCE/lane/hour less (after
congestion charge), and new flow (after congestion charge); this
calculation is similar to the delay calculation process explained previously
• Total cost due to one extra PCE – measured in $/mile; calculated using the
weighted average cost per vehicle at one PCE/lane/hour less (after
congestion charge) and the cost imposed on the entire traffic stream by
one extra PCE
• Resulting theoretical flow (i.e. equilibrium demand flow) – measured in
PCE/ln/hr; calculated using the initial flow conditions, assumed elasticity,
and varying percent change
• Resulting theoretical cost (i.e. equilibrium demand price) – measured in
$/PCE/mile; calculated using the weighted cost (per vehicle) to travel one
mile under initial flow conditions and varying percent change
Final outputs:
• Optimized congestion pricing – measured in $/PCE/mile; obtained from
the optimization model; the objective function is setup as follows:
Minimize: equilibrium demand flow - calculated flow with the congestion
charge
Subject to the constraint: equilibrium demand price = calculated total
cost due to one extra PCE
Variables: percent change; congestion charge
56
• Percent change – measured as a percentage; obtained from the
optimization model, where it is used to equate the equilibrium demand
price and equilibrium demand flow; this percentage corresponds to the
marginal cost of the system – the difference between the weighted cost
(per vehicle) to travel one mile under initial flow conditions and the
equilibrium demand price
4.3 Model Demonstration
In order to summarize accomplishments, this model utilizes the Solver tool in
Excel to find the congestion charge which equates the total cost due to one extra PCE
and the equilibrium demand price. The total cost due to one extra PCE varies with
the congestion charge and the consequent changes in traffic volumes and speeds,
taking into account changes in traffic composition by vehicle classification. The
equilibrium demand price varies in accordance with the assumed elasticity, with the
change in traffic conditions from the initial to the final condition determined by the
Excel model (Roth 2001). The objective function of this model forces the calculated
total cost due to one extra PCE to equal the equilibrium demand price; as a result,
users will pay the marginal cost of the system. This results in a system-optimized
network, where costs imposed by drivers are realized.
Figure 4-1 shows the model spreadsheet layout for an assumed elasticity of -
0.2 and an initial flow condition of 2,000 PCE/lane/hour. From the model’s
standpoint, a positive elasticity input of 0.2 actually corresponds to -0.2. From
Chapter 3, the initial proportion of traffic (based on the AM peak calculations) and
the total vehicle costs are obtained. All calculations are displayed, including optimal
57
congestion price ($0.14 per PCE per mile) and new anticipated flow (1,856
PCE/lane/hour). The yellow highlights denote variable inputs from the user and the
green highlights indicate variables utilized by the Solver tool in Excel.
58
FHWA Vehicle Classes
Description Units
Class 1 Class 2 Class 3 Class 4 Class 5 Class 6 Class 7 Class 8 Class 9 Class 10 Class 11 Class 12 Class 13
Total
speed = (a * flow^4) + (b * flow^3) –
(c * flow^2) + (d * flow) + 63.8
a = -0.000000000002
b = 0.000000006
c = 0.000007
d = 0.0021
average uncongested speed = 63.8 mph
user value of time + vehicle operating costs
$/hour 12.31 21.4 24.27 346.93 27.18 32.19 32.19 34.68 34.34 34.34 34.34 34.34 34.34
Initial flow PCE/lane/hour 2000
Initial proportion of traffic percentage 0.159% 83.177% 12.385% 0.683% 0.898% 0.582% 0.245% 0.224% 1.551% 0.058% 0.030% 0.006% 0.002% 100%
Initial number of vehicles PCEs 3 1664 248 14 18 12 5 4 31 1 1 0 0 2000
Initial speed mph 56.00 56.00 56.00 56.00 56.00 56.00 56.00 56.00 56.00 56.00 56.00 56.00 56.00
Initial cost (per vehicle) to travel 1 mile $/mile 0.21982 0.38214 0.43339 6.19518 0.48536 0.57482 0.57482 0.61929 0.61321 0.61321 0.61321 0.61321 0.61321
Congestion charge $/PCE/mile 0.14
Cost to travel 1 mile (with congestion charge) $/mile 0.36212 0.52445 0.57570 6.33748 0.62766 0.71712 0.71712 0.76159 0.75552 0.75552 0.75552 0.75552 0.75552
Elasticity 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2
Percent change in cost (after congestion
charge) percentage 64.74% 37.24% 32.83% 2.30% 29.32% 24.76% 24.76% 22.98% 23.21% 23.21% 23.21% 23.21% 23.21%
Percent change in flow (after congestion
charge) percentage 12.95% 7.45% 6.57% 0.46% 5.86% 4.95% 4.95% 4.60% 4.64% 4.64% 4.64% 4.64% 4.64%
Change in flow (after congestion charge) PCE/lane/hour 0 124 16 0 1 1 0 0 1 0 0 0 0
New flow (after congestion charge) PCE/lane/hour 3 1540 231 14 17 11 5 4 30 1 1 0 0 1856
New proportion of traffic (after congestion
charge) percentage 0.149% 82.966% 12.471% 0.733% 0.911% 0.596% 0.251% 0.230% 1.594% 0.060% 0.031% 0.006% 0.002%
New speed (after congestion charge) mph 58.22 58.22 58.22 58.22 58.22 58.22 58.22 58.22 58.22 58.22 58.22 58.22 58.22
Flow (with congestion charge) PCE/lane/hour 1856
Vehicle speed (with congestion charge) mph 58.22 58.22 58.22 58.22 58.22 58.22 58.22 58.22 58.22 58.22 58.22 58.22 58.22
Vehicle speed at one PCE/lane/hour less mph 58.23 58.23 58.23 58.23 58.23 58.23 58.23 58.23 58.23 58.23 58.23 58.23 58.23
Average cost per vehicle (at new vehicle
speed) $/mile 0.21145 0.36760 0.41690 5.95938 0.46688 0.55294 0.55294 0.59571 0.58987 0.58987 0.58987 0.58987 0.58987 0.42125
Average cost per vehicle at one PCE/lane/hour
less $/mile 0.21141 0.36752 0.41680 5.95805 0.46678 0.55282 0.55282 0.59558 0.58974 0.58974 0.58974 0.58974 0.58974 0.42115
Cost imposed on the entire traffic stream by
one extra PCE $/mile 0.17458
Total cost due to one extra PCE $/mile 0.59583
Percent change percentage 36.1
Elasticity 0.2
Initial flow PCE/lane/hour 2000
Speed under initial flow conditions mph 56.00 56.00 56.00 56.00 56.00 56.00 56.00 56.00 56.00 56.00 56.00 56.00 56.00
Cost (per vehicle) to travel 1 mile under initial
flow conditions $/PCE/mile 0.21982 0.38214 0.43339 6.19518 0.48536 0.57482 0.57482 0.61929 0.61321 0.61321 0.61321 0.61321 0.61321 0.43791
Resulting theoretical flow (based on elasticity
and % change) PCE/lane/hour 1856
Resulting theoretical cost (based on elasticity
and % change) $/PCE/mile 0.59583
(Resulting theoretical cost - Total cost due to
one extra PCE) $/PCE/mile 0.0
(Resulting theoretical flow - Flow with
congestion charge) PCE/lane/hour 0.0
Figure 4-1: Model Demonstration
59
4.4 Evaluations
As the observed traffic composition differs between AM and PM peaks on the
Capital Beltway, the two periods are examined as separate entities. Initial hourly
volumes are calculated based on averages obtained from all detector data across that
specific hour in 2007. For both the AM and PM peak periods, the average hourly
volumes are provided and optimal congestion charges for an assumed -0.2 elasticity
are displayed for each of the 13 FHWA vehicle classifications on a per-hour basis.
Additionally, the anticipated traffic composition as a result of congestion charging is
offered.
4.4.1 AM Peak
Table 4-1 and Table 4-2 show the average hourly flow and applicable
congestion charges, respectively, for the AM peak period on the Capital Beltway.
Table 4-3 presents the anticipated hourly traffic composition as a result of congestion
charging. Most notably, it is seen that for the AM peak, the optimal congestion
charge ranges from $0.05 to $0.08 per PCE per mile, based on average hourly flow
conditions on I-495. While these figures are applicable to passenger cars, the lowest
possible charges (for class 1 vehicles) range from $0.02 to $0.03 per mile and the
highest possible charges (for class 13 vehicles) range from $0.22 to $0.35 per mile.
The range in charges is directly obtained from the corresponding PCE factors –
vehicles are charged appropriately for the amount of road space that they utilize.
Information on potential charging for roadway sections with greater flow will be
discussed later.
60
Table 4-1: Average AM Peak Hourly Flow for I-495
HOUR OF DAY AVERAGE PCE/LANE/HOUR (2007)
6 (6AM) 1598
7 (7AM) 1743
8 (8AM) 1709
9 (9AM) 1653
Table 4-2: AM Peak Hourly Congestion Charges for I-495
Congestion Charge ($/mile) Vehicle
Classification
Description
PCE
Factor
6AM 7AM 8AM 9AM
1 Motorcycle 0.38 0.02 0.03 0.03 0.02
2 Passenger Cars 1.00 0.05 0.08 0.07 0.06
3 Other Two-Axle, Four-Tire single Unit Vehicles 1.13 0.06 0.09 0.08 0.07
4 Buses 2.38 0.12 0.19 0.17 0.14
5 Two-Axle, Six-Tire, Single-Unit Trucks 1.63 0.08 0.13 0.11 0.10
6 Three-Axle Single-Unit Trucks 1.56 0.08 0.13 0.11 0.09
7 Four or More Axle Single-Unit Trucks 2.00 0.10 0.16 0.14 0.12
8 Four or Fewer Axle Single-Trailer Trucks 2.75 0.14 0.22 0.19 0.17
9 Five-Axle Single-Trailer Trucks 4.00 0.20 0.32 0.28 0.24
10 Six or More Axle Single-Trailer Trucks 3.94 0.20 0.32 0.28 0.24
11 Five or Fewer Axle Multi-Trailer Trucks 4.25 0.21 0.34 0.30 0.26
12 Six-Axle Multi-Trailer Trucks 4.56 0.23 0.37 0.32 0.27
13 Seven or More Axle Multi-Trailer Trucks 4.31 0.22 0.35 0.30 0.26
Table 4-3: AM Peak Traffic Composition Resulting from Congestion Pricing
Traffic Composition (PCE/lane/hour)
6AM 7AM 8AM 9AM
Vehicle
Classification
Initial Final Initial Final Initial Final Initial Final
Total 1598 1550 1743 1668 1709 1641 1653 1596
1 3 2 3 3 3 3 3 2
2 1329 1288 1450 1385 1421 1363 1375 1326
3 198 193 216 207 212 204 205 198
4 11 11 12 12 12 12 11 11
5 14 14 16 15 15 15 15 14
6 9 9 10 10 10 10 10 9
7 4 4 4 4 4 4 4 4
8 4 4 4 4 4 4 4 4
9 25 24 27 26 27 26 26 25
10 1 1 1 1 1 1 1 1
11 0 0 1 1 1 0 0 0
12 0 0 0 0 0 0 0 0
13 0 0 0 0 0 0 0 0
4.4.2 PM Peak
Table 4-4 and Table 4-5 show the average hourly flow and applicable
congestion charges, respectively, for the PM peak period on the Capital Beltway.
61
Table 4-6 presents the anticipated hourly traffic composition as a result of congestion
charging. Most notably, it is seen that for the PM peak, the optimal congestion
charge ranges from $0.03 to $0.08 per PCE per mile, based on average hourly flow
conditions on I-495. While these figures are applicable to passenger cars, the lowest
possible charges (for class 1 vehicles) range from $0.01 to $0.03 per mile and the
highest possible charges (for class 13 vehicles) range from $0.13 to $0.35 per mile.
The range in charges is directly obtained from the corresponding PCE factors –
vehicles are charged appropriately for the amount of road space that they utilize.
Information on potential charging for roadway sections with greater flow will be
discussed later.
Table 4-4: Average PM Peak Hourly Flow for I-495
HOUR OF DAY AVERAGE PCE/LANE/HOUR (2007)
14 (2PM) 1733
15 (3PM) 1674
16 (4PM) 1583
17 (5PM) 1514
18 (6PM) 1439
Table 4-5: PM Peak Hourly Congestion Charges for I-495
Congestion Charge ($/mile) Vehicle
Classification
Description
PCE
Factor
2PM 3PM 4PM 5PM 6PM
1 Motorcycle 0.38 0.03 0.03 0.02 0.02 0.01
2 Passenger Cars 1.00 0.08 0.07 0.05 0.04 0.03
3 Other Two-Axle, Four-Tire single Unit Vehicles 1.13 0.09 0.08 0.06 0.05 0.03
4 Buses 2.38 0.19 0.17 0.12 0.10 0.07
5 Two-Axle, Six-Tire, Single-Unit Trucks 1.63 0.13 0.11 0.08 0.07 0.05
6 Three-Axle Single-Unit Trucks 1.56 0.13 0.11 0.08 0.06 0.05
7 Four or More Axle Single-Unit Trucks 2.00 0.16 0.14 0.10 0.08 0.06
8 Four or Fewer Axle Single-Trailer Trucks 2.75 0.22 0.19 0.14 0.11 0.08
9 Five-Axle Single-Trailer Trucks 4.00 0.32 0.28 0.20 0.16 0.12
10 Six or More Axle Single-Trailer Trucks 3.94 0.32 0.28 0.20 0.16 0.12
11 Five or Fewer Axle Multi-Trailer Trucks 4.25 0.34 0.30 0.21 0.17 0.13
12 Six-Axle Multi-Trailer Trucks 4.56 0.37 0.32 0.23 0.18 0.14
13 Seven or More Axle Multi-Trailer Trucks 4.31 0.35 0.30 0.22 0.17 0.13
62
Table 4-6: PM Peak Traffic Composition Resulting from Congestion Pricing
Traffic Composition (PCE/lane/hour)
2PM 3PM 4PM 5PM 6PM
Vehicle
Classification
Initial Final Initial Final Initial Final Initial Final Initial Final
Total 1733 1660 1674 1613 1583 1537 1514 1478 1439 1411
1 3 3 3 3 3 2 2 2 2 2
2 1504 1439 1453 1398 1374 1333 1314 1282 1249 1224
3 179 173 173 168 164 160 157 153 149 146
4 7 7 7 7 7 7 6 6 6 6
5 10 10 10 10 9 9 9 9 9 8
6 4 4 4 4 4 4 4 4 4 3
7 1 1 1 1 1 1 1 1 1 1
8 3 3 3 3 3 3 2 2 2 2
9 20 20 20 19 19 18 18 17 17 17
10 0 0 0 0 0 0 0 0 0 0
11 0 0 0 0 0 0 0 0 0 0
12 0 0 0 0 0 0 0 0 0 0
13 0 0 0 0 0 0 0 0 0 0
4.4.3 Discussion of Results
As seen in the two previous sections, the optimal AM and PM peak period
charges range from $0.03 to $0.08 per passenger car equivalent per mile. These
estimates are lower than the $0.08 to $0.50 per mile estimates, in 2007 dollars, taken
from existing literature. In terms of the city street methodology on which this study is
based, Roth and Villoria (2001) found optimal pricing in the range of $0.29 to $0.64
per passenger car equivalent per mile, in 2007 dollars. Based on these other figures,
it seems as if there could be other factors that this study did not take into account.
Other estimations may very well have other factors included. For this reason, these
results should be taken as rough approximations.
4.5 Sensitivity Analysis
With any model, it is important to analyze changes in input parameters to
determine the corresponding responses. This section focuses on the effects of direct
inputs into the model – assumed elasticity, traffic proportions, and value of time – on
63
the congestion charges computed. In a way, it is difficult to perform substantial
sensitivity analysis with an optimization model that outputs a single “best” answer.
There are relatively few parameters open for sensitivity analysis since the Solver tool
optimizes the data and the key speed-flow relationship is, more or less, obvious.
Initial flow is another direct input into the model, but is not available for sensitivity
analysis. It goes without saying that speed is a function of flow and that as flow
increases, the optimal congestion charges will increase, as congestion costs are
greater.
4.5.1 Effect of Elasticity
In the previous section, congestion charges were presented based on average
flow conditions in the AM and PM peak periods. This section will take a different
route and present AM and PM peak congestion charge estimates for varying elasticity
levels – flows ranging from 0 to 2,350 PCE/lane/hour (lane capacity) will be
addressed. Figures 4-2 and 4-3 show the sensitivity of AM and PM peak congestion
charges with respect to elasticity, respectively.
64
Flow vs. Congestion Charge - AM Peak
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.40
0 500 1000 1500 2000
Flow (PCE/lane/hour)
C
o
n
g
e
s
t
i
o
n
C
h
a
r
g
e
(
$
/
P
C
E
/
m
i
l
e
)
-0.1 Elasticity
-0.2 Elasticity
-0.3 Elasticity
-0.4 Elasticity
-0.5 Elasticity
-0.6 Elasticity
-0.7 Elasticity
-0.8 Elasticity
-0.9 Elasticity
-1.0 Elasticity
Figure 4-2: Sensitivity of Elasticity Values for Congestion Charges (AM Peak)
Flow vs. Congestion Charge - PM Peak
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.40
0 500 1000 1500 2000
Flow (PCE/lane/hour)
C
o
n
g
e
s
t
i
o
n
C
h
a
r
g
e
(
$
/
P
C
E
/
m
i
l
e
)
-0.1 Elasticity
-0.2 Elasticity
-0.3 Elasticity
-0.4 Elasticity
-0.5 Elasticity
-0.6 Elasticity
-0.7 Elasticity
-0.8 Elasticity
-0.9 Elasticity
-1.0 Elasticity
Figure 4-3: Sensitivity of Elasticity Values for Congestion Charges (PM Peak)
65
Especially interesting about this sensitivity analysis is that a large change in
assumed elasticity does not cause similarly large changes in the congestion charge. In
fact, the optimal charges at lower flow levels (less than about 1,500 PCE/lane/hour)
are very similar across all elasticity levels. It is only at higher flow levels that the
plots fan out from one another. At capacity, the charge varies from $0.09 to $0.38 per
PCE per mile for the AM peak and from $0.09 to $0.37 per PCE per mile for the PM
peak. Even though this is a spread increase of over four times, the total cost is still
not significant enough to claim that assumed elasticity has a large impact on optimal
congestion charges.
From these plots, the effects of elasticity can be easily seen. For an assumed
elasticity value of -1.0, it can be assumed that other transportation (i.e. public transit)
options are readily available. For this reason, there is a larger decrease in road usage
at a lower price. As elasticity go towards -0.1, there is not as much of a decrease in
road usage in the presence of pricing, so charges must be increased in order to cause a
decrease in road usage.
4.5.2 Effect of Traffic Proportions
Traffic proportions have an effect on congestion charges due to the different
total costs incurred per mile for each vehicle classification. For example, in the case
of the I-495 data used in this study, the vast majority of vehicles are passenger cars.
The total cost, per mile, to operate a passenger car is much less than the total cost, per
mile, to operate a seven or more axle multi-trailer truck. For this reason, the weighted
cost of the vehicles in the traffic stream will be lower when there is a greater
percentage of passenger cars rather than large trucks.
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To illustrate this, assume that the total flow is currently 2,000 PCE/lane/hour.
For simplicity’s sake, there are only two types of vehicles on the roadway: passenger
cars and seven or more axle multi-trailer trucks. Using the same values of time and
elasticity, the optimal congestion charge when the traffic consists of 75% passenger
cars and 25% seven or more axle multi-trailer trucks is $0.15 per PCE per mile.
When the traffic stream consists of 25% passenger cars and 75% seven or more axle
multi-trailer trucks, the optimal congestion charge is $0.19 per PCE per mile. For a
large change in traffic proportion conditions, there is a relatively small change in the
optimal congestion charge.
4.5.3 Effect of Value of Time and Vehicle Operating Costs
It is difficult to address the effect of value of time and vehicle operating costs
due to the fact that traffic proportions interact significantly with these values to
determine the optimal congestion charge. When previously analyzing the effect of
traffic proportions, it was assumed that total costs remained the same as they did
throughout the study. If the total costs for a certain vehicle are incredibly high and
there are none using the roadway, the weighted average of congestion costs across the
traffic stream will be much lower than if there are many of these vehicles on the
roadway. For this reason, the effect of total vehicle costs on optimal congestion
charge is deemed to be worthy of mention, along with the fact that there is a strong
correlation with traffic proportions.
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4.6 Summary
This chapter has shown that optimal AM and PM peak period charges range
from $0.03 to $0.08 per passenger car equivalent per mile in this study. These
estimates are lower than the $0.08 to $0.50 per mile estimates taken from existing
literature. Based on these figures, it seems as if there could be other factors that this
study did not take into account. Other estimations may very well have other factors
included. For this reason, these results should be taken as rough approximations.
Additionally, lower values infer less congestion – in this case, the congestion pricing
strategy should be examined to see that it is encompassing the hours of the day that
truly merit such pricing, based on the context of this study.
This thesis is limited by the fact that elasticity estimates are assumed
equivalent across the entire traffic population and value of time estimates are assumed
equal across similar vehicle types. In actuality, this would not be the case, as not
everyone is affected in the same way. It is difficult, however, to take these factors
into account and, thus, this study should be viewed under hypothetical pretenses.
Based on the results set forth in this chapter, it is determined that vehicle users
with a lower combined value of time and vehicle operating cost experience the most
change with congestion pricing. Fewer of these users utilize the roadway after
congestion pricing is implemented – this shows that, among other things, these users
either change their driving habits to occur in off-peak hours or they switch to other
forms of transportation. Commercial truck operations and commuters lacking
flexible work schedules are significantly affected by congestion pricing. These users
have a fixed schedule and lack options other than paying the congestion charge.
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Chapter 5: Implementation
5.1 Overview
While previous chapters have centered on such topics as calculations and data
management, this chapter will focus on the logistics behind implementing a
congestion pricing system for the Capital Beltway. The optimization model
developed in this study can be seen as a “first-best” congestion pricing strategy, as
users realize their full congestion costs and roads are used most efficiently.
Unfortunately, congestion charges that vary in real-time based on actual conditions
are not practical at this point in time. For the sake of feasibility in the Washington,
D.C. area, a “second-best” congestion pricing solution must be examined, where
charges varying on an hourly scale instead of smoothly time-varying charges. When
demonstrating the model in Chapter 4, this was the methodology considered. Without
a system like this, where the general public can be aware of the charges in advance in
order to make an informed decision about their driving habits, acceptance will be
lacking. After a “second-best” system is implemented, more advances can be made
towards a gradual “first-best” solution.
It is important to note that under a congestion pricing scheme, charges should
bear some relationship to congestion costs imposed and vary by time of day and by
location. Ideally, the congestion price they should equal the imposed costs (as
calculated with the optimization model in this study). Instead of paying a flat fee
when passing a cordon, charges should be assessed as vehicles pass pricing points
setup along the roadway and calculated based on miles driven. As described
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previously, this strategy falls somewhere in the middle of these requirements – hourly
charges enacted on a per-mile basis.
5.2 Congestion Pricing Strategy
This congestion pricing strategy is largely based on a review of other
implemented systems. Obtained data from select locations of I-495 have been
assumed representative across the entire Capital Beltway due to lack of other data. It
should be noted that a more effective approach would be to analyze smaller sections
independently (i.e. split I-495 into a number of predefined zones) based on observed
data in those sections. The congestion charges, therefore, would vary by zone instead
of being assumed representative of the entire roadway. For example, areas exhibiting
traffic flow conditions much greater than calculated averages would be assigned
charges that are higher than those assigned to sections exhibiting lower traffic flow
conditions.
5.2.1 Hours of Operation
The proposed hours of operation for this congestion charging system are
6:00AM – 10:00AM and 2:00PM – 7:00PM. These timeframes encompass the
morning and evening peak periods on the Capital Beltway, as exhibited in Chapter 4.
The hourly extent of the PM peak period is greater than the AM peak, as represented
by the proposed hours of operation. Future iterations of a congestion charging
strategy could add an additional morning hour from 5:00AM – 6:00AM or implement
24-hour charging on I-495. This system will operate only on weekdays, excluding
federal holidays – equating a total of 251 days per year.
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5.2.2 Charges
Table 5-1 shows the hourly congestion charges for this system, in dollars per
PCE per mile. Corresponding charges for each of the 13 FHWA vehicle
classifications can be obtained by multiplying the charge by the PCE factors that were
presented in Chapter 3.
Table 5-1: Hourly Congestion Charges for I-495
Hour
Charge
($/PCE/mile)
12:00AM - 12:59AM
1:00AM - 1:59AM
2:00AM - 2:59AM
3:00AM - 3:59AM
4:00AM - 4:59AM
5:00AM - 5:59AM
NO CHARGE
6:00AM - 6:59AM 0.05
7:00AM - 7:59AM 0.08
8:00AM - 8:59AM 0.07
9:00AM - 9:59AM 0.06
10:00AM - 10:59AM
11:00AM - 11:59AM
12:00PM - 12:59PM
1:00PM - 1:59PM
NO CHARGE
2:00PM - 2:59PM 0.08
3:00PM - 3:59PM 0.07
4:00PM - 4:59PM 0.05
5:00PM - 5:59PM 0.04
6:00PM - 6:59PM 0.03
7:00PM - 7:59PM
8:00PM - 8:59PM
9:00PM - 9:59PM
10:00PM - 10:59PM
11:00PM - 11:59PM
NO CHARGE
These charges were calculated based on an assumed elasticity estimate of -0.2,
which was discussed previously in Chapter 2 and is based on theoretical studies and
implementation in Stockholm. After implementation, the actual elasticity in regards
to pricing could be obtained and the charges recalculated, accordingly.
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5.2.3 Goals
The main goal of this congestion pricing strategy is drawn from the research
objectives of this study. As travelers fail to realize their role in congestion, these
charges attempt to equal their contributed congestion costs to the traffic stream.
Secondary goals are operating a system that pays for itself and does not require
subsidies and improved traffic conditions, among others. These are not focal points
of the congestion pricing system, but are worth mentioning as potential positive
outcomes.
5.2.4 Conditions
As evident with other pricing systems that are in-place, special conditions
under the system must be addressed. Pricing systems are typically bogged down with
numerous exemptions and this proposed system attempts to stray away from that
scenario.
For this system, transit and emergency vehicles will be granted free access.
While this is not specifically addressed in this study, the costs of these vehicles would
be subsidized in some way. Additionally, low-income motorists may be eligible for
toll credits that could be used as assistance. Prerequisites for these credits would
need to be determined before implementation. Hybrid vehicle owners will not
receive any discounts, although more stringent charges for vehicles exerting higher
levels of pollution could be considered.
System shut-off conditions must also be in-place to accommodate unforeseen
scenarios. Examples of this have not been found in existing literature and could be
brought on by severe weather or traffic incidents, as examples. Under these special
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circumstances, the system would be shifted into “no-charge” mode and operated
accordingly until the roadway network regains normal operating conditions. A full
outline of potential system shut-off scenarios would be created before
implementation.
5.2.5 Payment Options
Multiple payment options will exist for users of the Capital Beltway. The
most efficient method, by far, will be a direct withdrawal from a user account, which
travelers stock with funds in advance via the Internet, mail, or telephone. This
method would be comparable to the E-ZPass toll system that exists in the northeast
United States. Other post-travel options will also include Internet, mail, and
telephone-based payments.
Charges accrued that are not tied to a user account will be required monthly,
with users receiving a bill. In this light, congestion charges could be likened to a
monthly cable or telephone bill. Although a monthly billing system would be in-
place, payments would be accepted at any point in time. For example, a user could
pay their total charge on a daily basis instead of waiting until the end of the month to
pay all of the charges that have accumulated. If timely payments are not made, the
user could be assessed a penalty amounting to 20% of the total owed.
5.2.6 Revenue Spending
Revenue spending is a key concern for any congestion pricing system. For the
purposes of this system, revenue will be first utilized to cover start-up and ongoing
costs – these costs are evaluated in the next chapter. After system costs are met,
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excess revenue can be applied to supporting public transit and road improvements,
with public transit being a priority. By utilizing the revenue in this manner, the
public will know that they are benefiting from the congestion charging in a tangible
way.
5.2.7 Technology
Until recently, technology was not readily available to operate the proposed
congestion pricing system. As the cost of equipment has decreased, complex and
efficient systems are now quite possible. With the technological advances that have
been made since the idea of congestion pricing originated, implementation of a
pricing system is now easier than ever before. The following two sections address the
technology proposed for the I-495 congestion pricing system.
5.2.7.1 Open Road Tolling
Open road tolling refers to the process of collecting tolls on a roadway
without the use of toll plazas, where drivers are charged appropriately without having
to stop or slow down. The major advantage to open road tolling is just that - users are
not required to slow down and are able to maintain their highway travel speed. Tolls
are typically collected using radio frequency identification (RFID) systems – the E-
ZPass system utilized in the northeastern United States is an example of this. Figure
5-1 shows a typical open road tolling gantry setup.
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Figure 5-1: Open Road Tolling Gantry
The slight disadvantage to open road tolling is the small possibility of equipment not
correctly identifying vehicles. More research is required in this area, but it is not
expected to severely impact systems utilizing this technology.
5.2.7.2 Enforcement/Collection
The enforcement and collection of applicable congestion charges will be
overseen by a system of electronic toll collectors and cameras running to video
recognition software. Open road tolling technology goes hand-in-hand with
electronic toll collection (ETC). ETC systems generally use transponders to
automatically debit pre-paid accounts of registered cars without having them stop or
slow down – this method is, by far, most efficient. Electronic toll collection systems
are based on four key components, all of which are automated. These are:
• Vehicle identification
• Vehicle classification
• Transaction processing
• Violation enforcement
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As an added incentive for drivers to obtain transponders, 10,000 of them will
be given away before implementation.
In the circumstances where drivers do not have a registered transponder,
enforcement cameras will photograph the vehicle's license plate. Optical recognition
software will be utilized to translate the images into text, which can then be searched
for in the database maintained by the Department of Motor Vehicles. An example of
such software, as used in London, is shown in Figure 5-2. Figure 5-3 shows a typical
camera setup for the charging system implemented in Stockholm.
Figure 5-2: License Plate Recognition Software (London)
Source: Murray-Clark
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Figure 5-3: Typical Gantry Camera Setup (Stockholm)
(Source: Vägverket)
5.2.8 Comparisons to Existing Systems
Two of the most notable pricing schemes in existence are located in London
and Stockholm. This section aims to briefly compare key components of these
systems to the proposed implementation.
The main difference is that this study’s charging strategy is based per-mile. In
both Stockholm and London, charges are collected at cordons around the city and no
charging is based on actual miles driven. The essence of congestion pricing is based
on location, time, and amount driven. Out of the three, only the proposed Capital
Beltway strategy takes all of these components into account.
In terms of operating hours, both London and Stockholm operate from the
beginning of the morning peak until the end of the evening peak, including the time
between. For I-495, only the peak period hours are part of the charging strategy, as
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traffic flows throughout the day are not yet great enough to merit charging as a means
to relieve congestion. As the system progresses, however, this is a natural expansion.
Both London and Stockholm utilize cameras with license plate recognition
systems in order to charge drivers. The I-495 system will primarily use electronic toll
collection through transponders, with cameras as a backup option for vehicles that are
not equipped with the necessary transponder.
Revenue spending is a key concern for any pricing strategy. London spends
most of the revenue gained from the system (after ongoing and operating costs are
deducted) on improved bus services within the city. Stockholm, on the other hand,
uses all revenue solely for road construction. It is generally regarded that public
transportation and roadway improvements should be obtained from excess revenue,
as the public can then see, first-hand, how the collected money is being spent. For
this reason, all revenue collected on I-495 after start-up and operating costs are
obtained will be dedicated to these sources.
As a final point, both the London and Stockholm systems are full of
exemptions and discount options for various types of vehicles and residents. The
strategy proposed in this study aimed to avoid this scenario and have as few
exemptions as possible.
5.3 Equity Considerations
A major concern of congestion pricing is that it is unfair to certain groups of
people. This argument stems from the belief that congestion pricing favors the rich,
as the poor are unable to afford the charges. This is actually not the case, as low-
income users of public transportation may benefit greatly from transit improvements
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brought about by collected revenue and the fact that public transit vehicles are
sanctioned for use within congestion pricing areas, so greater reliability and decreased
travel times could be expected. A well-designed pricing plan can be less burdensome
to low-income citizens than current systems that are based on regressive taxes, such
as car registration fees, sales taxes and the gas tax (FHWA 2001). Hypothetically,
congestion pricing can easily be shown to increase social welfare by making travelers
pay an amount closer to the full social costs resulting from their driving decisions
(Harrington 1998).
Most equity arguments are assuaged though proper revenue recycling, that is,
by creating a focused public benefit instead of what appears to just be a tax. The true
equity impact of any roadway pricing scheme depends heavily on how the revenues
are reused in the transportation system. Equity concerns can be offset by filtering
revenue into programs that benefit lower-income people, such as public transit or
potential pricing credits.
Paying directly for road usage is actually more equitable and efficient, since
users pay in proportion to the costs they impose. Uncharged facilities force everyone
to pay (through congestion), including motorists who reduce their vehicle use. Paying
directly gives individual consumers the savings that result when they drive less,
providing a new opportunity to save money. From a public welfare standpoint, under
congestion conditions, everyone is worse off, whereas under an efficient system,
society as a whole is better off. Congestion is a public “bad” that the government has
the ability to increase the cost of in order to discourage (Department of Legislative
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Services 2005). Moreover, everyone wins with better air quality and increased
mobility.
As with any situation, there will be perceived winners and losers in regards to
congestion pricing on the Capital Beltway. Before implementation, these potential
conditions must be considered and evaluated in order to possibly mitigate less-than-
positive scenarios. Furthermore, significant public transit options must be improved
before any such system can be implemented. Without acceptable public
transportation options for drivers, a congestion pricing system lacks true equity.
5.4 Policy Limitations and Recommendations
Politics can be the downfall of any congestion pricing initiative. Without
political support, no system can see the light of day. As for the Capital Beltway, an
entire-roadway congestion pricing system is far more feasible than, say, a cordon area
surrounding Washington, D.C. Due to the amount of travelers that enter the city for
employment, a move like this would be seen as a commuter tax and fought hard by all
suburban centers. Unlike London or Stockholm, the Capital Beltway region is
encompassed by three jurisdictions (Maryland, Virginia, and the District of
Columbia), in addition to the federal government. While politics may be a hurdle, it
is one worth handling for the long-term societal good.
In terms of policy suggestions specifically for this study, opinions were
gathered from Patrick DeCorla-Souza, the Team Leader for Highway Pricing and
System Analysis in the Office of Transportation Policy Studies and the Program
Manager for the Urban Partnership Program at the Federal Highway Administration
(FHWA) in Washington, D.C. Although it is out of the scope of this study, it was
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suggested that it would probably make more sense to start pricing the entire freeway
system in the area – not just the Capital Beltway; a key to success with congestion
pricing systems is the comprehensiveness of the pricing network. To make the
system truly work, other taxation should be eliminated, as the system revenue would
hopefully be enough to cover these costs – this way, the public would be far more
accepting of road pricing. Additionally, finding funding sources for expanded transit
options, telecommuting programs, and things of that nature are critical steps towards
congestion pricing. Finally, there are a few political selling points that should be
addressed. These are as follows:
• The congestion pricing system is a replacement of the current taxation
system
• The system is fair – drivers who use more pay more
• The system is efficient – travel delay is decreased or eliminated, the
economy is boosted, and freeway productivity loss is avoided
• The system is good for the environment – lowered emissions through less
idling, positive global warming effect, etc.
Martin Richards, an expert on the London pricing scheme, addressed some
key issues at the Transportation Research Board (TRB) 2008 Annual Meeting. For a
successful system, the media and general public must be well-informed in advance of
any implementation. If this aspect is lacking, the public and media will come to
incorrect conclusions about the system and it then becomes easier for those opposed
to propagate misleading information – thus, rational discussion about the topic is
difficult. The success of system implementation is based on creating a clear vision,
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providing a clear execution pathway, strong leadership that won’t back down or
retract, and total and consistent commitment to the cause.
Lastly, there are multiple perspectives that should be reflected in any
congestion pricing system to ensure effectiveness and fairness – those of the users,
traffic authority, and society. The proposed system in this study addresses these
perspectives, but further examination should be done for each. An outline of
recommended principles for each perspective is as follows (Victoria Transport Policy
Institute 2007):
From the perspective of the user, a congestion pricing system should be easy
to understand, convenient (i.e. does not require vehicles to stop at toll booths), viable
transportation options should exist (i.e. alternative modes, travel times, routes, and
destinations), multiple easy-to-use payment options should exist (i.e. cash, prepaid
card, credit card, etc.), charges should be evident before a trip is undertaken, and the
privacy of users should be assured.
From the perspective of the traffic authority, a congestion pricing system
should consider traffic impacts (vehicles should not be required to stop at toll booths
or delay traffic in other ways), efficient and equitable charges should reflect true user
costs, the system should be effective in reducing traffic congestion and other
transportation problems by changing travel behavior, occasional users and different
vehicle types should be easily accommodated, minimal incorrect charges should
occur, minimal fraud or non-compliance should occur, there should be a positive
return on the system investment (i.e. cost effectiveness), there should be minimal
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disruption during any development phase, and the implementation should be available
for expansion, as needed.
From the perspective of society, a congestion pricing system should have
positive net benefits when all impacts are considered, political acceptability (i.e.
public perception of fairness and value), positive environmental impacts, and the
same integrated charging system should be able to be used to pay other public service
fees (i.e. parking, public transit, etc.).
5.5 Summary
In this chapter, the logistics behind implementing a congestion pricing system
for the Capital Beltway were presented. Effective between weekday hours of 6AM
and 10AM and 2PM and 7PM, the morning and evening peak periods on I-495 are
included. As noted, potential future iterations of a pricing system could expand the
hours of operation or switch to 24-hour pricing. In this study, the charges attempt to
cause roadway users to equal their contributed congestion costs to the traffic stream.
While other implementations are bogged down with exemptions and
discounts, the conditions of this study were relatively straightforward. Transit and
emergency vehicles will be granted free access and low-income users may be eligible
for travel credits. Multiple payment options via the Internet, mail, and telephone will
be available to travelers. System revenue will be first utilized to cover start-up and
ongoing costs. Afterward, excess revenue will be applied to supporting public transit
and road improvements, with public transit being a priority.
Equity considerations must be taken extremely seriously (through revenue
spending, etc.) and it must be realized that policy limitations exist. In order for a
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congestion pricing system to be taken seriously, citizens must believe that the system
is a replacement of the current taxation system, the system is fair (i.e. drivers who use
more pay more), the system is efficient (i.e. travel delay is decreased or eliminated,
the economy is boosted, and freeway productivity loss is avoided), and that the
system is good for the environment. Additionally, pricing on only I-495 is not a
likely option. If pricing were to exist on roadways in the Washington, D.C. area, it
should be implemented on all major roadways (I-495, I-270, I-70, I-95, etc.).
The financial implications for the proposed I-459 congestion pricing system
are presented in the next chapter.
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Chapter 6: Financial Implications
6.1 Costs
In the following sections, estimated cost information for the proposed Capital
Beltway congestion pricing system is provided.
6.1.2 Scenarios Examined
Two potential open road tolling/electronic toll collection setups were
considered in this study. Both involved overhead gantry systems, but differed in cost
due to the layout of the gantries. The premise of this system is that vehicles are
“tracked” at each gantry and if they don’t reach the next gantry within a certain time
(i.e. they exit I-495), their charge is calculated – this amount of time will have to
reflect possible congestion or other occurrences and is not the focus of this thesis.
The two strategies were as follows:
• Gantry setup directly on I-495 – across all four lanes in each direction
• Gantry setup on entrance and exit ramps to/from I-495 – gantries ranging
from 1- to 3-lanes for each entrance and exit ramp
Figures 6-1 and 6-2 show each of these layouts overlaid on the same I-495
interchange.
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Figure 6-1: I-495 Gantry Setup (Direct)
Figure 6-2: I-495 Gantry Setup (Entrance and Exit Ramps)
Using these two layout scenarios, cost information was estimated. The
Research and Innovative Technology Administration of USDOT operates a cost-
estimate database. The fairly recent study of I-75 and I-575 in Atlanta provided some
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cost estimates of not only gantries, but also all facets of project implementation for
HOT lanes – the cost estimate aspects of design, construction, maintenance, and
operation were extrapolated from their estimates for the components necessary for the
proposed congestion pricing system on I-495. Table 6-1 presents the system cost
breakdown for I-495 extrapolated from the USDOT database. Also factored into this
table are the yearly operating costs, which will be discussed later. These categories
are used for both potential scenarios.
6.1.2.1 Gantry Setup on I-495
Using a gantry setup directly on I-495 entails, on average, four 4-lane gantries
at each interchange. The reasoning behind this is that gantries cannot be placed only
before or after entrances and exits – they must be placed both before and after these
points in order to account for all vehicles. Using roadmaps, satellite imagery, and
general knowledge of the region, it is estimated that a total of 166 4-lane gantries
would be required for this scenario – 106 in Maryland and 60 in Virginia. As some
calculations deal with a per-lane basis, this equates to 664 total lanes – 424 in
Maryland and 240 in Virginia.
Using these costs, the proposed system setup on I-495 with gantries directly
on I-495 would be estimated at $58,066,275 – $35,730,075 in Maryland and
$22,336,200 in Virginia.
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Table 6-1: I-495 System Costs
Category Description Notes Cost ($)
Gantry structure - 4 lanes - 75000
Gantry structure - 3 lanes - 65000
Gantry structure - 2 lanes - 60000
Gantry structure - 1 lane - 30000
Toll & communication equipment building 1 per exit 30000
Electronic toll collection (ETC) reader 1 per gantry 4000
Transceiver 1 per gantry 3500
ETC reader controller 1 per gantry 4000
ETC power supply 1 per gantry 250
Camera 1 per gantry 3500
Camera power supply 1 per gantry 250
Image processor per state 6500
Optical character recognition (OCR) server per state 7000
OCR software/interface per state 60000
Vehicle detection sensor 1 per lane/per gantry 4500
Software, interface support, engineering support, and
documentation per state 12000
Lane controller 1 per gantry 12500
Lane cabinet and electronics 1 per gantry 6500
Lane software per state 200000
Variable message sign (approximately one per exit) 1 per exit 60000
Fixed overhead signs on gantry 1 per gantry 10000
Network equipment/connections per state 200000
Power - breaker panel 1 per exit 2000
Power - UPS & battery cabinet 1 per exit 5000
Power - conduit/wiring 1 per exit 20000
Power - disconnect & bypass switch 1 per gantry 3500
Power - generator unit 1 per exit 6500
Power - generator wiring 1 per exit 2000
Contingencies 25% of above total
Mobilization 10% of subtotal
Construction
Construction total All of the above
Design Engineering
and Administration
Design engineering and admin 20% of construction total
Host server and data storage per state 150000
Database software and licenses per state 50000
Host software per state 200000
System applications software per state 400000
Maintenance management per state 200000
Various other computer equipment per state 200000
Installation and configuration support per state 20000
Transponders (100,000 free units to commuters) split 50% 2500000
Customer service center per state 2000000
Capital Cost for
Operations
Capital cost for operations total All of the above
Maintenance costs (per year) 10% of capital costs
Transaction processing charge ($0.12 per transaction) -
85,000,000 transactions per year
split 50% 10200000 Yearly Costs
Yearly total All of the above
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6.1.2.2 Gantry Setup on Entrance and Exit Ramps
Using a gantry setup on I-495 entrance and exit ramps entails gantries ranging
from 1- to 3-lanes on each entrance and exit ramp to account for all vehicles entering
or exiting the roadway. Using roadmaps, satellite imagery, and general knowledge of
the region, it is estimated that the following gantries would be required for this
scenario:
Table 6-2: Gantry Totals on Entrance and Exit Ramps
1-lane 226
2-lane 15
Total
3-lane 3
1-lane 139
2-lane 7
Maryland
3-lane 3
1-lane 87
2-lane 8
Virginia
3-lane 0
As some calculations deal with a per-lane basis, this equates to 265 total lanes – 162
in Maryland and 103 in Virginia.
Using these costs, the proposed system setup on I-495 with gantries on I-495
entrance and exit ramps would be estimated at $53,732,550 – $ 31,968,075 in
Maryland and $21,764,475 in Virginia.
6.1.3 Chosen Scenario
Based on the cost estimates provided in the previous sections, a gantry setup
on I-495 entrance and exit ramps is the most cost-effective option. This presents a
significant cost savings of $4,333,725 compared to using a gantry setup directly on I-
495.
89
6.2 Revenue
In order to calculate revenue, the assumed flow during each hour of the
congestion pricing strategy is based on average flow across all detectors providing
data for that hour in 2007. The optimization model was run using these average flows
in order to determine the new flows that can be expected during each hour to provide
revenue estimates. Since no I-495 data is collected on average miles driven per
vehicle on I-495 during each peak period, National Household Travel Survey (NHTS)
data were analyzed to obtain estimates. Based on the NHTS 2001 trip information for
the United States, the data were split into 1-mile increments ranging from one mile to
thirty-two miles. This is based on the assumptions of a distance of one mile between
any two exits on the Capital Beltway and the fact that people will hypothetically
travel along one-half of the 64-mile long roadway, at a maximum. Even though this
method is not entirely precise, it is far more realistic in terms of potential revenue
estimation than splitting up mileage level groups evenly based on traffic flow. Figure
6-3 plots the frequency distribution of trip distances that will be applied to I-495.
90
Distribution of Trip Distances
0.000
0.020
0.040
0.060
0.080
0.100
0.120
0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32
Miles Driven
F
r
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q
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e
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c
y
Figure 6-3: Distribution of Trip Distances
Source: NHTS 2001
In applying these trip distribution frequencies to the Capital Beltway, many
assumptions were made. First, traffic in the Washington, D.C. area was assumed
similar to the nationwide traffic represented in the NHTS data. Additionally, it was
assumed that one-way trips on I-495 have the same trip distribution frequencies as
full trips (from beginning to end) at the national level. This is a large assumption, due
to the fact that travel on the Capital Beltway is only a portion of the commute
experienced by travelers. Regardless of the number of assumptions, national trip
distribution frequencies provide a much better estimation than uniform frequency
estimates for each distance.
By using the applicable hourly charges presented in this study and the
corresponding hourly flows and frequency estimates, daily revenue can be calculated.
As an example of how this calculation was accomplished, for the 6:00AM - 6:59AM
91
hour, the hourly flow on I-495 averages 1,598 PCE/lane/hour. Once congestion
pricing is implemented, the hourly flow is expected to drop to 1,550 PCE/lane/hour
and the associated charge is $0.05 per PCE per mile. The frequency of vehicles
traveling 1.5 miles on I-495 is 0.099. This results in 153 vehicles paying $0.05 per
mile for 1.5 miles – a total of roughly $11.48 for that portion of traffic (traveling in
one direction) during that hour. Similar calculations are then made for each of the 32
mileage ranges for the same hour and then for every operating hour afterwards. Daily
and yearly revenue estimates can then be obtained.
The total revenue per day for I-495 (in both directions) is estimated to be
$60,282.63. A total of 251 charging days per year equates to a yearly revenue
estimate of $15,130,939.61.
6.3 Break-Even Points/Payoff Calculations
In order to determine system break-even points and payoff calculations, the
system costs were examined over a 50-year period. Taking into account the yearly
costs of operation and maintenance, along with a 10-year equipment lifespan, these
yearly amounts were determined. After 10 years, it is assumed that 50% of the initial
system costs will be required to update the system, as some existing structure remains
usable. After 20 years, however, a complete system overhaul is required. Table 6-3
shows the yearly cumulative costs for the I-495 congestion pricing system. Similarly,
cumulative revenue estimates were made over a 50-year period (Table 6-4), assuming
constant yearly revenue. Payoff is equal to cumulative revenue divided by
cumulative cost for a given year and all estimates are kept in 2007 dollars to provide
easy comparison into the future.
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Table 6-3: I-495 System 50-Year Cumulative Costs
Description Year Cumulative Cost (2007 $)
Setup costs - 53732550
After 1 year of operation 1 64826550
After 2 years of operation 2 75920550
After 3 years of operation 3 87014550
After 4 years of operation 4 98108550
After 5 years of operation 5 109202550
After 6 years of operation 6 120296550
After 7 years of operation 7 131390550
After 8 years of operation 8 142484550
After 9 years of operation 9 153578550
After 10 years of operation (equipment lifespan) 10 164672550
After 11 years of operation 11 202632825
After 12 years of operation 12 213726825
After 13 years of operation 13 224820825
After 14 years of operation 14 235914825
After 15 years of operation 15 247008825
After 16 years of operation 16 258102825
After 17 years of operation 17 269196825
After 18 years of operation 18 280290825
After 19 years of operation 19 291384825
After 20 years of operation (2 equipment lifespans) 20 302478825
After 21 years of operation 21 367305375
After 22 years of operation 22 378399375
After 23 years of operation 23 389493375
After 24 years of operation 24 400587375
After 25 years of operation 25 411681375
After 26 years of operation 26 422775375
After 27 years of operation 27 433869375
After 28 years of operation 28 444963375
After 29 years of operation 29 456057375
After 30 years of operation (3 equipment lifespans) 30 467151375
After 31 years of operation 31 505111650
After 32 years of operation 32 516205650
After 33 years of operation 33 527299650
After 34 years of operation 34 538393650
After 35 years of operation 35 549487650
After 36 years of operation 36 560581650
After 37 years of operation 37 571675650
After 38 years of operation 38 582769650
After 39 years of operation 39 593863650
After 40 years of operation (4 equipment lifespans) 40 604957650
After 41 years of operation 41 669784200
After 42 years of operation 42 680878200
After 43 years of operation 43 691972200
After 44 years of operation 44 703066200
After 45 years of operation 45 714160200
After 46 years of operation 46 725254200
After 47 years of operation 47 736348200
After 48 years of operation 48 747442200
After 49 years of operation 49 758536200
After 50 years of operation (5 equipment lifespans) 50 769630200
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Table 6-4: I-495 System 50-Year Cumulative Revenue
Year Annual Revenue (2007 $) Cumulative Revenue (2007 $) Payoff %
1 15130939.61 15130939.61 0.233
2 15130939.61 30261879.23 0.399
3 15130939.61 45392818.84 0.522
4 15130939.61 60523758.46 0.617
5 15130939.61 75654698.07 0.693
6 15130939.61 90785637.68 0.755
7 15130939.61 105916577.30 0.806
8 15130939.61 121047516.91 0.850
9 15130939.61 136178456.53 0.887
10 15130939.61 151309396.14 0.919
11 15130939.61 166440335.76 0.821
12 15130939.61 181571275.37 0.850
13 15130939.61 196702214.98 0.875
14 15130939.61 211833154.60 0.898
15 15130939.61 226964094.21 0.919
16 15130939.61 242095033.83 0.938
17 15130939.61 257225973.44 0.956
18 15130939.61 272356913.05 0.972
19 15130939.61 287487852.67 0.987
20 15130939.61 302618792.28 1.000
21 15130939.61 317749731.90 0.865
22 15130939.61 332880671.51 0.880
23 15130939.61 348011611.13 0.893
24 15130939.61 363142550.74 0.907
25 15130939.61 378273490.35 0.919
26 15130939.61 393404429.97 0.931
27 15130939.61 408535369.58 0.942
28 15130939.61 423666309.20 0.952
29 15130939.61 438797248.81 0.962
30 15130939.61 453928188.42 0.972
31 15130939.61 469059128.04 0.929
32 15130939.61 484190067.65 0.938
33 15130939.61 499321007.27 0.947
34 15130939.61 514451946.88 0.956
35 15130939.61 529582886.50 0.964
36 15130939.61 544713826.11 0.972
37 15130939.61 559844765.72 0.979
38 15130939.61 574975705.34 0.987
39 15130939.61 590106644.95 0.994
40 15130939.61 605237584.57 1.000
41 15130939.61 620368524.18 0.926
42 15130939.61 635499463.79 0.933
43 15130939.61 650630403.41 0.940
44 15130939.61 665761343.02 0.947
45 15130939.61 680892282.64 0.953
46 15130939.61 696023222.25 0.960
47 15130939.61 711154161.87 0.966
48 15130939.61 726285101.48 0.972
49 15130939.61 741416041.09 0.977
50 15130939.61 756546980.71 0.983
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This revenue estimation is used, along with other potential scenarios involving
yearly revenue growth, to plot system payoff potential over time. Figure 6-4
showcases the results.
System Payoff Over Time (Using Average Revenue Estimates)
0.000
0.200
0.400
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1.000
1.200
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%
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Constant Revenue 0.5% Growth 1.0% Growth 1.5% Growth 2.0% Growth 2.5% Growth Break-Even
Figure 6-4: Yearly I-495 System Payoff
Looking at system payoff time based on different estimates of yearly revenue
growth produces interesting results. The following can be seen:
• Assuming constant revenue, the system pays for itself every 20 years, but
doesn't ever become profitable
• Assuming a 0.5% growth in revenue every year, the system becomes
profitable after 27 years
• Assuming a 1.0% growth in revenue every year, the system becomes
profitable after 24 years
95
• Assuming a 1.5% growth in revenue every year, the system becomes
profitable after 15 years
• Assuming a 2.0% growth in revenue every year, the system becomes
profitable after 14 years
• Assuming a 2.5% growth in revenue every year, the system becomes
profitable after 12 years
As the proposed system at least breaks even with no ongoing debt, it is in the
common good.
6.4 Assumptions and Conclusions
As with other sections of this study, certain assumptions were required to
obtain cost and revenue estimates. First, HOT project estimates from the USDOT
Research and Innovative Technology Administration were assumed representative of
cost estimates for this congestion pricing system. Implementing a HOT lane is
different than an entire-facility system, so this fact was taken into account with the
cost estimates. Secondly, for cumulative cost estimates, 50% rebuild costs were
assumed at 10 years and complete system rebuild costs were assumed at 20 years –
this was based on the fact that the system equipment has a projected lifespan of 10
years. Lastly, NHTS trip data was assumed representative of one-way trips on I-495.
This data was utilized assuming a distance of one mile between any two exits on I-
495 and the fact that people will hypothetically travel one-half of the 64-mile long
Beltway, as a maximum. As stated previously, even though this method is not
entirely precise, it is far more realistic in terms of potential revenue estimation than
splitting up mileage level groups evenly based on traffic flow.
96
Due to the fact that charges have been estimated to be lower than previous
research indicates, revenue figures have also been underestimated. In light of this
situation, a congestion pricing system in the Washington, D.C. area could potentially
exhibit faster turnaround and pay for itself in fewer years. Excess revenue could then
be spent on public transportation improvements in the area.
97
Chapter 7: Conclusions and Recommendations
7.1 Summary of Results
Road users must be held accountable for the true cost of highways. As travel
is free on the Capital Beltway surrounding Washington, D.C., there is no current
financial incentive to utilize public transportation, alter the timing of necessary trips,
reduce unnecessary trips, or increase carpooling. This thesis aimed to hold users of I-
495 accountable for their role in congestion by calculating appropriate congestion
charges on a per-mile basis. The goal of this thesis was to calculate the appropriate
charges required for users of I-495 in order to fulfill their portion of congestion costs.
This goal was reached within the study, as a model was developed from
existing data on the Capital Beltway that showcases traffic characteristics that cause
congestion, necessary charges for vehicle users to realize the congestion costs that
their vehicles impose on the rest of the traffic stream were calculated, and potential
financial implications (costs and revenue) that would be associated with congestion
pricing were examined.
AM peak period charges ranging from $0.05 to $0.08 per PCE per mile cause
drivers to realize their contribution to congestion and charges ranging from $0.03 to
$0.08 per PCE per mile in the PM peak period accomplish the same. Tables breaking
these charges down across FHWA vehicle classifications were shown in Chapter 4,
along with summaries of anticipated traffic composition after implementing a
congestion pricing system on I-495. These estimates are lower than those based on
prior research, where efficient peak-hour congestion charges have been calculated to
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be between $0.08 and $0.50 per mile. This discrepancy in charging amounts can
most likely be associated with additional factors that were not taken into account in
this study. Chapter 6 showed that the proposed system with constant revenue will be
able to pay for itself with no yearly subsidy required. If revenue increases are
obtained, however, the system will both pay for itself and provide excess funds for
use in transit improvements or minor roadway improvements. Additionally, since the
charging estimates set forth in this thesis may be considered conservative
approximations, a congestion pricing system on the Capital Beltway may be more
cost effective than this study shows, with the system paying for itself in less time.
7.2 Conclusions
As mentioned previously, the proposed congestion system for the Capital
Beltway is a "second-best" solution – containing charges varying on an hourly scale
instead of smoothly time-varying charges. We are a long way from a potential "first-
best" solution, with congestion charges varying in real-time based on actual
conditions, as such a system is not practical at this point in time. Based on this fact,
any solution is better than no solution – a Washington, D.C. area congestion pricing
system needs to start somewhere. This study provides a good building block to the
positives of congestion pricing, but there is still much ground to be covered.
Although this study is a, more-or-less, hypothetical scenario, hopefully it can
pave the way for future discussion and research into facility-wide per-mile pricing
systems in the United States. Based on the results of this study, the charges necessary
for people to realize their congestion costs are not exorbitant. Education is key to
enlightenment, however, as most people truly fail to realize how paying for
99
something like road usage can be more beneficial for society. Proponents of
congestion pricing must increase their public education efforts in hopes to gain
further support. Through all of this, we must all also realize that there is not one
perfect solution for congestion management – all available options must be
considered, including transit advancements and pricing.
7.3 Recommendations for Future Research
In closing, as there remains much ground for future research, the following
suggestions are made:
1. The entire regional freeway system should be examined in light of this
study, not just the Capital Beltway – network comprehensiveness is a
critical component of a successful congestion pricing strategy
2. Based on the lack of data for this study, more functioning traffic detectors
are needed to collect valid speed, volume, and vehicle classification data –
new sensor installations along with updates to the existing sensor network
are necessary to gather more precise data. Additionally, data collection
standards should exist for comprehensiveness between jurisdictions. In
terms of costs, discussion with various transportation professionals has
provided that installation costs for a fixed sensor network are estimated
between $7,500 and $20,000 per site. The range in cost is due primarily to
the extent to which existing infrastructure can be reused. Reuse of
existing poles, sign trusses, and existing power and communications feeds
reduce cost. Methods and technology that allow for reuse of existing
100
infrastructure, though more expensive, may prove to be the more cost
effective option overall.
3. Congestion charging based on smaller time increments (or even real-time)
would require data in much smaller increments instead of the hourly
aggregations utilized in this study – various charging options should be
evaluated.
4. Instead of utilizing NHTS data to estimate one-way trips during AM and
PM peaks on I-495, surveys could be conducted in order to have a more
precise estimate of revenue possibilities.
5. This study focused on gantries, cameras, and license plate reader
technology, as costs were able to be obtained. Different technology may
be cheaper and easier to install – for example, charges related to mileage
driven in a priced region may be assessed by utilizing in-vehicle units
(IVUs), such as those in-place in Singapore, with no need for gantries or
cameras.
6. User value of time and vehicle operating cost estimates could be evaluated
more precisely instead relying on FHWA estimates – future surveys and
experiments could be conducted to gather this data.
7. While this study focuses on charging across all lanes on the Capital
Beltway, a similar analysis could be accomplished using a HOT lane
setup, like those being constructed in the region.
101
8. Environmental costs such as air pollution caused by idling vehicles were
not considered in this thesis – special attention should be focused on
various environmental costs for future work.
9. A variation of this study could be focused on finding the number of
vehicles that need to be removed from a traffic stream at a given time in
order to reach a certain level of service (LOS), average speed, or some
other performance metric. Using a revised version of this model,
corresponding pricing can be set in order to reach these traffic volume
goals.
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Appendix
Avg. Hourly Speed - Link 90138
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Avg. Hourly Speed by Year - Link 90138
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Avg. Hourly PCE Flow - Link 90138
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V/C Ratio - Link 90138
I-495 Capacity = 2,350 pc/ln/hr
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Avg. Hourly Speed - Link 90202
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Avg. Hourly Speed by Year - Link 90202
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Figure A-7: Average Hourly Speed by Year – Detector 90202
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Avg. Hourly PCE Flow by Year - Link 90202
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Figure A-9: Average Hourly Flow by Year – Detector 90202
V/C Ratio - Link 90202
I-495 Capacity = 2,350 pc/ln/hr
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Avg. Hourly Speed - Link 90275
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Avg. Hourly Speed by Year - Link 90275
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Avg. Hourly PCE Flow - Link 90275
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V/C Ratio - Link 90275
I-495 Capacity = 2,350 pc/ln/hr
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Avg. Hourly Speed by Year - Link 190004
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Avg. Hourly PCE Flow by Year - Link 190004
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Figure A-19: Average Hourly Flow by Year – Detector 190004
V/C Ratio - Link 190004
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Figure A-21: Average Hourly Speed – Detector 190057
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20.00
30.00
40.00
50.00
60.00
70.00
80.00
2005 2006 2007
Year
S
p
e
e
d
(
m
p
h
)
12AM 1AM 2AM 3AM 4AM 5AM 6AM 7AM 8AM 9AM 10AM 11AM
12PM 1PM 2PM 3PM 4PM 5PM 6PM 7PM 8PM 9PM 10PM 11PM
Figure A-22: Average Hourly Speed by Year – Detector 190057
113
Avg. Hourly PCE Flow - Link 190057
0
500
1000
1500
2000
2500
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
Hour of Day
P
C
E
F
l
o
w
2003
2005
2006
2007
Figure A-23: Average Hourly Flow – Detector 190057
Avg. Hourly PCE Flow by Year - Link 190057
0
500
1000
1500
2000
2500
2003 2005 2006 2007
Year
P
C
E
F
l
o
w
12AM 1AM 2AM 3AM 4AM 5AM 6AM 7AM 8AM 9AM 10AM 11AM
12PM 1PM 2PM 3PM 4PM 5PM 6PM 7PM 8PM 9PM 10PM 11PM
Figure A-24: Average Hourly Flow by Year – Detector 190057
114
V/C Ratio - Link 190057
I-495 Capacity = 2,350 pc/ln/hr
0.00
0.10
0.20
0.30
0.40
0.50
0.60
0.70
0.80
0.90
1.00
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
Hour of Day
V
/
C
R
a
t
i
o
2003
2005
2006
2007
Figure A-25: Hourly Volume-to-Capacity Ratio – Detector 190057
115
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