Description
Abstract explain flight schedule punctuality control and management a stochastic approach.
Transportation Planning and Technology, August 2003
Vol. 26, No. 4, pp. 313–330
FLIGHT SCHEDULE PUNCTUALITY
CONTROL AND MANAGEMENT: A
STOCHASTIC APPROACH
CHENG-LUNG WU
a
and ROBERT E. CAVES
b
a
Department of Aviation, University of New South Wales, Sydney, NSW 2052,
Australia;
b
Transport Studies Group, Department of Civil and Building
Engineering, Loughborough University, Loughborough LE11 3TU, United
Kingdom
(Received 22 January 2001; In ?nal form 10 October 2003)
The insuf?ciency of infrastructure capacity in an air transport system is usually blamed
for poor punctuality performance when implementing ?ight schedules. However,
investigations have revealed that ground operations of airlines have become the second
major cause of ?ight delay at airports. A stochastic approach is used in this paper to
model the operation of aircraft turnaround and the departure punctuality of a turnaround
aircraft at an airport. The aircraft turnaround model is then used to investigate the
punctuality problem of turnaround aircraft. Model results reveal that the departure
punctuality of a turnaround aircraft is in?uenced by the length of scheduled turnaround
time, the arrival punctuality of inbound aircraft as well as the operational ef?ciency of
aircraft ground services. The aircraft turnaround model proposed is then employed to
evaluate the endogenous schedule punctuality of two turnaround aircraft. Model results,
when compared with observation data, show that the operational ef?ciency of aircraft
ground services varies among turnarounds. Hence, it is recommended that the improve-
ment of departure punctuality of turnaround aircraft may be achieved from two
approaches: airline scheduling control and the management of operational ef?ciency of
aircraft ground services.
Keywords: Airlines; Airports; Aircraft operations; Schedule punctuality; Stochastic
models
1. INTRODUCTION
Poor schedule punctuality costs passengers, airports and airlines a
considerable amount of money. The insuf?ciency of infrastructure
ISSN 0308-1060 print: ISSN 1029-0354 online © 2003 Taylor & Francis Ltd
DOI: 10.1080/03081060310001635869
314 C.-L. WU AND R.E. CAVES
capacity, which includes airport and airspace capacity, is usually
blamed for poor schedule punctuality in the air transport system when
implementing ?ight schedules. However, a rigorous investigation
into the punctuality issue at London Gatwick Airport revealed that
airport and air traf?c control (ATC) related reasons were responsible
for 53% of total delayed ?ights [1]. The other delay causes resulted
from poor airline services and aircraft ground operations at airports.
61% of ?ights delayed by airline operations resulted in more than
20 minutes delay, while only 39% of ?ights were delayed by
more than 20 minutes due to airport and ATC reasons during the
period of investigation. A con?dential review paper available to the
authors from a European air carrier also drew similar conclusions as
those in the report by the European Civil Aviation Community
(ECAC).
After understanding the causes of poor punctuality in the air
transport system, airlines such as Lufthansa and Austrian Airlines have
task-force projects to improve schedule punctuality [2]. It is generally
realized in the airline industry that good management of aircraft
rotation improves the punctuality of ?ight schedules and also saves
delay-related costs of airlines. Although hard evidence is not available
from the industry, it is generally believed that good control of aircraft
turnaround operation and aircraft rotational strategies maintain the
competitive edge of low-cost airlines in the European aviation market
[3].
The ?ight schedule punctuality problem has generally been
approached in the literature by conventional statistic analyses, which
can only provide basic information about punctuality instead of
reasons why aircraft are delayed ([4]). It is hypothesized in this paper
that the endogenous schedule punctuality has been set after a ?ight
schedule is designed by an airline. In other words, the hypothesis is
that it is feasible for an airline to manage schedule punctuality by
optimizing its ?ight schedules and utilizing available resources.
It is apparent from the literature that the aircraft turnaround problem
has been mainly investigated using the Critical Path Method (CPM)
[5]. This method is usually employed to study an operational
procedure consisting of several work ?ows in order to identify critical
paths in the operation. Hence, CPM is commonly used by airlines to
investigate the turnaround procedure of aircraft because of the
complexity of the aircraft turnaround operation. In addition to CPM,
stochastic models have also been developed to model the uncertainty
of aircraft punctuality performance and airport gate occupancy time
315 FLIGHT SCHEDULE PUNCTUALITY
[6]. However, the stochastic model proposed in the literature captures
only the stochastic effects from arrival punctuality of inbound aircraft
without considering possible in?uences of operational disruptions on
the aircraft turnaround process.
The aim of this paper is to approach the ?ight schedule punctuality
problem from a more complete stochastic point of view. Stochastic
theories are used to model the departure punctuality of a turnaround
aircraft to account for uncertainties involved in the implementation of
?ight schedules. The aircraft turnaround process is simulated by a
turnaround model to represent the operational ef?ciency of aircraft
ground services. The turnaround model is then used to evaluate the
departure punctuality of turnaround aircraft under current ?ight sched-
ules. Operational strategies of schedule punctuality management are
discussed in this paper in two aspects, namely airline scheduling
control and the management of operational ef?ciency of aircraft
ground services. Two case studies are carried out using ?ight data
from a European airline to demonstrate the effectiveness of the aircraft
turnaround model.
The paper is organized into six sections. The aircraft turnaround
model is described succinctly in Section 2. The application of the
turnaround model is given in Section 3, Model Applications. Case
studies are given in Section 4, and discussions of schedule punctuality
management are shown in Section 5, Strategies for Punctuality Man-
agement. Concluding remarks are drawn in the ?nal section.
2. AIRCRAFT TURNAROUND MODEL
2.1. De?nitions and Terminology of Aircraft Turnaround
The ‘turnaround’ of an aircraft at an airport gate is de?ned as the
procedure to provide required services (such as catering, cabin clean-
ing and fuelling) to an aircraft in order to carry out a following ?ight
to another airport. Delays measured in this paper are based on the
scheduled time of arrival (STA), i.e., the on-chock time, and the
scheduled time of departure (STD), i.e. the off-chock time, of a
turnaround aircraft. The duration between STA and STD is de?ned as
the ‘scheduled ground time/scheduled turnaround time’ (denoted by
T
SG
in equation (1)) which consists of the ‘standard aircraft ground
service time’ (denoted by T
G
) and the ‘schedule buffer time’ (denoted
by T) as shown in equation (2). The schedule buffer time in the ground
316 C.-L. WU AND R.E. CAVES
time of a turnaround aircraft is usually designed to accommodate
potential delays from late inbound aircraft and delays from aircraft
turnaround operation. ‘Ground services’ of an aircraft include all
necessary services, e.g., cabin cleaning, engineering check, aircraft
fuelling, for an aircraft to carry out a following ?ight [7].
STD?STA?T
SG
(1)
T
SG
?T?T
G
(2)
2.2. Aircraft Turnaround Model
A mathematical model is developed in this paper to simulate aircraft
turnaround operations. The aircraft turnaround model is based on the
formulation of the stochastic departure punctuality of a turnaround
aircraft in terms of schedule buffer time (T) and the operational
ef?ciency of aircraft ground services (m
2
). The objective of this model
is to minimize system costs (C
T
), which include passenger delay costs
(C
P
), aircraft delay costs (C
A
) and the schedule time cost of an airline
(C
AL
). A longer ground time for a turnaround aircraft maintains the
required punctuality for a turnaround aircraft, though it reduces the
productivity of an aircraft. The dilemma between schedule punctuality
and aircraft productivity faced by an airline is modelled in the pro-
posed turnaround model by a weight factor, . The formulation of the
aircraft turnaround model is summarized by equations (3) to (10) [8].
To minimize C
T
:
C
T
?C
D
?(1 ?)C
AL
(3)
where
0 ??1 (4)
C
D
?E[C
u
(s)] ??C
u
(s)g(s)ds (5)
C
u
(s) ?C
p
(s) ?C
A
(s) (6)
C
AL
(T) ??C
m
AL
(T?T
A
)dT (7)
g(s) ?F[f(t), T, m
2
]*?J
s
? (8)
s ?m
1
*(t ?T
A
) T
A
?t ?T (9)
s ?m
1
*(T?T
A
) ?m
2
*(t ?T) T?t ?T
max
(10)
where m
1
?(m
2
/T
max
?T
A
)*(T
max
?T) T
A
?T?T
max
317 FLIGHT SCHEDULE PUNCTUALITY
The objective function in equation (3) is formulated to minimize the
system cost of a turnaround aircraft, which includes the expected delay
cost of an aircraft and on-board passengers (denoted by C
D
) and the
opportunity cost of schedule buffer time of an aircraft (denoted by
C
AL
). The delay cost functions of passengers (C
P
in equation (6)) and
the delay cost of an aircraft (C
A
in equation (6)) are both assumed to
be linear with respect to delay duration (s), though more general forms
may be used in this model. It is generally realized that the schedule
time opportunity cost becomes higher when the saved schedule time
becomes long enough for an aircraft to carry out an additional ?ight.
Hence, the airline schedule time cost C
AL
(T) in equation (7) is assumed
to have a linear marginal cost function to account for an increasing
opportunity cost when the schedule buffer time of a turnaround aircraft
increases and consequently C
AL
(T) becomes a quadratic function of
buffer time, (T).
The ?rst term (denoted by C
D
in equation (3)) in the objective
function calculates the expected delay cost of a delayed aircraft and
on-board passengers by using a probabilistic density function (PDF) of
a departure aircraft (denoted by g(s)) as shown in equation (8). The
departure time (denoted by s in equation (9) and (10)) of a turnaround
aircraft is formulated as a function of schedule buffer time (T) and the
operational ef?ciency of aircraft ground services (m
2
). The Operational
ef?ciency of aircraft ground services, which is denoted by m
1
/m
2
in
equation (9) and (10), is modelled by a step-wise linear function to
account for the delay absorption effects of the scheduled buffer time in
the ground time of a turnaround aircraft. The second term (denoted by
C
AL
in equation (3)) in the objective function estimates the cost of
implementing schedule buffer time in the ground time of a turnaround
aircraft. The weight factor, , in equation (3) is used to explain the
trade-off condition by balancing the cost of delays and the cost of
schedule time.
The value of the unit delay cost of a passenger (C
p
(s) in equation
(6)) used in case studies is US$0.9/min, which is equivalent to a delay
cost of US$54 per hour, per passenger [9]. The value of the unit delay
cost of an aircraft (C
A
(s) in equation (6)) is US$45/min for ground
delays, which is equivalent to a delay cost of US$2,700 per hour per
aircraft (in this case a Boeing 757). The opportunity cost of schedule
buffer time (C
m
AL
in equation (7)) is US$2.5/min, which is equivalent to
US$4,500 per hour for a European short-haul route. Equal weights, i.e.
?0.5, on the delay cost of passengers and the airline schedule time
cost are used in the following numerical analyses.
318 C.-L. WU AND R.E. CAVES
3. MODEL APPLICATIONS
3.1. Schedule Control – The Use of Schedule Buffer Time
Beta functions are chosen to model the PDF of inbound aircraft (f(t) in
equation (8)) because of its analytical tractability in mathematical
modelling. The PDF of a departing turnaround aircraft (g(s) in equa-
tion (8)) is determined by its corresponding arrival time of inbound
aircraft (f(t)), schedule buffer time (T) in the ground time of a
turnaround aircraft, and the operational ef?ciency of aircraft ground
services (m
2
) formulated in equation (9) and (10). For instance,
Beta(10,3) distribution is used to model the arrival pattern of Flight_A
which has 20% on-time arrivals and 99% of ?ights arriving within
20-minute delay. The corresponding departure PDFs (g(s)) of Flight_A
are shown in Figure 1. It is observed from Figure 1 that the more
schedule buffer time is scheduled in the ground time of Flight_A, the
more punctual turnaround departure ?ights will be. The maximum
schedule buffer time (T
max
in equation (10)) for Flight_A is 20 minutes,
as it is long enough to include 99% of arrivals within buffer limits in
this case.
However, it might be argued that the shape of aircraft arrival time
PDFs could be centrally distributed. Hence, a further analysis was
conducted to investigate the in?uence of shapes of quasi-normal
distributions on model outputs. Three centrally distributed PDFs,
FIGURE 1 Departure PDFs corresponding to different punctuality buffer time.
319 FLIGHT SCHEDULE PUNCTUALITY
FIGURE 2 PDFs of Beta(10,10), Beta(5,5) and Beta(3,3) functions.
Beta(3,3), Beta(5,5) and Beta(10,10) were used to test the aircraft
turnaround model. The illustration of PDFs of these Beta functions is
given in Figure 2. The STA of these cases is set at zero hour in the
range between ?0.5 and 0.5 hour, so the arrival punctuality in all
three cases is 50%. The model outputs of three ?ights are shown in
Figure 3. It is found that the shape difference of PDFs causes a change
in the expected delay cost, C
D
(illustrated by dotted lines) and conse-
quently a change of total system cost, C
T
(illustrated by hashed lines).
The schedule time cost, C
AL
remains the same for all three cases, as
these ?ights are operated by the same airline. Hence, the optimal
schedule buffer time is found to be 15, 15 and 10 minutes for the case
of Beta(3,3), Beta(5,5) and Beta(10,10) respectively when the system
cost has its minimum.
It is seen in Figure 3 that the total system cost of the Beta(3,3) case
is the highest among the three cases. The high system cost of the
Beta(3,3) case is contributed by the high expected delay cost because
of the shape of Beta(3,3) functions. It is seen in Table I that three
PDFs have the same mean value of 0.5 but have different standard
deviation. Beta(3,3) has the highest standard deviation which results in
the ‘?atter’ shape of Beta(3,3) as illustrated in Figure 2. As a result,
the arrival CDFs of three cases differ from each other as shown in
Figure 4. It can be seen in Figure 4 that it takes 0.15, 0.2 and 0.25
hours of delay for Beta(10,10), Beta(5,5) and Beta(3,3) case respect-
ively to achieve the cumulative arrival punctuality of 90%. Hence, the
expected delay cost of the Beta(3,3) case is higher than the other two
320 C.-L. WU AND R.E. CAVES
FIGURE 3 In?uence of aircraft arrival PDFs on model outputs.
cases. Therefore, it is found from the previous discussion that the
arrival pattern of inbound aircraft in?uences the optimal use of sched-
ule buffer time through the expected delay of inbound aircraft, i.e. the
arrival punctuality of inbound aircraft, instead of the shape of PDFs of
inbound aircraft.
3.2. In?uence of Arrival Punctuality of Inbound Aircraft on Air-
craft Turnaround Punctuality
It is realized from empirical punctuality analysis that arrival aircraft
exhibit different punctuality patterns, which might result from enroute
TABLE I Descriptive statistics of chosen Beta
functions
Standard
Mean
a
Median deviation
Beta(10,10) 0.5 0.5 0.14
Beta(5,5) 0.5 0.5 0.18
Beta(3,3) 0.5 0.5 0.21
a
The range of the independent variable in this case is
between 0 and 1.
321 FLIGHT SCHEDULE PUNCTUALITY
FIGURE 4 CDFs of Beta(10,10), Beta(5,5) and Beta(3,3) functions.
airspace congestion and aircraft turnaround delays at outstations [8]. It
is also found from empirical analysis in relevant literature that the
departure punctuality of a turnaround aircraft is related to the arrival
punctuality of inbound aircraft [6]. However, the uncertainties in
aircraft turnaround operation were not included in previous research.
Hence, it is of interest in this paper to investigate how the relationship
develops between the arrival punctuality and the departure punctuality
of a turnaround aircraft when considering the operational ef?ciency of
aircraft turnarounds.
For instance, Flight_A of Airline R in Figure 5 exhibits an arrival
pattern of Beta(10,3) with a STA time of 40 minutes within an arrival
time domain of 60 minutes, i.e. 99% of ?ights arrive with the
maximum arrival delay of 20 minutes. A similar arrival time
distribution is observed from Flight_B but with a STA time of 30
minutes, i.e. worse arrival punctuality. The simulated departure PDFs
of these two ?ights are shown in Figure 5. It is seen that Flight_B
incurs longer departure delay than Flight_A under the same arrival
pattern but different arrival punctuality of inbound aircraft. Therefore,
it is found that the departure punctuality of a turnaround aircraft is
sensitive to the arrival punctuality of inbound aircraft.
Since different punctuality performance is observed from different
routes, the improvement of gate-to-gate punctuality in the air transport
system relies on scheduling strategies and turnaround operational
ef?ciency of an airline. As seen in Figure 5, the arrival punctuality of
inbound aircraft in?uences the departure punctuality of a turnaround
322 C.-L. WU AND R.E. CAVES
FIGURE 5 In?uence of arrival punctuality of inbound aircraft on departure PDFs.
aircraft. As a consequence, different schedule buffer time should
be applied to different ?ights in order to maintain a consistent
schedule punctuality. Flight_B, in this example needs a longer buffer
time than Flight_A due to the latter’s better arrival punctuality. The
implication of this example is that aircraft operations at outstation
stops also play an important role in the improvement of schedule
punctuality of turnaround aircraft at an airport as well as the schedule
reliability of aircraft rotations between airports. Operational improve-
ments are generally undertaken at a single airport to improve the
performance of schedule delivery. However, it is found in this exam-
ple that improvements at a single airport do not necessarily achieve
the system optimum, unless the system is optimized on a network
scale.
3.3. Aircraft Ground Services
The scheduled ground time of an aircraft is designed to accommodate
the service time of aircraft turnaround and potential delays from
inbound aircraft as well as delays from aircraft turnaround operations.
The arrival delay of an aircraft causes a late start of aircraft ground
services and is likely to result in a late ?nish of aircraft turnaround. As
a consequence, the scheduling of equipment and staff of ground
services is in?uenced. The most serious in?uence of ground service
disruption is the knock-on effect of disruptions to stand plans of the
323 FLIGHT SCHEDULE PUNCTUALITY
other aircraft on the ground waiting for services. When the arrival
delay of a turnaround aircraft disturbs stand plans of airport gates,
departure delay will probably happen and even deteriorate during
turnaround operations if the operation of aircraft turnaround is not well
managed. To further explain this situation, the operational ef?ciency of
aircraft ground services is described in the aircraft turnaround model
by a stochastic variable, m
2
in equation (9) and (10). When the
schedule perturbation is not suf?ciently signi?cant to disturb
turnaround operations and the ground handling agent is able to control
service time, m
2
is assigned a value which is equal to or less than unity
in equation (9), i.e., no further delays result from turnaround disrup-
tions in this case. Hence, a higher value of m
2
means that departure
delay of a turnaround aircraft is contributed partially by the arrival
delay of inbound aircraft and partially by the operational delay from
aircraft turnaround.
To investigate the in?uence of ground service ef?ciency on aircraft
turnaround punctuality, a numerical study was carried out in this paper
by simulating a turnaround aircraft which shows Beta(10,3) arrival
punctuality with a STA of zero hour within an arrival time domain
between ?0.5 and 0.5 and 10 minutes schedule buffer time. It is seen
in Figure 6 that if schedule disturbance from arrival delay is signi?cant
to aircraft ground services (in this case, m
2
is 2), the departure PDF of
turnaround aircraft (illustrated by the dotted line in Figure 6) exhibits
a longer right tail. On the other hand, when the better management of
FIGURE 6 In?uence of ground service ef?ciency on departure punctuality of a
turnaround aircraft.
324 C.-L. WU AND R.E. CAVES
turnaround services can be achieved by operational means [9], the
departure delay of the turnaround aircraft becomes less and the right
tail of the departure PDF becomes shorter (represented by the solid
line in Figure 6). Therefore, it is found that the ef?ciency of aircraft
turnaround operation signi?cantly in?uences the departure punctuality
of turnaround aircraft. Evidence from the air transport industry also
revealed that low-cost airlines in Europe reduce operational costs
through minimizing aircraft turnaround time on the ground and maxi-
mizing aircraft turnaround ef?ciency at hub airports to increase aircraft
productivity [3].
4. CASE STUDIES
Two case studies were carried out to demonstrate the effectiveness of
the aircraft turnaround model proposed above. Flight data collected in
the summer of 1999 from a European airline, Airline R, were used in
these case studies. Flight data represent three-month operations of two
typical European city-pair ?ights RR-X and RR-Y which were turned
around at the base airport of Airline R. RR-X was scheduled to arrive
at 18.45 hours and to depart at 19.45 hours. RR-Y was scheduled to
arrive at 16.30 hours and to leave at 17.35 hours. A Boeing 757
aircraft was used to carry out these two ?ights during operations in
1999. Arrival PDFs of these two ?ights are statistically ?tted from
?ight data as shown in Figure 7. Both PDFs past the K-S Goodness of
Fit Test as shown in Table II and therefore, were used to simulate
arrival punctuality of these two ?ights. There were 55% punctual
?ights for RR-X and 60% for RR-Y.
The aircraft turnaround model was applied to simulate the
turnaround operation of RR-X as well as the departure punctuality of
RR-X. The CDFs of departure punctuality of RR-X from model results
are shown in Figure 8. Different lengths of schedule buffer time were
applied in the turnaround model of RR-X and it resulted in different
expected departure CDFs. It is seen from Figure 8 that the longer the
buffer time is scheduled in the turnaround time of RR-X, the more
punctual departure ?ights will be. The observed departure punctuality
of RR-X is illustrated in Figure 8 by a thick solid line. It is seen in
Figure 8 that the observed departure punctuality of RR-X is close to
the estimated departure CDF having a schedule buffer time set at 0.7
hours with respect to the STA of 1/3, i.e., about 20 minutes schedule
buffer time in this case.
325 FLIGHT SCHEDULE PUNCTUALITY
FIGURE 7 Arrival PDFs of RR-X and RR-Y.
TABLE II K-S test of ?tted arrival PDFs of RR-X and RR-Y
K-S
test Sample Signi?cant Goodness
PDF value size K-S value of ?t
RR-X Beta(4,9) 0.0528 51 0.1679 Yes
RR-Y Beta(2,5) 0.1042 82 0.1331 Yes
The scheduled ground time of RR-X was 60 minutes and conse-
quently the schedule buffer time was about 20 minutes when turning
around the Boeing 757 aircraft. Compared with model results, the
observed turnaround punctuality of RR-X is found to be commensurate
with the 20-minute buffer time. However, it is also found in Figure 8
that the observed cumulative departure punctuality of RR-X is rela-
tively better within short departure delays (5 minutes) than model
results and is relatively worse than model results in some departures
which have longer departure delays (more than 20 minutes). It is found
from observations of aircraft turnarounds by Airline R that longer
delays to turnaround aircraft resulted from longer arrival delays of
inbound aircraft as well as from delays due to disruptions to aircraft
turnaround operations. As a consequence, a thicker right tail is found
in observed departure punctuality CDF of RR-X due to some extreme
cases in observations. It is also realized that the proposed aircraft
turnaround model is not good at modeling extreme cases, i.e. inbound
326 C.-L. WU AND R.E. CAVES
FIGURE 8 Departure punctuality of RR-X from observations and simulations.
aircraft with very long arrival delays, by using an aggregate model
because futher departure delays might result from stand plan disrup-
tions.
The second case study was undertaken by applying RR-Y’s ?ight
data to the turnaround model. The comparison between observed
departure punctuality from Airline R and estimated departure CDFs of
RR-Y are shown in Figure 9. The observed departure CDF of RR-Y
(represented by a thick solid line) develops closely to the estimated
CDF having a schedule buffer time set at 1/3 with respect to the STA
of 1/3, i.e., no buffer time included in this case. From the given ?ight
schedule of RR-Y, it is known that the scheduled ground time of RR-Y
was 65 minutes which included 25 minutes buffer time when turning
around a Boeing 757 aircraft. Model results show that 25-minute
buffer time ought to be long enough to include 95% of delayed
arrivals. However, it is seen from Figure 9 that the turnaround
punctuality of RR-Y was not commensurate with the amount of buffer
time in RR-Y’s schedule. In other words, the implemented schedule
punctuality of RR-Y did not match the endogenous punctuality re-
quirement in RR-Y’s schedule.
5. STRATEGIES FOR PUNCTUALITY MANAGEMENT
A hypothesis made earlier in this paper is that the endogenous
schedule punctuality has been set after a ?ight schedule is chosen by
327 FLIGHT SCHEDULE PUNCTUALITY
FIGURE 9 Departure punctuality of RR-Y from observations and simulations.
an airline. In other words, the hypothesis states that it is feasible
for an airline to manage its schedule punctuality by changing its
?ight schedules. As demonstrated in the case studies, RR-X exhibits
good turnaround punctuality with respect to its scheduled turnaround
time as shown in Figure 8. On the other hand, the turnaround
punctuality of RR-Y (illustrated in Figure 9) matches the estimated
departure CDF which includes no schedule buffer time, despite
actually having a buffer of 25 minutes for the turnaround. It is found
from case studies that the turnaround time of RR-Y was not long
enough to absorb potential delays from inbound aircraft as well as
delays from aircraft turnaround operations. Yet the endogenous
schedule punctuality of a turnaround aircraft can be achieved by good
management of turnaround operations such as ?ight RR-X. Hence, the
schedule punctuality of RR-X is expected to be as good as it is to
commensurate with the amount of schedule buffer time included in its
schedule.
It is usually argued by airlines that ?ight delays are mainly caused
by uncontrollable factors such as air traf?c ?ow management, passen-
ger boarding delays, inclement weather and so forth. However,
cases like ?ight RR-Y are not unusual for airlines and passengers. The
case study of RR-Y offers airlines some clues towards the better
management of schedule punctuality. Managerial strategies to improve
schedule punctuality of turnaround aircraft are therefore, recom-
mended to focus on two aspects: airline scheduling control and the
management of operational ef?ciency of aircraft ground services.
328 C.-L. WU AND R.E. CAVES
It is feasible for an airline to manage schedule punctuality by
optimally scheduling ?ights. For instance, ?ight RR-Y did not achieve
its endogenous punctuality performance, even though 25 minutes of
buffer time has been scheduled in the turnaround time. Airline R,
therefore, can improve RR-Y’s departure punctuality by scheduling
longer turnaround time at the airport, if a longer ground time is
needed. In addition, the improvement of the arrival punctuality of
inbound aircraft of RR-Y can also help improve turnaround punctual-
ity of RR-Y at the study airport. As a result, the departure punctuality
of RR-Y can be improved by optimizing scheduling control at the base
airport and outstations.
The management of schedule punctuality can also be achieved by
the improvement of operational ef?ciency of aircraft turnaround. It has
been demonstrated previously in this paper how signi?cantly the
departure punctuality of a turnaround aircraft is affected by the
ef?ciency of aircraft ground services. Although short aircraft
turnaround time increases the productivity of aircraft, it also risks
airlines and passengers suffering delays because of a lack of delay
absorption ability in a tight turnaround schedule. On the other hand,
the operation of aircraft ground services should be able to absorb
operational delays to aircraft turnaround by operational means when
delays are about to happen [5, 9, 10]. Most low-cost airlines in Europe
operate tight aircraft turnaround schedules at their base airports be-
cause the operational ef?ciency of aircraft turnaround can be fully
controlled and managed by these airlines. Maintaining the ef?ciency of
aircraft turnaround is believed to be the key factor for low-cost airlines
to deliver a reliable schedule of aircraft rotations [3]. However, there
is still some potential risks for airlines operating tight aircraft
turnaround and rotational schedules. When schedule irregularities oc-
cur, the most likely solution to elimilate knock-on delays in intensive
aircraft rotation schedules is to cancel ?ights.
6. CONCLUSIONS
A stochastic approach was used in this paper to model the operation of
aircraft turnaround and the departure punctuality of a turnaround
aircraft at an airport. The aircraft turnaround model was then used to
investigate the punctuality problem of turnaround aircraft. Model
results revealed that the departure punctuality of a turnaround aircraft
is in?uenced by the length of scheduled turnaround time, the arrival
329 FLIGHT SCHEDULE PUNCTUALITY
punctuality of inbound aircraft as well as the operational ef?ciency of
aircraft ground services. The proposed aircraft turnaround model was
also employed to evaluate the endogenous schedule punctuality of two
turnaround aircraft. Model results, when compared with observation
data, showed that the operational ef?ciency of aircraft ground services
varies among turnarounds. As a consequence, the departure punctual-
ity of some turnaround aircraft matches the endogenous schedule
punctuality, but some others do not.
Therefore, it is recommended that the improvement of departure
punctuality of turnaround aircraft may be achieved from two ap-
proaches: airline scheduling control and the management of oper-
ational ef?ciency of aircraft ground services. It is also realized that
the departure punctuality of a turnaround aircraft is in?uenced
signi?cantly by the arrival punctuality of inbound aircraft. Arrival
delays of inbound aircraft not only consume the scheduled turnaround
time of an aircraft, but also disturb stand plans of an airport and might
lead to a longer aircraft ground service time than scheduled. Therefore,
it is suggested that future research focus on the in?uence of aircraft
turnaround operations on the schedule punctuality of aircraft rotation
in a network of airports in order to improve the schedule reliability of
aircraft rotation on a network scale.
Acknowledgements
The provision of ?ight data from an anonymous European airline is
highly appreciated by the authors.
References
[1] ECAC (1996) ECAC Guidelines on Monitoring and Analysis of Delays at Airports
(European Civil Aviation Community, Paris).
[2] Airline Business (1999) Hubbing on Time, August, 62–64.
[3] ACI (2000) Low-cost Airlines Bring New Blood to Airports (Airport Council
International-Europe, Brussels).
[4] Luo, S. and Yu, G. (1997) ‘On the Airline Schedule Perturbation Problem Caused
by the Ground Delay Program’, Transportation Science 31, 298–311.
[5] Braaksma, J. P. and Shortreed, J. H. (1971) ‘Improving Airport Gate Usage with
Critical Path’, Transportation Engineering 97, 187–203.
[6] Hassounah, M. I. and Steuart, G. N. (1993) ‘Demand for Aircraft Gates’,
Transportation Research Record 1423, 26–33.
[7] IATA (1997) Airport Handling Manual, 17th Edition (International Air Transport
Association, Geneva).
330 C.-L. WU AND R.E. CAVES
[8] Wu, C. L. (2000) The In?uence of Aircraft Turnaround Operation on the
Scheduling of Aircraft Rotation in a Network of Airports. Unpublished PhD
Thesis (Loughborough University, United Kingdom).
[9] Ashford, N., Stanton, H. P. M. and Moore, C. A. (1997) Airport Operations
(McGraw Hill, London).
[10] Wu, C. L. and Caves, R. E. (2000) ‘Aircraft Operational Costs and Turnaround
Ef?ciency at Airports’, Air Transport Management 6, 201–8.
doc_367009146.pdf
Abstract explain flight schedule punctuality control and management a stochastic approach.
Transportation Planning and Technology, August 2003
Vol. 26, No. 4, pp. 313–330
FLIGHT SCHEDULE PUNCTUALITY
CONTROL AND MANAGEMENT: A
STOCHASTIC APPROACH
CHENG-LUNG WU
a
and ROBERT E. CAVES
b
a
Department of Aviation, University of New South Wales, Sydney, NSW 2052,
Australia;
b
Transport Studies Group, Department of Civil and Building
Engineering, Loughborough University, Loughborough LE11 3TU, United
Kingdom
(Received 22 January 2001; In ?nal form 10 October 2003)
The insuf?ciency of infrastructure capacity in an air transport system is usually blamed
for poor punctuality performance when implementing ?ight schedules. However,
investigations have revealed that ground operations of airlines have become the second
major cause of ?ight delay at airports. A stochastic approach is used in this paper to
model the operation of aircraft turnaround and the departure punctuality of a turnaround
aircraft at an airport. The aircraft turnaround model is then used to investigate the
punctuality problem of turnaround aircraft. Model results reveal that the departure
punctuality of a turnaround aircraft is in?uenced by the length of scheduled turnaround
time, the arrival punctuality of inbound aircraft as well as the operational ef?ciency of
aircraft ground services. The aircraft turnaround model proposed is then employed to
evaluate the endogenous schedule punctuality of two turnaround aircraft. Model results,
when compared with observation data, show that the operational ef?ciency of aircraft
ground services varies among turnarounds. Hence, it is recommended that the improve-
ment of departure punctuality of turnaround aircraft may be achieved from two
approaches: airline scheduling control and the management of operational ef?ciency of
aircraft ground services.
Keywords: Airlines; Airports; Aircraft operations; Schedule punctuality; Stochastic
models
1. INTRODUCTION
Poor schedule punctuality costs passengers, airports and airlines a
considerable amount of money. The insuf?ciency of infrastructure
ISSN 0308-1060 print: ISSN 1029-0354 online © 2003 Taylor & Francis Ltd
DOI: 10.1080/03081060310001635869
314 C.-L. WU AND R.E. CAVES
capacity, which includes airport and airspace capacity, is usually
blamed for poor schedule punctuality in the air transport system when
implementing ?ight schedules. However, a rigorous investigation
into the punctuality issue at London Gatwick Airport revealed that
airport and air traf?c control (ATC) related reasons were responsible
for 53% of total delayed ?ights [1]. The other delay causes resulted
from poor airline services and aircraft ground operations at airports.
61% of ?ights delayed by airline operations resulted in more than
20 minutes delay, while only 39% of ?ights were delayed by
more than 20 minutes due to airport and ATC reasons during the
period of investigation. A con?dential review paper available to the
authors from a European air carrier also drew similar conclusions as
those in the report by the European Civil Aviation Community
(ECAC).
After understanding the causes of poor punctuality in the air
transport system, airlines such as Lufthansa and Austrian Airlines have
task-force projects to improve schedule punctuality [2]. It is generally
realized in the airline industry that good management of aircraft
rotation improves the punctuality of ?ight schedules and also saves
delay-related costs of airlines. Although hard evidence is not available
from the industry, it is generally believed that good control of aircraft
turnaround operation and aircraft rotational strategies maintain the
competitive edge of low-cost airlines in the European aviation market
[3].
The ?ight schedule punctuality problem has generally been
approached in the literature by conventional statistic analyses, which
can only provide basic information about punctuality instead of
reasons why aircraft are delayed ([4]). It is hypothesized in this paper
that the endogenous schedule punctuality has been set after a ?ight
schedule is designed by an airline. In other words, the hypothesis is
that it is feasible for an airline to manage schedule punctuality by
optimizing its ?ight schedules and utilizing available resources.
It is apparent from the literature that the aircraft turnaround problem
has been mainly investigated using the Critical Path Method (CPM)
[5]. This method is usually employed to study an operational
procedure consisting of several work ?ows in order to identify critical
paths in the operation. Hence, CPM is commonly used by airlines to
investigate the turnaround procedure of aircraft because of the
complexity of the aircraft turnaround operation. In addition to CPM,
stochastic models have also been developed to model the uncertainty
of aircraft punctuality performance and airport gate occupancy time
315 FLIGHT SCHEDULE PUNCTUALITY
[6]. However, the stochastic model proposed in the literature captures
only the stochastic effects from arrival punctuality of inbound aircraft
without considering possible in?uences of operational disruptions on
the aircraft turnaround process.
The aim of this paper is to approach the ?ight schedule punctuality
problem from a more complete stochastic point of view. Stochastic
theories are used to model the departure punctuality of a turnaround
aircraft to account for uncertainties involved in the implementation of
?ight schedules. The aircraft turnaround process is simulated by a
turnaround model to represent the operational ef?ciency of aircraft
ground services. The turnaround model is then used to evaluate the
departure punctuality of turnaround aircraft under current ?ight sched-
ules. Operational strategies of schedule punctuality management are
discussed in this paper in two aspects, namely airline scheduling
control and the management of operational ef?ciency of aircraft
ground services. Two case studies are carried out using ?ight data
from a European airline to demonstrate the effectiveness of the aircraft
turnaround model.
The paper is organized into six sections. The aircraft turnaround
model is described succinctly in Section 2. The application of the
turnaround model is given in Section 3, Model Applications. Case
studies are given in Section 4, and discussions of schedule punctuality
management are shown in Section 5, Strategies for Punctuality Man-
agement. Concluding remarks are drawn in the ?nal section.
2. AIRCRAFT TURNAROUND MODEL
2.1. De?nitions and Terminology of Aircraft Turnaround
The ‘turnaround’ of an aircraft at an airport gate is de?ned as the
procedure to provide required services (such as catering, cabin clean-
ing and fuelling) to an aircraft in order to carry out a following ?ight
to another airport. Delays measured in this paper are based on the
scheduled time of arrival (STA), i.e., the on-chock time, and the
scheduled time of departure (STD), i.e. the off-chock time, of a
turnaround aircraft. The duration between STA and STD is de?ned as
the ‘scheduled ground time/scheduled turnaround time’ (denoted by
T
SG
in equation (1)) which consists of the ‘standard aircraft ground
service time’ (denoted by T
G
) and the ‘schedule buffer time’ (denoted
by T) as shown in equation (2). The schedule buffer time in the ground
316 C.-L. WU AND R.E. CAVES
time of a turnaround aircraft is usually designed to accommodate
potential delays from late inbound aircraft and delays from aircraft
turnaround operation. ‘Ground services’ of an aircraft include all
necessary services, e.g., cabin cleaning, engineering check, aircraft
fuelling, for an aircraft to carry out a following ?ight [7].
STD?STA?T
SG
(1)
T
SG
?T?T
G
(2)
2.2. Aircraft Turnaround Model
A mathematical model is developed in this paper to simulate aircraft
turnaround operations. The aircraft turnaround model is based on the
formulation of the stochastic departure punctuality of a turnaround
aircraft in terms of schedule buffer time (T) and the operational
ef?ciency of aircraft ground services (m
2
). The objective of this model
is to minimize system costs (C
T
), which include passenger delay costs
(C
P
), aircraft delay costs (C
A
) and the schedule time cost of an airline
(C
AL
). A longer ground time for a turnaround aircraft maintains the
required punctuality for a turnaround aircraft, though it reduces the
productivity of an aircraft. The dilemma between schedule punctuality
and aircraft productivity faced by an airline is modelled in the pro-
posed turnaround model by a weight factor, . The formulation of the
aircraft turnaround model is summarized by equations (3) to (10) [8].
To minimize C
T
:
C
T
?C
D
?(1 ?)C
AL
(3)
where
0 ??1 (4)
C
D
?E[C
u
(s)] ??C
u
(s)g(s)ds (5)
C
u
(s) ?C
p
(s) ?C
A
(s) (6)
C
AL
(T) ??C
m
AL
(T?T
A
)dT (7)
g(s) ?F[f(t), T, m
2
]*?J
s
? (8)
s ?m
1
*(t ?T
A
) T
A
?t ?T (9)
s ?m
1
*(T?T
A
) ?m
2
*(t ?T) T?t ?T
max
(10)
where m
1
?(m
2
/T
max
?T
A
)*(T
max
?T) T
A
?T?T
max
317 FLIGHT SCHEDULE PUNCTUALITY
The objective function in equation (3) is formulated to minimize the
system cost of a turnaround aircraft, which includes the expected delay
cost of an aircraft and on-board passengers (denoted by C
D
) and the
opportunity cost of schedule buffer time of an aircraft (denoted by
C
AL
). The delay cost functions of passengers (C
P
in equation (6)) and
the delay cost of an aircraft (C
A
in equation (6)) are both assumed to
be linear with respect to delay duration (s), though more general forms
may be used in this model. It is generally realized that the schedule
time opportunity cost becomes higher when the saved schedule time
becomes long enough for an aircraft to carry out an additional ?ight.
Hence, the airline schedule time cost C
AL
(T) in equation (7) is assumed
to have a linear marginal cost function to account for an increasing
opportunity cost when the schedule buffer time of a turnaround aircraft
increases and consequently C
AL
(T) becomes a quadratic function of
buffer time, (T).
The ?rst term (denoted by C
D
in equation (3)) in the objective
function calculates the expected delay cost of a delayed aircraft and
on-board passengers by using a probabilistic density function (PDF) of
a departure aircraft (denoted by g(s)) as shown in equation (8). The
departure time (denoted by s in equation (9) and (10)) of a turnaround
aircraft is formulated as a function of schedule buffer time (T) and the
operational ef?ciency of aircraft ground services (m
2
). The Operational
ef?ciency of aircraft ground services, which is denoted by m
1
/m
2
in
equation (9) and (10), is modelled by a step-wise linear function to
account for the delay absorption effects of the scheduled buffer time in
the ground time of a turnaround aircraft. The second term (denoted by
C
AL
in equation (3)) in the objective function estimates the cost of
implementing schedule buffer time in the ground time of a turnaround
aircraft. The weight factor, , in equation (3) is used to explain the
trade-off condition by balancing the cost of delays and the cost of
schedule time.
The value of the unit delay cost of a passenger (C
p
(s) in equation
(6)) used in case studies is US$0.9/min, which is equivalent to a delay
cost of US$54 per hour, per passenger [9]. The value of the unit delay
cost of an aircraft (C
A
(s) in equation (6)) is US$45/min for ground
delays, which is equivalent to a delay cost of US$2,700 per hour per
aircraft (in this case a Boeing 757). The opportunity cost of schedule
buffer time (C
m
AL
in equation (7)) is US$2.5/min, which is equivalent to
US$4,500 per hour for a European short-haul route. Equal weights, i.e.
?0.5, on the delay cost of passengers and the airline schedule time
cost are used in the following numerical analyses.
318 C.-L. WU AND R.E. CAVES
3. MODEL APPLICATIONS
3.1. Schedule Control – The Use of Schedule Buffer Time
Beta functions are chosen to model the PDF of inbound aircraft (f(t) in
equation (8)) because of its analytical tractability in mathematical
modelling. The PDF of a departing turnaround aircraft (g(s) in equa-
tion (8)) is determined by its corresponding arrival time of inbound
aircraft (f(t)), schedule buffer time (T) in the ground time of a
turnaround aircraft, and the operational ef?ciency of aircraft ground
services (m
2
) formulated in equation (9) and (10). For instance,
Beta(10,3) distribution is used to model the arrival pattern of Flight_A
which has 20% on-time arrivals and 99% of ?ights arriving within
20-minute delay. The corresponding departure PDFs (g(s)) of Flight_A
are shown in Figure 1. It is observed from Figure 1 that the more
schedule buffer time is scheduled in the ground time of Flight_A, the
more punctual turnaround departure ?ights will be. The maximum
schedule buffer time (T
max
in equation (10)) for Flight_A is 20 minutes,
as it is long enough to include 99% of arrivals within buffer limits in
this case.
However, it might be argued that the shape of aircraft arrival time
PDFs could be centrally distributed. Hence, a further analysis was
conducted to investigate the in?uence of shapes of quasi-normal
distributions on model outputs. Three centrally distributed PDFs,
FIGURE 1 Departure PDFs corresponding to different punctuality buffer time.
319 FLIGHT SCHEDULE PUNCTUALITY
FIGURE 2 PDFs of Beta(10,10), Beta(5,5) and Beta(3,3) functions.
Beta(3,3), Beta(5,5) and Beta(10,10) were used to test the aircraft
turnaround model. The illustration of PDFs of these Beta functions is
given in Figure 2. The STA of these cases is set at zero hour in the
range between ?0.5 and 0.5 hour, so the arrival punctuality in all
three cases is 50%. The model outputs of three ?ights are shown in
Figure 3. It is found that the shape difference of PDFs causes a change
in the expected delay cost, C
D
(illustrated by dotted lines) and conse-
quently a change of total system cost, C
T
(illustrated by hashed lines).
The schedule time cost, C
AL
remains the same for all three cases, as
these ?ights are operated by the same airline. Hence, the optimal
schedule buffer time is found to be 15, 15 and 10 minutes for the case
of Beta(3,3), Beta(5,5) and Beta(10,10) respectively when the system
cost has its minimum.
It is seen in Figure 3 that the total system cost of the Beta(3,3) case
is the highest among the three cases. The high system cost of the
Beta(3,3) case is contributed by the high expected delay cost because
of the shape of Beta(3,3) functions. It is seen in Table I that three
PDFs have the same mean value of 0.5 but have different standard
deviation. Beta(3,3) has the highest standard deviation which results in
the ‘?atter’ shape of Beta(3,3) as illustrated in Figure 2. As a result,
the arrival CDFs of three cases differ from each other as shown in
Figure 4. It can be seen in Figure 4 that it takes 0.15, 0.2 and 0.25
hours of delay for Beta(10,10), Beta(5,5) and Beta(3,3) case respect-
ively to achieve the cumulative arrival punctuality of 90%. Hence, the
expected delay cost of the Beta(3,3) case is higher than the other two
320 C.-L. WU AND R.E. CAVES
FIGURE 3 In?uence of aircraft arrival PDFs on model outputs.
cases. Therefore, it is found from the previous discussion that the
arrival pattern of inbound aircraft in?uences the optimal use of sched-
ule buffer time through the expected delay of inbound aircraft, i.e. the
arrival punctuality of inbound aircraft, instead of the shape of PDFs of
inbound aircraft.
3.2. In?uence of Arrival Punctuality of Inbound Aircraft on Air-
craft Turnaround Punctuality
It is realized from empirical punctuality analysis that arrival aircraft
exhibit different punctuality patterns, which might result from enroute
TABLE I Descriptive statistics of chosen Beta
functions
Standard
Mean
a
Median deviation
Beta(10,10) 0.5 0.5 0.14
Beta(5,5) 0.5 0.5 0.18
Beta(3,3) 0.5 0.5 0.21
a
The range of the independent variable in this case is
between 0 and 1.
321 FLIGHT SCHEDULE PUNCTUALITY
FIGURE 4 CDFs of Beta(10,10), Beta(5,5) and Beta(3,3) functions.
airspace congestion and aircraft turnaround delays at outstations [8]. It
is also found from empirical analysis in relevant literature that the
departure punctuality of a turnaround aircraft is related to the arrival
punctuality of inbound aircraft [6]. However, the uncertainties in
aircraft turnaround operation were not included in previous research.
Hence, it is of interest in this paper to investigate how the relationship
develops between the arrival punctuality and the departure punctuality
of a turnaround aircraft when considering the operational ef?ciency of
aircraft turnarounds.
For instance, Flight_A of Airline R in Figure 5 exhibits an arrival
pattern of Beta(10,3) with a STA time of 40 minutes within an arrival
time domain of 60 minutes, i.e. 99% of ?ights arrive with the
maximum arrival delay of 20 minutes. A similar arrival time
distribution is observed from Flight_B but with a STA time of 30
minutes, i.e. worse arrival punctuality. The simulated departure PDFs
of these two ?ights are shown in Figure 5. It is seen that Flight_B
incurs longer departure delay than Flight_A under the same arrival
pattern but different arrival punctuality of inbound aircraft. Therefore,
it is found that the departure punctuality of a turnaround aircraft is
sensitive to the arrival punctuality of inbound aircraft.
Since different punctuality performance is observed from different
routes, the improvement of gate-to-gate punctuality in the air transport
system relies on scheduling strategies and turnaround operational
ef?ciency of an airline. As seen in Figure 5, the arrival punctuality of
inbound aircraft in?uences the departure punctuality of a turnaround
322 C.-L. WU AND R.E. CAVES
FIGURE 5 In?uence of arrival punctuality of inbound aircraft on departure PDFs.
aircraft. As a consequence, different schedule buffer time should
be applied to different ?ights in order to maintain a consistent
schedule punctuality. Flight_B, in this example needs a longer buffer
time than Flight_A due to the latter’s better arrival punctuality. The
implication of this example is that aircraft operations at outstation
stops also play an important role in the improvement of schedule
punctuality of turnaround aircraft at an airport as well as the schedule
reliability of aircraft rotations between airports. Operational improve-
ments are generally undertaken at a single airport to improve the
performance of schedule delivery. However, it is found in this exam-
ple that improvements at a single airport do not necessarily achieve
the system optimum, unless the system is optimized on a network
scale.
3.3. Aircraft Ground Services
The scheduled ground time of an aircraft is designed to accommodate
the service time of aircraft turnaround and potential delays from
inbound aircraft as well as delays from aircraft turnaround operations.
The arrival delay of an aircraft causes a late start of aircraft ground
services and is likely to result in a late ?nish of aircraft turnaround. As
a consequence, the scheduling of equipment and staff of ground
services is in?uenced. The most serious in?uence of ground service
disruption is the knock-on effect of disruptions to stand plans of the
323 FLIGHT SCHEDULE PUNCTUALITY
other aircraft on the ground waiting for services. When the arrival
delay of a turnaround aircraft disturbs stand plans of airport gates,
departure delay will probably happen and even deteriorate during
turnaround operations if the operation of aircraft turnaround is not well
managed. To further explain this situation, the operational ef?ciency of
aircraft ground services is described in the aircraft turnaround model
by a stochastic variable, m
2
in equation (9) and (10). When the
schedule perturbation is not suf?ciently signi?cant to disturb
turnaround operations and the ground handling agent is able to control
service time, m
2
is assigned a value which is equal to or less than unity
in equation (9), i.e., no further delays result from turnaround disrup-
tions in this case. Hence, a higher value of m
2
means that departure
delay of a turnaround aircraft is contributed partially by the arrival
delay of inbound aircraft and partially by the operational delay from
aircraft turnaround.
To investigate the in?uence of ground service ef?ciency on aircraft
turnaround punctuality, a numerical study was carried out in this paper
by simulating a turnaround aircraft which shows Beta(10,3) arrival
punctuality with a STA of zero hour within an arrival time domain
between ?0.5 and 0.5 and 10 minutes schedule buffer time. It is seen
in Figure 6 that if schedule disturbance from arrival delay is signi?cant
to aircraft ground services (in this case, m
2
is 2), the departure PDF of
turnaround aircraft (illustrated by the dotted line in Figure 6) exhibits
a longer right tail. On the other hand, when the better management of
FIGURE 6 In?uence of ground service ef?ciency on departure punctuality of a
turnaround aircraft.
324 C.-L. WU AND R.E. CAVES
turnaround services can be achieved by operational means [9], the
departure delay of the turnaround aircraft becomes less and the right
tail of the departure PDF becomes shorter (represented by the solid
line in Figure 6). Therefore, it is found that the ef?ciency of aircraft
turnaround operation signi?cantly in?uences the departure punctuality
of turnaround aircraft. Evidence from the air transport industry also
revealed that low-cost airlines in Europe reduce operational costs
through minimizing aircraft turnaround time on the ground and maxi-
mizing aircraft turnaround ef?ciency at hub airports to increase aircraft
productivity [3].
4. CASE STUDIES
Two case studies were carried out to demonstrate the effectiveness of
the aircraft turnaround model proposed above. Flight data collected in
the summer of 1999 from a European airline, Airline R, were used in
these case studies. Flight data represent three-month operations of two
typical European city-pair ?ights RR-X and RR-Y which were turned
around at the base airport of Airline R. RR-X was scheduled to arrive
at 18.45 hours and to depart at 19.45 hours. RR-Y was scheduled to
arrive at 16.30 hours and to leave at 17.35 hours. A Boeing 757
aircraft was used to carry out these two ?ights during operations in
1999. Arrival PDFs of these two ?ights are statistically ?tted from
?ight data as shown in Figure 7. Both PDFs past the K-S Goodness of
Fit Test as shown in Table II and therefore, were used to simulate
arrival punctuality of these two ?ights. There were 55% punctual
?ights for RR-X and 60% for RR-Y.
The aircraft turnaround model was applied to simulate the
turnaround operation of RR-X as well as the departure punctuality of
RR-X. The CDFs of departure punctuality of RR-X from model results
are shown in Figure 8. Different lengths of schedule buffer time were
applied in the turnaround model of RR-X and it resulted in different
expected departure CDFs. It is seen from Figure 8 that the longer the
buffer time is scheduled in the turnaround time of RR-X, the more
punctual departure ?ights will be. The observed departure punctuality
of RR-X is illustrated in Figure 8 by a thick solid line. It is seen in
Figure 8 that the observed departure punctuality of RR-X is close to
the estimated departure CDF having a schedule buffer time set at 0.7
hours with respect to the STA of 1/3, i.e., about 20 minutes schedule
buffer time in this case.
325 FLIGHT SCHEDULE PUNCTUALITY
FIGURE 7 Arrival PDFs of RR-X and RR-Y.
TABLE II K-S test of ?tted arrival PDFs of RR-X and RR-Y
K-S
test Sample Signi?cant Goodness
PDF value size K-S value of ?t
RR-X Beta(4,9) 0.0528 51 0.1679 Yes
RR-Y Beta(2,5) 0.1042 82 0.1331 Yes
The scheduled ground time of RR-X was 60 minutes and conse-
quently the schedule buffer time was about 20 minutes when turning
around the Boeing 757 aircraft. Compared with model results, the
observed turnaround punctuality of RR-X is found to be commensurate
with the 20-minute buffer time. However, it is also found in Figure 8
that the observed cumulative departure punctuality of RR-X is rela-
tively better within short departure delays (5 minutes) than model
results and is relatively worse than model results in some departures
which have longer departure delays (more than 20 minutes). It is found
from observations of aircraft turnarounds by Airline R that longer
delays to turnaround aircraft resulted from longer arrival delays of
inbound aircraft as well as from delays due to disruptions to aircraft
turnaround operations. As a consequence, a thicker right tail is found
in observed departure punctuality CDF of RR-X due to some extreme
cases in observations. It is also realized that the proposed aircraft
turnaround model is not good at modeling extreme cases, i.e. inbound
326 C.-L. WU AND R.E. CAVES
FIGURE 8 Departure punctuality of RR-X from observations and simulations.
aircraft with very long arrival delays, by using an aggregate model
because futher departure delays might result from stand plan disrup-
tions.
The second case study was undertaken by applying RR-Y’s ?ight
data to the turnaround model. The comparison between observed
departure punctuality from Airline R and estimated departure CDFs of
RR-Y are shown in Figure 9. The observed departure CDF of RR-Y
(represented by a thick solid line) develops closely to the estimated
CDF having a schedule buffer time set at 1/3 with respect to the STA
of 1/3, i.e., no buffer time included in this case. From the given ?ight
schedule of RR-Y, it is known that the scheduled ground time of RR-Y
was 65 minutes which included 25 minutes buffer time when turning
around a Boeing 757 aircraft. Model results show that 25-minute
buffer time ought to be long enough to include 95% of delayed
arrivals. However, it is seen from Figure 9 that the turnaround
punctuality of RR-Y was not commensurate with the amount of buffer
time in RR-Y’s schedule. In other words, the implemented schedule
punctuality of RR-Y did not match the endogenous punctuality re-
quirement in RR-Y’s schedule.
5. STRATEGIES FOR PUNCTUALITY MANAGEMENT
A hypothesis made earlier in this paper is that the endogenous
schedule punctuality has been set after a ?ight schedule is chosen by
327 FLIGHT SCHEDULE PUNCTUALITY
FIGURE 9 Departure punctuality of RR-Y from observations and simulations.
an airline. In other words, the hypothesis states that it is feasible
for an airline to manage its schedule punctuality by changing its
?ight schedules. As demonstrated in the case studies, RR-X exhibits
good turnaround punctuality with respect to its scheduled turnaround
time as shown in Figure 8. On the other hand, the turnaround
punctuality of RR-Y (illustrated in Figure 9) matches the estimated
departure CDF which includes no schedule buffer time, despite
actually having a buffer of 25 minutes for the turnaround. It is found
from case studies that the turnaround time of RR-Y was not long
enough to absorb potential delays from inbound aircraft as well as
delays from aircraft turnaround operations. Yet the endogenous
schedule punctuality of a turnaround aircraft can be achieved by good
management of turnaround operations such as ?ight RR-X. Hence, the
schedule punctuality of RR-X is expected to be as good as it is to
commensurate with the amount of schedule buffer time included in its
schedule.
It is usually argued by airlines that ?ight delays are mainly caused
by uncontrollable factors such as air traf?c ?ow management, passen-
ger boarding delays, inclement weather and so forth. However,
cases like ?ight RR-Y are not unusual for airlines and passengers. The
case study of RR-Y offers airlines some clues towards the better
management of schedule punctuality. Managerial strategies to improve
schedule punctuality of turnaround aircraft are therefore, recom-
mended to focus on two aspects: airline scheduling control and the
management of operational ef?ciency of aircraft ground services.
328 C.-L. WU AND R.E. CAVES
It is feasible for an airline to manage schedule punctuality by
optimally scheduling ?ights. For instance, ?ight RR-Y did not achieve
its endogenous punctuality performance, even though 25 minutes of
buffer time has been scheduled in the turnaround time. Airline R,
therefore, can improve RR-Y’s departure punctuality by scheduling
longer turnaround time at the airport, if a longer ground time is
needed. In addition, the improvement of the arrival punctuality of
inbound aircraft of RR-Y can also help improve turnaround punctual-
ity of RR-Y at the study airport. As a result, the departure punctuality
of RR-Y can be improved by optimizing scheduling control at the base
airport and outstations.
The management of schedule punctuality can also be achieved by
the improvement of operational ef?ciency of aircraft turnaround. It has
been demonstrated previously in this paper how signi?cantly the
departure punctuality of a turnaround aircraft is affected by the
ef?ciency of aircraft ground services. Although short aircraft
turnaround time increases the productivity of aircraft, it also risks
airlines and passengers suffering delays because of a lack of delay
absorption ability in a tight turnaround schedule. On the other hand,
the operation of aircraft ground services should be able to absorb
operational delays to aircraft turnaround by operational means when
delays are about to happen [5, 9, 10]. Most low-cost airlines in Europe
operate tight aircraft turnaround schedules at their base airports be-
cause the operational ef?ciency of aircraft turnaround can be fully
controlled and managed by these airlines. Maintaining the ef?ciency of
aircraft turnaround is believed to be the key factor for low-cost airlines
to deliver a reliable schedule of aircraft rotations [3]. However, there
is still some potential risks for airlines operating tight aircraft
turnaround and rotational schedules. When schedule irregularities oc-
cur, the most likely solution to elimilate knock-on delays in intensive
aircraft rotation schedules is to cancel ?ights.
6. CONCLUSIONS
A stochastic approach was used in this paper to model the operation of
aircraft turnaround and the departure punctuality of a turnaround
aircraft at an airport. The aircraft turnaround model was then used to
investigate the punctuality problem of turnaround aircraft. Model
results revealed that the departure punctuality of a turnaround aircraft
is in?uenced by the length of scheduled turnaround time, the arrival
329 FLIGHT SCHEDULE PUNCTUALITY
punctuality of inbound aircraft as well as the operational ef?ciency of
aircraft ground services. The proposed aircraft turnaround model was
also employed to evaluate the endogenous schedule punctuality of two
turnaround aircraft. Model results, when compared with observation
data, showed that the operational ef?ciency of aircraft ground services
varies among turnarounds. As a consequence, the departure punctual-
ity of some turnaround aircraft matches the endogenous schedule
punctuality, but some others do not.
Therefore, it is recommended that the improvement of departure
punctuality of turnaround aircraft may be achieved from two ap-
proaches: airline scheduling control and the management of oper-
ational ef?ciency of aircraft ground services. It is also realized that
the departure punctuality of a turnaround aircraft is in?uenced
signi?cantly by the arrival punctuality of inbound aircraft. Arrival
delays of inbound aircraft not only consume the scheduled turnaround
time of an aircraft, but also disturb stand plans of an airport and might
lead to a longer aircraft ground service time than scheduled. Therefore,
it is suggested that future research focus on the in?uence of aircraft
turnaround operations on the schedule punctuality of aircraft rotation
in a network of airports in order to improve the schedule reliability of
aircraft rotation on a network scale.
Acknowledgements
The provision of ?ight data from an anonymous European airline is
highly appreciated by the authors.
References
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330 C.-L. WU AND R.E. CAVES
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