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Transportation Research Part D 89 (2020) 102634
1361-9209/© 2020 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license
(http://creativecommons.org/licenses/by-nc-nd/4.0/).
Reducing airport environmental footprint using a
disruption-aware stand assignment approach
Margarita Bagamanova
a
,
c
,
*
, Miguel Mujica Mota
b
a
Aeronautics and Logistics Departmental Unit, School of Engineering, Autonomous University of Barcelona, Bellaterra 08193, Spain
b
Aviation Academy, Amsterdam University of Applied Sciences, Weesperzijde 190, Amsterdam 1097 DZ, the Netherlands
c
Department of IT & Logistics, Amsterdam School of International Business, Amsterdam University of Applied Sciences, Fraijlemaborg 133,
Amsterdam 1102 CV, the Netherlands
ARTICLE INFO
Keywords:
Pollutant emissions
Capacity optimisation
Flight delays
Capacity management
Congestion
Capacity allocation
Decision support
Sociotechnical system
ABSTRACT
Modern airport management is challenged by the task of operating aircraft parking positions most
efciently while complying with environmental policies, restrictions, schedule disruptions, and
capacity limitations. This study proposes a novel framework for the stand allocation problem that
uses a divide-and-conquer approach in combination with Bayesian modelling, simulation, and
optimisation to produce less-pollutant solutions under realistic conditions. The framework pre-
sents three innovative aspects. First, inputs from the stochastic analysis module are used in a
multivariate optimisation for generating variability-robust solutions. Second, a combination of
optimisation and simulation is used to nely explore the impact of realistic uncertainty uncap-
tured by the framework. Lastly, the framework considers the role of human beings as the nal
control of operational conditions. A case study is presented as a proof of concept and demon-
strates results achievable and benets of the framework proposed. The experimental results
demonstrate that the framework generates less-pollutant solutions under realistic conditions.
1. Introduction
Air transportation provides global freedom of movement for people and cargo. In 2018, approximately four billion passengers and
64 million tons of cargo travelled over 22,000 routes, generating more than 65 million jobs, and a GDP of approximately $2.7 trillion
(IATA, 2019a). The demand for air transport passenger services is growing; according to IATA (2018), this trend is expected to
continue, and by 2037, the number of passengers travelling by air is expected to double, reaching approximately eight billion pas-
sengers per year. The demand for air cargo transportation is also growing. Boeing (2018) predicted annual growth of 4.3% for air cargo
operations in terms of revenue tonne-kilometres. The constant growth of demand for air transport services creates additional chal-
lenges for airport capacity management and airport environmental protection goals.
With the growth of air transport, related pollutant emissions have been increasing. Graver et al. (2018) reported that CO
2
emissions
from aviation increased by 32% in the previous ve years. Currently, global aviation generates approximately 2% of all human-
induced emissions and 12% of all transport-related emissions (ATAG, 2019). These percentages are expected to increase (Graver
et al., 2018), creating additional sustainability challenges for air transport stakeholders.
Aircraft fuel burn is considered to be the main source of air transport pollutant emissions, which include carbon dioxide, nitrogen
* Corresponding author.
E-mail addresses: mm.bagamanova@hva.nl (M. Bagamanova), m.mujica.mota@hva.nl (M. Mujica Mota).
Contents lists available at ScienceDirect
Transportation Research Part D
journal homepage: www.elsevier.com/locate/trd
https://doi.org/10.1016/j.trd.2020.102634
Transportation Research Part D 89 (2020) 102634
2
oxides, and noise. The largest proportion of these emissions occurs during the cruise phase; however, ground movement of aircraft,
including landing, taxiing, and take-off, also contributes signicantly to total emissions and affects inhabitants in the proximity of
airports (ICAO, 2019a). Aircraft taxiing between the runway exit and the designated stand can generate over one-third of all aircraft
emissions outside of the cruise phase, and mostly depends on the distance between the stand and the runway exit/entry points (Fleuti
and Maraini, 2017). Thus, it is important to allocate scheduled ights to minimise taxi distance and related fuel burn and emissions.
The stand allocation schedule is often disrupted by changes in ight schedule. Such perturbations may lead to increased turnaround
time and decreased airport terminal performance, thereby affecting the level of emissions. Owing to airport congestion, aircraft may
have to wait on the ground with their engines on or perform holding manoeuvres in the terminal manoeuvring area (TMA), leading to
additional fuel consumption and related emissions. Inefcient management of terminal facilities can propagate schedule perturbations
to successive ights and connected airports, increasing the risk of additional emissions. Therefore, efcient management of airport
facilities, including stands, is necessary to increase airport capability for addressing perturbations and reducing emissions generated
during aircraft ground operations.
This study proposes a novel emission-aware stand assignment approach, based on a disruption-aware stand assignment approach
(DASA) introduced in a seminal study by Bagamanova et al. (2020). The methodology proposed in this study combines the benets of
data-mining, evolutionary optimisation, and simulation for generating a stand assignment that minimises pollutant emissions and
increases robustness to possible ight schedule deviations while ensuring passenger service quality. The presented emission- and
delay-aware stand assignment approach (E-DASA) makes use of airport historical performance data, from which the algorithm learns
probabilities of schedule deviations based on characteristics of scheduled ights using Bayesian distributional modelling. The prob-
abilities are considered in calculating the most likely or user-dened level of deviation for each ight in the target ight schedule. The
deviations are considered in generating the stand assignment, which is optimised to minimise emissions generated during aircraft
taxiing.
The rest of this article is organised as follows. Section 2 reviews related research publications. Section 3 presents the E-DASA
methodology and its novel emission-aware component. A case study is presented in Section 4. Conclusions and future research are
presented in Section 5.
2. Related research
The stand assignment problem (SAP) approached in this study has been similarly considered by many researchers as the gate
assignment problem (GAP). These problems have been researched for many decades from various perspectives in a single-objective as
well as in a multi-objective formulation. First works did not consider airport system stochasticity and were more concentrated on
minimisation of passenger walking distances (Babi´
c et al., 1984; Hu and Di Paolo, 2007; Mangoubi and Mathaisel, 1985). With the
development of the air transport industry, the researchers started to consider technical requirements for aircraft ground-handling (Yan
and Tang, 2007) and additional objectives. More attention has been paid to minimisation of towing and stands usage cost (Jo et al.,
1997; Prem Kumar and Bierlaire, 2014; van Schaijk and Visser, 2017), improvement of passenger service level and transfer facilitation
(Ali et al., 2019; Benlic et al., 2017; Deng et al., 2018; Dijk et al., 2019; Kim et al., 2013a), and maximisation of contact stands use (Dijk
et al., 2019; Gu´
epet et al., 2015). Some researchers considered the taxiing phase on the airport ground as a part of their gate/stand
assignment study. They concentrated on the minimisation of aircraft idle/taxi time on the ground and therefore, minimisation of
taxiways congestion and airline costs. Maharjan and Matis (2012) attempted to minimise taxi-related fuel burn as a part of their binary
integer multi-commodity ow network model for the gate assignment. Kim et al. (2013b) proposed gate assignment approach to
minimise ramp congestion, as well as passenger transit time in the terminal. Behrends and Usher (2017) proposed to generate gate
assignment to minimise aircraft taxi time and applied random selection, genetic algorithm and simulated annealing for optimisation.
Some authors considered real-life stochasticity in the form of schedule perturbations in stand assignments without focusing on taxi
movement. They often mitigated disruptions by inserting a uniform buffer time between consecutive ights assigned to the same gate/
stand (Deng et al., 2018; Gu´
epet et al., 2015; Maharjan and Matis, 2012). Some researchers instead of applying the uniform buffer
times for all assignments proposed to increase individual buffer times on a historical ight disruption value, based on a 95% percentile;
thus considering a wider range of possible deviations (Kim et al., 2013a; Prem Kumar and Bierlaire, 2014). In general, inserting buffer
times has been proved as an effective solution for minor deviations (up to 30 min) (Hassounah and Steuart, 1993; Yan et al., 2002; Yan
and Chang, 1998; Yan and Huo, 2001). Although such buffer times helped to reduce the number of gate conicts, they also resulted in
an increment of assignment problem complexity, increasing the required computational time and leading to lower quality of the
outcome of the considered objectives (Prem Kumar and Bierlaire, 2014). Considering future growth of demand, new techniques that go
beyond the buffer solution must be developed; buffering signicantly reduces airport terminal capacity and may be unfeasible at
congested airports.
In the last years, more attention has been paid to the problem of pollutant emissions and their correlation with the growth of
economic activities and transportation (Egilmez and Park, 2014; Fisch-Romito and Guivarch, 2019; Wang et al., 2019, 2018). Ac-
cording to Grampella et al. (2017), 1% increment in air trafc movements leads to 1.05% increment in total airport environmental
effects. As air transport demand grows, the development of measures for its emissions mitigation becomes highly important for
researchers.
Nikoleris et al. (2011) estimated that idling and taxiing states of aircraft movement are the greatest sources of fuel consumption and
emissions in an airport, and therefore represent a signicant research interest. Many researchers have investigated methods to mitigate
pollutant emissions during taxiing through technical improvements. Duinkerken et al. (2013), Ithnan et al. (2013), and Li and Zhang
(2017) estimated different taxiing approaches, which included using only one aircraft engine and external engine power, and showed
M. Bagamanova and M. Mujica Mota
Transportation Research Part D 89 (2020) 102634
3
that signicant emission reduction can be achieved. Zhang et al. (2019) optimised aircraft taxi time by considering taxiway conicts
and aircraft fuel consumption.
Some researchers concentrated on waiting time emissions reduction by applying different runway congestion-related strategies
such as pushback rate control (Simaiakis et al., 2014), runway departure sequence optimisation (Simaiakis and Balakrishnan, 2016;
S¨
olveling et al., 2011), gate holding, de-rated take-offs (Ashok et al., 2017), and departure metering (Murça, 2017). Although the
measures proposed by these works helped to reduce the negative environmental impact by almost a third, they also led to increasing
stand occupancy times, thereby signicantly reducing airport capacity which can be problematic in congested airports.
Many published methods successfully reduced the level of pollutant emissions, however, up to our knowledge, none of them
specically addressed a combination of environmental footprints of schedule disruptions, stand occupancy conicts, nor human
intervention stochasticity on the operational level. Hao et al. (2016) estimated that the lack of predictability in ight times contributes
a 1% increase in the amount of fuel consumed, which proportionally increases the emission footprint. Thus, combined measures are
necessary that simultaneously address both the level of pollutant emissions from aircraft ground movements, stand capacity usage
optimisation and the stand assignment resilience to schedule disruptions under realistic conditions.
To ll the gap in this area, this study proposes an innovative approach that considers disruptions for each ight to create an efcient
stand assignment with reduced environmental impact. Furthermore, this study introduces a technique to address the SAP using a
divide-and-conquer approach, rst identifying the most promising region to explore for the best solution using the optimisation
element of the algorithmic architecture, and then focusing on the local exploration for solutions by introducing the stochasticity of the
system in a simulation model. The proposed approach is illustrated with a case study in airport infrastructure, in which the stand
assignment optimisation algorithm addresses assignment priorities in the scope of emissions. Furthermore, this study demonstrates
how the proposed combination of optimisation techniques with Bayesian inference and human intervention can contribute to the
airport sociotechnical system while minimising emissions from ground operations and what would be the impact of human in-
terventions on the passenger service level.
3. Methodology
To reduce the negative impact of schedule disruptions on airport operations and efciency of airport environmental policy, this
study uses E-DASA methodology that addresses operational stochasticity and environmental footprint reduction objectives. This
section gives a brief description of E-DASA algorithm, which is the base of this study. The approach presented in this study is an
emission-aware instance of the general algorithmic architecture presented by Bagamanova et al. (2020) in their seminal study.
E-DASA consists of two components, each with its own functionality and algorithmic logic. Data ow and architecture of E-DASA
are illustrated in Fig. 1.
Module I uses an inference technique to learn probabilities of ight disruptions by analysing historical airport performance data.
These probabilities are estimated by application of Bayesian distributional modelling, where the target variable (ight arrival time
deviation in the scope of this study) is described through its predictors (other variables present in the historical data). The predictor
variables could be weather conditions, information about the airline, type of aircraft, aircraft emissions factor, and other variables
available in the historical performance data.
Fig. 1. Architecture of E-DASA.
M. Bagamanova and M. Mujica Mota
Transportation Research Part D 89 (2020) 102634
4
Inference of schedule disruptions probabilities in Module I is implemented via Bayesian distributional regression modelling. In this
technique, response distribution location and shape parameters (e.g. mean, scale, and/or shape) are estimated through predicting
variables and response dependence expressed based on the Bayes rule (Stuart and Ord, 2010). In this way, a Bayesian distributional
model with the response variable y, adopting a certain distribution D, and observation i can be expressed through yiD(θ1i,θ2i,⋯),
where θ
p
are the parameters of the response distribution D. Each parameter θ
p
is regressed on its own predictor factor
η
p through the
inverse link function fp as θpi =fp
η
pi2. The linear predicting factor
η
p can generally be written as
η
p=Xβp+Zup, where βp and up are
the regression coefcients at population-level and group-level, respectively, and X and Z are the corresponding design matrices
(Bürkner, 2018).
When the probabilities of ight disruptions are learnt, their corresponding Bayesian distributional models are transferred as inputs
to Module II. In this module, the target ight schedule is analysed, and the most probable ight deviations are calculated based on the
Bayesian distributional models from Module I and the characteristics of each scheduled ight. The minimum probability level for
generated ight deviations can be set up by the user in the algorithm’s input settings, or exact ight deviation values can be drawn
randomly from the distributional models for the user-dened probability interval. Such a feature enables the generation of different
risk scenarios of stand assignments, which correspond to different levels of likelihood.
When ight deviations are computed, Module II generates a new ight schedule; block occupancy times for each ight are
calculated as originally scheduled block occupancy time plus most probable ight schedule deviation value. Module II performs the
assignment of an updated schedule to available airport parking positions, considering the probable schedule deviation and optimi-
sation objectives. These objectives can be ne-tuned based on current user preferences. Such exibility allows for different stand
assignments, satisfying different user preferences and goals without the need for reprogramming the entire module.
Owing to stochasticity in the airport system, the solution generated by E-DASA may become unfeasible at some moment during
operations. In this case, it is necessary to act to resolve assignment conicts and maintain the required airport performance level. As it
is illustrated in Fig. 1, E-DASA-generated stand assignment can be controlled for feasibility by airport trafc control (ATC) on the day
of operations. If any of the planned assignments become infeasible (for instance, due to ight regulation en-route or temporal un-
availability of a stand due to technical problems with its equipment or other sources of disturbances not captured by the framework),
ATC can reassign the arriving ight to another suitable stand/apron area. How efcient such reassignment is in terms of passenger
comfort and taxi-related emissions, depends on the available decision time and availability of fast-working decision support tools for
ATC. Therefore, it is necessary to experiment with such interventions to see how they can impact stand assignment KPIs. E-DASA
intends to produce a stand assignment with a certain resilience and in such a way that contributes to a better performance of the ATC
sociotechnical system.
Modied optimisation component of Module II
The optimisation component presented in this study is an emission-aware modication of the general multi-objective approach rst
introduced by Bagamanova et al. (2020). We refer to this new algorithm as E-DASA. To consider environmental footprint reduction
while providing competitive passenger service, the objective function of Module II optimisation in this study is dened as:
minimise(w1*Owalk +w2*Oopen +w3*Oemis +w4*Oidle)(1)
In this formula the following individual objectives are considered:
1. Owalk – the objective to minimise total walking distance for potential transfer passengers:
Owalk =
I
i=1
Npaxidwalk /
I
i=1
Npaxidmaxwalk
where Npaxi is the number of transferring passengers per i ight, dwalk is the walking distance to a potential connection ight; dmaxwalk is
the walking distance between two gates located the furthest from each other, and I is the total number of ights with transfer
passengers.
2. Oopen – the objective to minimise the number of aircraft assigned to remote stands and to serve more passengers through contact
stands:
Oopen = (Npo*Nopen )/(Np*N)
where Npo is the number of passengers in the aircraft assigned to remote stands, Nopen is the number of aircraft assigned to remote
stands; Np is the total number of passengers on scheduled ights, and N is the total number of aircraft in the schedule.
3. Oemis – the objective to minimise taxi-related pollutant emissions:
Oemis =
N
n=1
E
e=1
BnHeFne(Tn+DT n)/
N
n=1
E
e=1
BnHeFne(Thold *N)Ct
M. Bagamanova and M. Mujica Mota
Transportation Research Part D 89 (2020) 102634
5
where Bn is the fuel burn rate for aircraft n; He is the hazard weight assigned to the emission e; Fne is the emission factor e for aircraft n
per unit of fuel burnt; Tn is the taxi time for aircraft n; DTn is the time penalty if aircraft n is assigned to a ‘dummy’ stand; Thold is the
holding manoeuvre time; N is the total number of aircraft in the schedule; Ct is the holding emission factor increment, calculated as
Ct=fappr/ftaxi , where fappr and ftaxi are the engine thrust levels for the approach and taxi phases, respectively. In practice, airport
stakeholders can choose the values of He to emphasise the impact of certain pollutants according to their toxicity level during the stand
allocation.
4. Oidle – the objective to minimise the number of aircraft not assigned to any stand and related pollutant emissions:
Oidle =Nidle/N
where Nidle is the number of aircraft that have been assigned to a ‘dummy’ stand and N is the total number of aircraft in the schedule.
5. w1,w2,w3,w4 – indicate priority weights for the corresponding assignment priorities. For practical implementations, different
airport stakeholders can decide the weights to reect different priorities.
In the presented objective function (1), there are conicting objectives due to the nature of the actors involved. For instance,
airlines aim to minimise passenger walking distance (Owalk) by locating connecting ights as close as possible to each other. In contrast,
airport operators prefer to use contact stands (Oopen ) as often as possible to provide the best service for the airlines and spread allocation
for even use of infrastructure. An airport would like to minimise taxi-related emissions and taxi time to the stand (Oidle); this objective
may conict with airline preference, as some ights must be allocated to the certain terminal area due to border control procedures,
requiring passengers to walk a greater distance to their transfer connection.
Every airport has a stand assignment policy, which implies certain restrictions for the use of stands. The following are the re-
strictions and assumptions considered in the presented algorithm:
•Domestic and international ights must be assigned to specic stands in the designated zones. These are internal specications of
the airport; e.g. international ights are assigned to stands that have access to designated border control areas.
•An assigned stand must correspond to the size of the aircraft (large aircraft require extra space owing to larger wingspan). This is
implemented through the identication of allowed stands for each ight at the input data processing stage in Module II.
•An assigned stand must correspond to airline preferences. This is implemented through the identication of preferred/contracted
stands for each ight at the input data processing stage in Module II.
•No aircraft towing movements from one stand to another are considered in the algorithm. Each aircraft occupies its assigned stand
for the time equal to its ground-handling time and then taxies to the runway for departure from the airport.
•Flight delays must be considered in the assignment (according to conditional probability distributions from Module I). In this study,
only arrival time disruptions are considered in the case study due to unavailability of ground handling data and correspondence of
arriving aircraft to departing aircraft.
•When no parking positions are available at the moment of arrival, aircraft should wait on the apron until a position becomes
available. This is implemented in the algorithm by assigning the ight to a ‘dummy’ stand and incrementally delaying its in-block
time on DTn until a suitable stand becomes available.
•For the calculation purposes, holding manoeuvre time Thold should be larger than the maximum possible airport unimpeded taxi
time.
•Engine thrust levels for the approach phase fappr and the taxi phase ftaxi are equal to 30% and 7%, respectively, based on the ICAO
LTO cycle settings (ICAO, 2019b).
The next step in the algorithmic implementation is to consider the stochasticity of the system by simulating the target ight
schedule. This is performed using a discrete-event simulation (DES) model of the actual airport system discussed in Section 4. In the
model, the obtained stand allocations are simulated under different schedule disruptions scenarios for seven days and the results are
discussed.
Table 1
Mexico City International Airport characteristics (AICM and SCT, 2019; IAS, 2019).
Terminal 1 Terminal 2
Surface area 54.8 ha 24.2 ha
Contact aircraft parking positions 33 23
Remote aircraft parking positions 11 17
Airlines 20 6
Passenger throughput in 2019 29.5 million passengers 20.8 million passengers
M. Bagamanova and M. Mujica Mota
Transportation Research Part D 89 (2020) 102634
6
4. Case study: Mexico City international airport
Mexico City International Airport (IATA code: MEX) is the main airport in Mexico and 20th in the world ranking of airports by the
largest number of aircraft movements, with approximately 450,000 landings and take-offs annually. Twenty-six airlines operate in two
terminals at MEX, with international and domestic ights. Terminal buildings are separated by two parallel runways that are not
operated simultaneously due to lack of separation distance between them. Such a design signicantly restricts MEX capacity; since
2017 MEX has been assessed with a capacity of 61 movements per hour, with a maximum of 40 landings (SCT, 2017). Other relevant
information about MEX considered in this study is presented in Table 1.
Fig. 2 illustrates the layout of MEX. Two runways run in parallel from southwest-northeast; runway conguration 05R is most often
used for landings, with 05L used for departures. Both terminals have remote parking positions located near runway exits with the
shortest taxi distance to them. Approximate location of these positions is shown in Fig. 2.
As observed in Fig. 2, Terminal 2 is located further away from the runways. The average taxi distance for stands in Terminal 1 is 4.2
km, and for stands in Terminal 2 is 5.6 km, which is 33% greater than the average taxi distance for Terminal 1.
4.1. MEX schedule perturbations and emissions
Since 2010, passenger trafc at MEX has grown by an average of 8.5% annually; the number of aircraft movements has grown an
average of 4% annually (AICM, 2019). MEX suffers from noticeable schedule disruptions. In 2018, only 67% of all ights at MEX
complied with the schedule (SCT, 2019). In 2018, more than 20% of departing ights were delayed, with an average delay of
approximately 46 min (Flightstats, 2018).
According to Graver et al. (2018), in 2018 Mexico generated approximately 1.5% of global air passenger trafc-related emissions.
The ofcial MEX website does not disclose any information about the level of MEX emissions, or information concerning measures to
mitigate the environmental impact of its operations. However, in 2017, Mexico ofcially joined the global air transport initiative for
carbon–neutral operations on a state level, which means that all its airports, including MEX, must follow ICAO emission reduction
policies and standards (ICAO, 2020).
Considering the elevated level of schedule perturbations and the recent entry of MEX into the global carbon emission reduction
initiative, MEX is an ideal candidate for the current approach to estimate potential emissions reduction.
4.2. Implementation of E-DASA
To estimate the environmental effects of the application of E-DASA at MEX, an ofcial on-time performance report for one week has
been used in this study (AICM, 2018). This report consisted of actual and scheduled times of arrival for 3914 ights from 28 May 2018
to 03 June 2018; 53% of the ights were operated by airlines allocated to Terminal 2, and the rest of the ights were operated by
airlines located in Terminal 1. In the studied week, the level of schedule disruptions was signicant. More than 53% of scheduled
ights arrived with a delay of more than 15 min, and more than 36% of ights arrived more than 15 min earlier than scheduled.
In additions to the one-week ight schedule retrieved from the MEX performance report, the following data have been used as input
for correct schedule generation in Module II:
•Stand/aircraft size/type of ight correspondence matrix
Fig. 2. MEX layout: runways and terminal buildings (Universal Weather and Aviation, 2019).
M. Bagamanova and M. Mujica Mota
Transportation Research Part D 89 (2020) 102634
7
•Stand/airline correspondence matrix. As actual data about stands preferred/contracted by specic airlines were not available, it
was assumed that any airline could use any stand, as long as it corresponded to the airline allocation terminal (retrieved from
(AICM, 2017)), type of ight (domestic or international) and aircraft size
•Unimpeded taxi time per stand for the considered runway conguration 05R-landings/05L-departures
•Walking distances matrix for contact stands with walking distance penalisations for remote stands
•Ratio of connecting passengers per ight based on ight origin. Due to unavailability of actual data, these ratios were adapted from
IATA (2019b).
•List of airlines offering connecting ights. As actual data were not available, it was assumed that airlines belonging to the same
alliance provide such connecting ights.
•Emission factors CO, NOx, HC, and CO
2
and fuel burn rate per aircraft type.
Owing to the unavailability of actual data for the calculation of block occupancy times, the ground-handling times were assumed
based on the slots scheduled for the corresponding airlines and aircraft types from AICM (2020). When there was no information
available for an airline or aircraft type, ground-handling was assumed to be 120 min for international ights and 60 min for domestic
ights. This assumption resulted in the values presented in Table 2. By assuming ground handling times equal to the ofcially pub-
lished slots, it was intended to make the calculations as close to reality as possible despite the unavailability of actual data. In real-life
operations, ground handling times depend on the aircraft type, airline, airport and available resources among others and can often
become one of the sources of disruptions (Fricke and Schultz, 2009; Schultz and Fricke, 2016). In this article, the ground handling time
disruptions were not considered, however it would be benecial for E-DASA to include the probable turnaround time disruptions in the
future work.
Furthermore, there were no data available on aircraft engines specications for the studied ights. Therefore, the aircraft engines
and corresponding emissions factors were adapted from ICAO Aircraft Engine Emissions Databank (ICAO, 2019b), as presented in
Table 3. This databank contains rates of fuel burn and emissions with CO, NO and HC rates specied for different types of aircraft and
various engines, and CO
2
rate calculated as a constant of 3.15 kg of CO
2
per one kg of fuel burnt.
As the considered aircraft emissions depend on the amount of fuel burnt and generated exhaust, CO, NOx, HC and CO2 emissions
were calculated as emissionfactor*fuelburnrate*numberofengines. Assumptions presented in Table 3 were necessary for illustrative
purposes; however, for a real-world application where actual data are available, values corresponding to the actual engines speci-
cations should be used for more accurate results.
Due to congestion at MEX and its location in an urban area, it was decided to heavily penalise assignments to a ‘dummy’ stand. MEX
aerodrome territory does not have sufcient space to safely allocate many waiting aircraft on the apron and holding manoeuvres
greatly affect local noise and pollution levels. Thus, for the Module II optimisation algorithm Thold was assumed to be 60 min (compared
to the maximum MEX unimpeded taxi time of 12 min). To get an insight on overall MEX emissions, it was decided to assume hazard
weight He to be equal to 1 for all considered emissions.
Following the workow in Fig. 1, the target ight schedule was processed in Module I and the corresponding Bayesian distribu-
tional models were built for arrival time deviations, describing the likelihood of delays and early arrivals based on the assumed
correlation of disruptions with airline and hour of scheduled arrival.
An extract of the obtained model parameters is presented in Table 4. The complete list of model parameters can be found in
Table 2
Assumed ground-handling times, minutes.
Aircraft type Min of GH time Average of GH time Max of GH time
A388 120 120 120
AT42 40 41 70
AT76 55 55 70
B737 60 60 60
B73B 50 62 120
B73S 60 60 60
B73W 50 90 120
B748 120 120 120
B74F 120 120 120
B757 70 70 70
B767 50 92 120
B777 120 120 120
B788 40 109 120
B789 120 120 120
E170 60 64 120
E190 55 66 120
EA19 35 76 120
EA21 30 63 120
EA32 30 67 120
EA33 105 105 105
EA34 120 120 120
SU95 25 59 120
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Transportation Research Part D 89 (2020) 102634
8
Appendix A. In Table 4, the “Population-Level Effects” contains levels of the predictor variable; “Estimate” and “Estimation Error”
columns contain mean and standard deviation of the effect of the corresponding predictor; columns “Q2.5” and “Q97.5” show limits of
95% condence interval for the mean effect value. Negative estimate values correspond to ight arrivals earlier than scheduled,
positive values correspond to ights delays.
Table 3
Assumed emission factors per aircraft type.
Aircraft type Number of engines Engine type Fuel burn, kg/s/
engine
CO, kg/s/
engine
NOx, kg/s/engine HC, kg/s/engine CO
2
, kg/s/
engine
A388 4 8RR046 0.3 0.004530 0.001530 0.00006000 0.945
AT42 2 PW124B 0.0988 0.0023771 0.000524628 0.000026 0.31122
AT76 2 PW124B 0.0988 0.0023771 0.000524628 0.000026 0.31122
B737 2 3CM032 0.109 0.002398 0.0004796 0.0002616 0.34335
B73B 2 3CM032 0.109 0.002398 0.0004796 0.0002616 0.34335
B73S 2 1CM004 0.1140 0.003922 0.0004446 0.0002599 0.3591
B73W 2 8CM051 0.1130 0.002124 0.0005311 0.0002147 0.35595
B748 4 11GE139 0.2160 0.004093 0.0009569 0.0001231 0.6804
B74F 4 2GE045 0.1990 0.003827 0.0009413 0.0003065 0.62685
B757 2 5RR038 0.1800 0.003659 0.0007920 0.00004860 0.567
B767 2 1GE012 0.1500 0.004230 0.0005100 0.0009420 0.4725
B777 2 8GE100 0.2960 0.003756 0.001803 0.0001214 0.9324
B788 2 11GE136 0.1990 0.004302 0.0008438 0.0001612 0.62685
B789 2 12RR055 0.2370 0.002003 0.001296 0.00001185 0.74655
E170 2 8GE108 0.06400 0.001162 0.0002950 0.000008320 0.2016
E190 2 11GE146 0.08800 0.003672 0.0003247 0.0003538 0.2772
EA19 2 3CM027 0.09400 0.002820 0.0003572 0.0005828 0.2961
EA21 2 3IA008 0.1363 0.001270 0.0007142 0.00001363 0.429345
EA32 2 3CM026 0.1040 0.002434 0.0004472 0.0004784 0.3276
EA33 2 14RR071 0.2700 0.006472 0.001258 0.0006642 0.8505
EA34 2 8RR045 0.2300 0.002291 0.001401 0.00002990 0.7245
SU95 2 11PJ002 0.10000 0.002755 0.0003820 0.00008200 0.315
Table 4
Sample of obtained regression models characteristics.
Population-Level Effects Estimate Estimation Error Q2.5 Q97.5
Intercept −10,24 2,02 −14,15 −6,32
Airline AFR 10,21 7,27 −2,63 27,35
Airline AIJ 7,60 1,07 5,52 9,68
Airline AMX 5,32 1,10 3,16 7,46
Airline VOI 9,67 1,18 7,38 11,99
Scheduled arrival hour 03 −5,74 4,11 −13,98 2,26
Scheduled arrival hour 05 8,10 2,02 4,19 12,02
Scheduled arrival hour 06 6,69 1,88 2,98 10,35
Scheduled arrival hour 16 9,07 1,92 5,36 12,72
Scheduled arrival hour 23 0,21 2,03 −3,84 4,19
Fig. 3. MEX simulation model framework.
M. Bagamanova and M. Mujica Mota
Transportation Research Part D 89 (2020) 102634
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After learning Bayesian distributional models for schedule disruptions, Module II used distributional models to generate the new
stand occupancy times, allocated aircraft based on the data matrixes, and optimised the obtained allocation, following the objective
expressed in Formula (1). In this study, the new stand allocation schedule was generated considering arrival time deviations with a
minimum probability of 60%.
To further estimate the stand assignment generated by E-DASA in close-to-reality conditions, a series of experiments in a simulation
model of MEX was executed. A general description of the used MEX simulation model can be found in the next section.
4.3. Simulation model
The MEX simulation model was built under the paradigm of Discrete Event System (DES) (Ramadge and Murray Wonham, 1989).
This approach implies a dynamic system, whose discrete state values change abruptly due to occurring events (Silva, 2018). The model
was built following the concept shown in Fig. 3.
The model consists of the runway system, taxiways, apron areas and stands, which are interconnected by a network of edges and
nodes and replicate MEX layout shown in Fig. 2. Entities (aircraft) use those edges as paths to land and depart and to move towards the
stands and from them. The edges are scaled to the real distance they represent; all aircraft movements calculations are based on
Newton’s laws considering the distance, speed, and acceleration of the aircraft. The ground handling operations are modelled by a time
consumed by the aircraft at the corresponding stand (server). The taxi operations are modelled by the movement of the aircraft along
the edge according to the corresponding taxiing speed limits. The movements of the passengers, buses, pushback tractors and other
service vehicles are not modelled.
The MEX model is composed of entities, servers, attributes, and activities. An entity is an object that can move through the system
and perform or be a subject of different activities. A server is an object that simulates certain activities of the entities by incurring on a
delay that can be deterministic or stochastic. In MEX model, entities represent aircraft; servers represent remote and contact stands, as
well as runways. Every entity has attributes which describe its characteristics and can be specied by the user, like the speed of
movement, size, ight number, etc. Furthermore, every server has its attributes like processing time, capacity. Activity means a period
of time of the specied length. In the model, the following are the activities considered: ground handling, aircraft movement on the
runway, aircraft waiting in the arrival/departure queue.
MEX simulation model was implemented using a general-purpose DES commercial simulation software. Nevertheless, the pre-
sented framework can be implemented in any DES or multi-agent simulation software. A more detailed description and validation of
the MEX simulation model can be found in Mujica Mota and Flores (2019).
4.4. Simulation experiments
The main goal of using a simulation model in this research is to capture sources of stochasticity that occur in the system that were
not considered in the allocation algorithm, to make the solutions more realistic. For instance, E-DASA does not consider potential
aircraft waiting at the stand due to occupancy of a taxiway or stop-and-go situations that may occur on the airport apron due to
numerous aircraft taxiing simultaneously. Such conditions may result in longer taxi times and therefore more emissions. We use the E-
DASA output as the input for the simulation model, which enables us to evaluate the potential of the algorithm in more realistic
conditions.
4.4.1. Reducing the search space
The SAP is an NP-hard problem in its nature (Gu´
epet et al., 2015); considering the possible combinations of optimisation objectives
weights in Formula (1), the set of possible solutions is too large to be entirely tested in the simulation model. Thus, we reduce the
search space, identify the most promising area, and then evaluate solutions located in this area under the stochastic conditions of the
simulation model.
To restrict the set of possible solutions, the objective function weights w1,w2,w3, corresponding to the minimisation of walking
distance, remote stands, and emissions, respectively, were limited to discrete numbers 0 and 1 and the resulting stand allocations were
simulated in MEX model. Only w4, corresponding to the minimisation of unassigned aircraft, remained set to 1 through all scenarios as
the stand allocation feasibility requires a minimum number of unallocated aircraft. The results of these simulations compared to the
Table 5
Stand allocations characteristics for different values of objective function weights.
Scenario Number of
arrivals
Number of
replications
w1 w2 w3 w4 I
i=1Npaxidwalk ,
pax*km
Npo*Nopen ,
pax*stand N
n=1E
e=1BnHeFne(Tn+DTn),
tons (average)
N
idle
I 3 914 30 1 1 1 1 77 768 297 206 741 1 804.6 0
II 3 914 30 0 1 1 1 78 280 294 015 502 1 803.5 0
III 3 914 30 1 0 1 1 77 605 331 294 112 1 804.1 0
IV 3 914 30 1 1 0 1 77 656 294 949 215 1 823.8 0
V 3 914 30 0 0 1 1 78 232 378 324 408 1 760.9 0
VI 3 914 30 0 1 0 1 78 738 282 749 621 1 811.2 0
VII 3 914 30 1 0 0 1 77 520 339 779 232 1 821.7 0
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stand allocation with all weights set to 1 are presented in Table 5. The lowest values for each objective are shown in bold.
From Table 5, all generated stand allocations had zero instances of unassigned aircraft. The lowest product of walking distance and
transfer passenger number corresponds to scenario VII for all priorities set to 0 except w1. The lowest product of passenger number and
number of aircraft assigned to open stands was obtained in scenario VI, when w1 and w3 were set to 0. In scenarios VI and VII, the level
of emissions resulted in a high value.
The difference between the level of emissions in scenario I and scenario V shows that including passenger comfort priorities in the
stand allocation optimisation increases the level of emissions by 2.5%. When minimisation of emissions is completely omitted from the
goal, as in scenario IV, the resulting stand allocation produces 3.6% more emissions than in scenario V. The lowest emissions value
corresponds to scenario V; thus, the solutions generated with this set of weights in the objective function (1) represent the greatest
interest for simulation.
The results presented in Table 5 suggest that prioritising only on emission reduction results in a more environmentally friendly
stand allocation than with a complex objective. However, as airport stand allocation planning involves many interested parties, such a
simplication is not acceptable for airport stakeholders. Nevertheless, generating a stand assignment with a simplied objective
function can be useful for analysis of allocation limitations in terms of environmental footprint or any other chosen priority.
4.4.2. Stochastic search
Walking distance and contact stand priority weights set to 0 results in solutions with less pollutant footprint; thus, we discarded
other possible combinations of weights and focused on the solutions generated under w1 and w2 set to 0. The corresponding stand
allocations generated by E-DASA were evaluated for MEX emissions reduction potential with the following simulation experiments.
Table 6 summarises ve scenarios executed in the MEX simulation model. These scenarios represent different approaches for stand
allocation, where planning is optimised to minimise the emissions level. For each scenario, the corresponding CO, HC, NOx, and CO
2
emissions were tracked in the simulation model.
The presented scenarios can be described as follows:
1. Scenario A - a base case, representing ideal on-time arrivals with no disruptions. This scenario shows the level of emissions that can
be achieved by pure allocation optimisation without the inuence of schedule perturbations.
2. Scenario B - shows emissions that occur under disrupted arrivals if the allocation plan does not consider schedule disruptions and
aircraft use only originally planned stands. This scenario includes stochastic arrival time deviations generated with distributions
from Module I. If the planned stand is not available at the arrival, aircraft must wait on the apron for the planned stand to become
available.
3. Scenario C – the allocation plan does not consider disruptions. This scenario reproduces involvement of ATC (airport trafc control)
that manually reassigns aircraft to a random suitable stand if the planned stand is not available at aircraft arrival due to disruptions.
This scenario includes stochastic arrival time deviations generated with distributions from Module I.
4. Scenario D – the application of E-DASA that considers probable disruptions in the allocation plan; all aircraft must follow this plan.
This scenario includes stochastic arrival time deviations generated with distributions from Module I. If the planned stand is not
available at the arrival, aircraft must wait on the apron for stand availability.
5. Scenario E – the application of E-DASA with the involvement of ATC that manually reassigns aircraft to any other available suitable
stand if the planned stand is not available at aircraft arrival due to disruptions. This scenario includes stochastic arrival time
deviations generated with distributions from Module I.
To replicate close-to-reality airport operations, scenarios C and E simulate possible ATC intervention in daily operations to resolve
assignment conicts. Such interventions often occur in the stochastic airport environment, and often ATC has limited time to deter-
mine another stand from the available stands. Due to such time limitations, these decisions are often made without consideration of
assignment optimisation, which can impact airport footprint. In such a way, scenarios C and E consider the impact of unoptimised
manual reassignments performed by ATC.
4.5. Experiments results and discussion
Each scenario presented in Table 6, was run for 178 simulation hours, which is equivalent to seven days of simulated ight schedule
plus extra hours for possible arrival time deviations. The stand assignment schedules generated with E-DASA did not require specic
Table 6
List of simulation experiment scenarios.
Scenario
name
Number of
replications
Number of
arrivals
Schedule
disruptions
Schedule disruptions
considered
Original assignment plan
optimisation
Manual reallocation (no
optimisation)
A 30 3914 – – Yes –
B 30 3914 Yes – Yes –
C 30 3914 Yes – Yes Yes
D 30 3914 Yes Yes Yes –
E 30 3914 Yes Yes Yes Yes
M. Bagamanova and M. Mujica Mota
Transportation Research Part D 89 (2020) 102634
11
buffer times between consecutive ights assigned to the same stand, which are often used by airports to absorb arrival deviations and
inefciencies of the turnaround operations (Fricke and Schultz, 2009; Schultz and Fricke, 2016). Excluding mandatory buffer times
from allocation allows full observation of the effects of schedule disruption on the emissions level.
It is important to note, that for the simulation purposes it was assumed that an aircraft starts to emit as soon as it leaves the stand
and begins the taxi procedure. However, in real-life operations aircraft often start their engines only after being pushed back to the
taxiway by a towing tractor, which can be electric or use diesel or LPG. Nevertheless, for the proof of concept objective, which was the
goal of the simulation experiments, such detailed modelling of the taxi procedure was considered not essential and therefore was
omitted.
The results of executed simulation scenarios for weekly total emission levels statistics are shown in Fig. 4. The results for the total
number of aircraft assigned to remote stands weighted to the passengers’ number and total walking distance weighted to the transfer
passengers’ number are shown in Fig. 5.
Scenario A, the base case, does not show any variability in emissions, as all operations were on time and no aircraft waited for stand
availability. Emissions produced in this scenario are the lowest among all experiments. When the stochasticity of arrivals is introduced
into the simulation in scenario B, total emissions increased by 6%, and there was considerably more variation in total produced
emissions. In this scenario, the schedule perturbations were left unattended, and many aircraft waited for the planned stand to become
available. It can be concluded that not considering schedule disruptions and not reallocating conicted ights to another stand results
in increased airport pollution.
When manual reassignment of conicted aircraft by ATC was introduced into the simulation, it decreased unnecessary waiting
time. As a result, overall emissions decreased 3.5% compared to scenario B. However, there was still much variation in emissions in
scenario C and the average emissions level was 2.4% higher than in scenario A.
The E-DASA allocation, tested in scenario D, was able to decrease emissions by 1.5% compared to the disruption-unaware stand
allocation plan in scenario B. However, it could not decrease emissions as well as ATC-assisted reallocation in scenario C. Emissions in
scenario D were 2.1% higher than in scenario C. The lowest emissions level in conditions of disrupted arrivals was demonstrated in
scenario E. In this scenario, disruption-aware planning generated by E-DASA, combined with ATC assistance for conicted assign-
ments, reduced emissions by 4.5% compared to scenario B.
Prioritising emissions mitigation penalised passenger walking distance and usage of contact stands, as it can be seen in Fig. 5. The
best scenario in terms of emissions (scenario E) resulted in longer walking distances for transfer passengers and lower usage of stands
equipped with air bridges. This illustrates the contradictory optimisation objectives considered in Formula (1) that make this situation
a challenge for airport decision-makers. In the real-life stand allocation planning, each airport should decide priority weights for each
optimisation perspective of the multi-objective function (1). As it is illustrated, in some cases passenger comfort might be sacriced for
improving the environmental situation, but it might positively impact the price of air ticket for passengers owing to the reduction of
carbon-offset (Jou and Chen, 2015).
The experimental results demonstrate the advantage of disruption-aware planning for real-life emission reduction. Scenario E
illustrated that when E-DASA is not able to address all the stochasticity, the intervention of ATC helps in performing the reallocation
with a certain passenger service penalty. These measures allow reducing airport carbon emissions by almost four thousand tons
annually, which is equal to the annual CO
2
emissions of 873 typical passenger vehicles (US EPA, 2018).
5. Conclusions and future work
This study presents an innovative approach that combines Bayesian modelling, a multi-objective heuristic optimisation, and
simulation for solving airport stand allocation problems. We used a divide-and-conquer approach to reduce the search space, aiming to
minimise allocation-related emissions for airports. The presented work utilised simulation to include the variability of real systems and
possible stop-and-go conditions that might occur on the airport apron with numerous aircraft taxiing simultaneously. Furthermore, it
was demonstrated that the complexity of the stand allocation problem could be reduced by making an initial deterministic optimi-
sation for identifying promising regions that can be further nely explored making use of simulation techniques.
An illustrative case study conrmed the effectiveness of the methodology presented aiming at reducing allocation-related pollutant
emissions. The lowest emissions levels could be achieved by relaxing the stand assignment priorities, and by combining the outcome of
the framework with airport trafc control intervention if needed. In such a way, the experiments demonstrated that the integration of
the presented approach into a sociotechnical airport management system can reduce nearly four thousand tons of emissions per year
for the case study presented. The methodology is generic and can be applied to any airport irrespective of the layout, however, it would
be more benecial for large international hubs where the different elements play an important role in the decision process of the
allocation of gates.
Besides the contribution of this study, it opens opportunities for further research. For instance, other variables may be considered in
Module I to provide increased accuracy in expected schedule deviations like meteorological information and ground-handling dis-
ruptions. One of the limitations of the study that can be investigated further is that we did not disaggregate the pushback operation
from the complete taxi-out process. The consideration of the pushback will allow the algorithm to prioritise stands that are more
environmentally friendly or/and provide a source of aircraft fuel burn reduction e.g. use electric vehicles, ground electricity, pre-
conditioned air. Moreover, it would be important to investigate how changing emissions hazard weights in the objective function
would impact the quality of stands assignments.
M. Bagamanova and M. Mujica Mota
Transportation Research Part D 89 (2020) 102634
12
Declaration of Competing Interest
The authors declare that they have no known competing nancial interests or personal relationships that could have appeared to
inuence the work reported in this paper.
Acknowledgements
The authors would like to thank the Autonomous University of Barcelona and the Aviation Academy of the Amsterdam University
of Applied Sciences for supporting this study, and the Dutch Benelux Simulation Society (www.dutchbss.org) and EUROSIM for the
dissemination of the ndings of this study. Furthermore, we would like to express additional gratitude towards the reviewers and
Fig. 4. Experimental results for taxi-related emissions.
Fig. 5. Experimental results for the passenger-weighted number of aircraft assigned to remote stands O
open (1) and transfer passenger-weighted
walking distance Owalk (2).
M. Bagamanova and M. Mujica Mota
Transportation Research Part D 89 (2020) 102634
13
editors of this paper for their valuable comments and suggestions that helped to improve the article. The research presented in this
paper did not receive any specic grant from funding agencies in the public, commercial, or not-for-prot sectors.
Appendix A. Module I output
Population-Level Effects Estimate Estimation Error Q2.5 Q97.5
Intercept −10,24 2,02 −14,15 −6,32
Airline ABX 12,92 6,86 −0,38 26,21
Airline ACA 2,40 2,51 −2,78 7,10
Airline AFR 10,21 7,27 −2,63 27,35
Airline AIJ 7,60 1,07 5,52 9,68
Airline AJT −1,91 11,23 −25,46 18,22
Airline AMX 5,32 1,10 3,16 7,46
Airline ANA 2,31 5,00 −7,08 12,45
Airline ARE 118,79 66,99 35,23 217,63
Airline ASA 1,02 2,88 −4,52 6,78
Airline AVA 14,71 2,47 9,83 19,62
Airline AZA 1,17 5,29 −9,41 11,58
Airline BAW 0,85 4,31 −7,89 9,00
Airline CHH −3,57 9,39 −19,80 14,89
Airline CKS 80,03 79,31 −45,68 269,10
Airline CLU 36,43 53,99 −39,37 119,48
Airline CLX 8,12 5,93 −2,71 20,43
Airline CMP −0,70 1,76 −4,18 2,69
Airline CPA 9,14 13,15 −5,69 44,40
Airline CSN 9,23 9,03 −7,15 29,95
Airline DAL 1,42 1,69 −1,93 4,69
Airline DLH 2,51 4,06 −5,23 10,37
Airline ESF 23,35 3,39 16,60 29,95
Airline GEC −7,74 8,99 −26,17 8,46
Airline GMT 16,60 2,66 11,51 21,89
Airline GTI 190,34 17,29 159,57 221,68
Airline IBE 2,88 2,99 −2,99 8,58
Airline ICL 46,61 12,75 22,16 71,47
Airline JBU −8,53 2,17 −12,77 −4,30
Airline JOS 10,05 4,63 1,18 19,35
Airline KLM 10,23 4,39 1,02 18,53
Airline LAN 23,80 4,55 14,10 32,35
Airline LPE 1,79 4,08 −6,48 9,57
Airline MAA 58,98 31,69 5,18 112,37
Airline QCL 7,92 10,40 −11,98 29,05
Airline QTR 9,24 7,54 −5,23 24,95
Airline RPB −0,11 4,94 −9,51 9,99
Airline SKU 210,35 223,77 −69,48 457,40
Airline SLI 4,78 1,05 2,73 6,83
Airline SWA 2,88 1,86 −0,78 6,56
Airline TAI −0,70 3,00 −6,50 5,41
Airline TAM 12,66 4,51 3,46 21,46
Airline TAO 7,11 1,34 4,53 9,73
Airline TNO 8,32 2,99 2,68 14,37
Airline TPU 9,33 4,87 0,50 20,09
Airline UAE −1,27 7,42 −14,49 14,96
Airline UAL 3,48 1,42 0,71 6,34
Airline VIV 8,91 1,31 6,39 11,47
Airline VOC 20,09 4,20 11,75 28,27
Airline VOI 9,67 1,18 7,38 11,99
Airline WJA 6,27 2,59 1,26 11,28
Scheduled arrival hour 00 0,27 2,43 −4,29 4,71
Scheduled arrival hour 01 0,23 2,30 −4,33 4,68
Scheduled arrival hour 02 0,72 4,00 −7,53 8,18
Scheduled arrival hour 03 −5,74 4,11 −13,98 2,26
Scheduled arrival hour 04 −5,39 2,48 −10,30 −0,62
Scheduled arrival hour 05 8,10 2,02 4,19 12,02
Scheduled arrival hour 06 6,69 1,88 2,98 10,35
Scheduled arrival hour 07 2,87 1,95 −0,99 6,64
Scheduled arrival hour 08 0,11 1,89 −3,69 3,77
Scheduled arrival hour 09 1,68 1,90 −2,09 5,42
Scheduled arrival hour 10 4,12 1,90 0,37 7,82
Scheduled arrival hour 11 1,92 1,92 −1,86 5,69
Scheduled arrival hour 12 1,27 1,92 −2,49 5,06
(continued on next page)
M. Bagamanova and M. Mujica Mota
Transportation Research Part D 89 (2020) 102634
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(continued)
Population-Level Effects Estimate Estimation Error Q2.5 Q97.5
Scheduled arrival hour 13 2,04 1,91 −1,81 5,71
Scheduled arrival hour 14 2,41 1,95 −1,46 6,18
Scheduled arrival hour 15 4,95 1,90 1,10 8,58
Scheduled arrival hour 16 9,07 1,92 5,36 12,72
Scheduled arrival hour 17 8,61 1,93 4,76 12,25
Scheduled arrival hour 18 5,46 1,96 1,60 9,31
Scheduled arrival hour 19 5,33 1,94 1,41 9,11
Scheduled arrival hour 20 6,42 1,94 2,61 10,15
Scheduled arrival hour 21 10,13 1,93 6,26 13,83
Scheduled arrival hour 22 0,23 2,06 −3,74 4,21
Scheduled arrival hour 23 0,21 2,03 −3,84 4,19
Family: student
Formula: Delay ~ Airline +Hour
Samples: 3 chains, each with iterations =3500; warmup =1750; thin =1; total post-warmup samples =5250
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