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Citation: Moreira, H.; Ferreira, L.P.;
Fernandes, N.O.; Ramos, A.L.; Ávila,
P. Analysis of Boarding Strategies on
an Airbus A320 Using Discrete Event
Simulation. Sustainability 2023,15,
16476. https://doi.org/10.3390/
su152316476
Academic Editors: Ali Bahadori-
Jahromi and Maxim A. Dulebenets
Received: 19 August 2023
Revised: 14 November 2023
Accepted: 27 November 2023
Published: 1 December 2023
Copyright: © 2023 by the authors.
Licensee MDPI, Basel, Switzerland.
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4.0/).
sustainability
Article
Analysis of Boarding Strategies on an Airbus A320 Using
Discrete Event Simulation
Hélio Moreira 1, Luís Pinto Ferreira 1, 2, * , Nuno O. Fernandes 3,4 , Ana Luísa Ramos 5and Paulo Ávila 1,6
1ISEP—School of Engineering, Polytechnic of Porto, 4200-072 Porto, Portugal
2INEGI—Instituto de Ciência e Inovação em Engenharia Mecânica e Engenharia Industrial,
4200-465 Porto, Portugal
3Department of Industrial Engineering, Instituto Politécnico de Castelo Branco,
6000-767 Castelo Branco, Portugal
4ALGORITMI Research Unit, University of Minho, Campus de Gualtar, 4710-057 Braga, Portugal
5
Competitiveness and Public Policies (GOVCOPP), Industrial Engineering and Tourism (DEGEIT), University
of Aveiro, 3810-193 Aveiro, Portugal
6INESC TEC—Instituto de Engenharia de Sistemas e Computadores, 4200-465 Porto, Portugal
*Correspondence: lpf@isep.ipp.pt
Abstract:
Boarding time constitutes a critical element of turnaround time, which is used to measure
the efficiency of airline operations. Therefore, to reduce boarding time, it is imperative to reconsider
traditional passenger boarding strategies to make them more efficient. In this sense, this study seeks
to analyze the impact of different strategies on boarding times using discrete event simulation on an
Airbus 320. Seven boarding strategies have been identified and considered in our study, as follows:
random, back-to-front, outside-in, reverse pyramid, blocks, Steffen, and modified optimal. The
impact of carrying hand luggage and the presence of priority passengers has been considered, as well
as the impact of having a continuous arrival of passengers during the boarding process versus having
all passengers available at boarding time. In general, simulation results have pointed out that the
outside-in and reverse pyramid strategies are the most effective, improving boarding time by up to
15%, when compared to the random strategy. Moreover, the back-to-front strategy, which is generally
implemented by airline companies, has been shown to be the most inefficient strategy. Efficient
boarding strategies are expected to contribute to the sustainability of air travel by minimizing the
turnaround time, improving operational efficiency, and reducing emissions.
Keywords: boarding strategies; turnaround time; simulation; sustainability
1. Introduction
Aircraft have become an essential means of transport and, as such, air travel has
increased dramatically over the last decades [
1
]. This demand for air travel has caused
enormous competition in the aviation sector with a view to reducing costs, increasing
efficiency, and meeting customer satisfaction [
2
,
3
]. To avoid congestion at airports, as well as
to enhance operational efficiency, airlines have been compelled to reduce their turnaround
time [
4
]. This is because airlines only generate revenue when planes fly, as having aircraft
on the ground is considered unproductive [
3
,
5
]. The turnaround time mainly consists
of passengers deboarding, cleaning, and passengers boarding; however, the most critical
point resides in the boarding activity. It is estimated that a 1 min reduction in boarding
time represents a saving of $30 United States Dollars (USD) for each turnaround [
2
].
Nevertheless, the process of boarding passengers on an aircraft is not always carried
out in the best possible manner [
6
], with airline companies having limited control over
passengers [5].
To reduce boarding time, the amount of interference amongst passengers should be
minimized. This means that airlines must adopt an efficient boarding strategy to control
Sustainability 2023,15, 16476. https://doi.org/10.3390/su152316476 https://www.mdpi.com/journal/sustainability
Sustainability 2023,15, 16476 2 of 12
the order in which passengers enter the aircraft [
3
,
5
]. The literature addressing strategies to
improve the boarding process is still rather scant [
2
,
3
,
5
,
7
]. Boarding processes, if executed
incorrectly, can lead to delays and additional costs for the airline [8].
In the case of well-implemented strategies, the three main parts involved—airlines,
airport operators, and passengers—ultimately benefit from this reduction in boarding
time [
6
]. Additionally, passengers valorize solutions that minimize waiting time at the
boarding gate [9].
The main purpose of our study is to design a simulation tool that will be able to
analyze different boarding strategies on an Airbus A320. This aircraft, which can carry up
to 156 passengers, is used for short- and medium-haul flights and is commonly used by
many airlines. This work adds to scientific knowledge by analyzing the performance of
different boarding strategies under both the continuous arrival of passengers during the
boarding process and the availability of all passengers at the beginning of the boarding
process. The model was developed in a flexible manner, allowing for the simulation of
different strategies, which can be adapted to the percentage of passengers carrying hand
luggage, as well as the number of priority passengers involved in the boarding process. One
can, thus, acquire a better understanding of which strategies present a greater efficiency in
the context of specific scenarios.
The field of aviation has been requested to minimize its carbon footprint. To this end,
a significant contribution includes the implementation of sustainable boarding procedures,
thus ensuring that the aviation sector moves further along the path of environmentally
friendly and responsible practices [
10
–
13
]. There are several external factors that impact
airline boarding procedures, such as the following: the layout of the airport, security
regulations, type of aircraft, weather conditions, gate availability, customer service, among
others. To ensure a straightforward and efficient boarding process, boarding strategies
must be adapted to these variables.
The remainder of the paper is organized as follows: Section 2comprises an overview
of the current literature concerning the boarding of passengers on an aircraft. Section 3
describes the methods used to carry out the study, including the simulation model and
considered assumptions. The simulation results and a discussion of these are both in-
cluded in Section 4. Lastly, Section 5concludes the study and defines guidelines for future
research work.
2. Literature Review
Marelli et al. [
14
] define the turnaround time of an aircraft as “the time required to
unload an airplane after its arrival at the gate and to prepare it for departure again”. During
this time, several events occur, namely: deboarding and boarding of passengers, unloading
and loading of luggage and/or cargo, refueling, crew replacement, cabin cleaning, and
kitchen maintenance [
1
,
3
,
5
]. The study developed by Van Landeghem & Beuselinck [
4
]
concluded from interviews that the turnaround time can range from 30 to 60 min. Theoret-
ically, the activity of deboarding requires approximately 10 to 15 min, cleaning about 15
to 20 min, and boarding approximately 10 min. Yet, in practical terms, the latter is almost
always exceeded, often reaching 30 min [
4
]. Average boarding speed has seen a drop in the
last 30 years of about 55% [
14
]. This decline in the efficiency of the boarding process can be
attributed to the more generalized use of carry-on baggage, a greater convenience on the
part of passengers, and passenger demographic data, as well as the strategies implemented
by an airline and the flight distance [
2
]. Lower boarding rates will certainly lead to an
increase in boarding times.
The main cause of delay in passenger boarding is interference among passengers.
Soolaki et al. [
3
] define this interference in boarding as an instance when a passenger
blocks another passenger or the aisle itself, or when passenger access to a seat is obstructed.
Interference can be classified into the following two types: aisle interference and seat
interference. Aisle interference occurs when passengers wish to reach their seats and are
blocked in the aisle by other passengers who have stopped in front of them, usually stowing
Sustainability 2023,15, 16476 3 of 12
hand luggage in the upper lockers. Seat interference occurs, for example, when the window
passenger wishes to take his seat and must ask the passenger already sitting in the aisle
seat or in the middle to get up and allow their passage. According to Delcea et al. [
15
]
and Cotfas et al. [
16
], there are four types of seat interference that passengers are faced
with during their journey. Moreover, according to the same authors [
15
,
16
], the greatest
interference delay is generated by type 1, during which the passenger with a window
seat is required to wait for the other two passengers to move out before occupying their
corresponding seat. The second longest delay, generated by the fact that a window seat
passenger must wait for the occupant of the middle seat to clear the way is presented as
a type 2 seat interference. Types 3 and 4, which refer to the passenger in the middle or
window seat waiting for the passenger in the aisle seat to clear the way, both generate an
identical delay time, which is still shorter than the first two types.
To reduce passenger interference and, in turn, boarding time, several boarding strate-
gies have been considered. The main boarding strategies used by airlines are summarized
as follows [7,17]:
•
Random: One single boarding group of passengers randomly accesses the plane’s entry
point. This procedure is often used as a point of reference for subsequent comparison
with other boarding methods [17] (see Figure 1a).
•
Back-to-Front: In this method of boarding, the first passengers to board are those in the
last rows of the plane. Boarding continues until the front rows are reached. The rows
on the plane are divided into zones (or blocks). Any number can be attributed to these
zones, from two to the total number of actual rows. Despite being a straightforward
strategy to implement, it can easily result in inefficiency, as congestion often occurs in
the boarding queues [17] (see Figure 1b).
•
Outside-In: also denominated as WMA or Wilma (Window–Middle–Aisle), this
method first boards passengers who have window seats and, subsequently, those
in the middle seats, finally followed by passengers sitting next to the aisle. This
method has so far led to very efficient boarding times, eliminating seat interference [
5
]
(see Figure 1c).
•
Reverse Pyramid: In this method, the boarding of passengers occurs from the external
rear to the inner front section of the cabin. In fact, it combines the back-to-front
and outside-in strategies, so that simultaneous boarding occurs on the aircraft from
back-to-front and from the outside-in. During this procedure, the first passengers
to board are those with a window seat and a middle seat located at the rear of the
airplane. Passengers with an aisle seat at the front of the plane are the last to board.
This strategy has proved to be an efficient method and is implemented by American
West Airlines [5] (see Figure 1d).
•
Blocks: In this case, the rows in an aircraft are divided into zones or blocks, each
consisting of several rows, with each passenger assigned to a designated block. This
method first boards passengers seated in the last rows (block 1) and then passengers
that are in the front rows (block 2). Subsequently, the order proceeds once again,
beginning with the farthest zone (last unoccupied rows), then the front rows, and so
forth. The positive aspect of this procedure is that when passengers enter the aircraft
from the back and front, they do not block each other’s paths [5] (see Figure 1e).
•
Steffen: The Steffen method organizes passengers in a specific order. Boarding is
carried out from back to front and from the windows to the corridor. Passengers
occupying a specific seat in the row are seated two rows from each other, in the same
seat position (e.g., 12F, 10F, 8F, 6F, 4F, 2F). Firstly, on each side of the cabin, passengers
are seated according to even and odd rows, occupying the window seats, then the
middle seats, and, finally, the aisle seats [17] (see Figure 1f).
•
Modified Optimal: This method consists of boarding passengers in alternating queues,
providing them with enough space to carry their luggage. Passengers are divided
into four boarding groups. The first of these consists of all those passengers who will
occupy seats in the even rows, which are limited to the right or left sides of the plane
Sustainability 2023,15, 16476 4 of 12
only. The second group includes all the passengers who will sit on the unoccupied
side of the plane. The third and fourth groups consist of passengers occupying seats
in the odd rows on each side of the plane [5] (see Figure 1g).
Sustainability 2023, 15, x FOR PEER REVIEW 4 of 13
divided into four boarding groups. The first of these consists of all those passengers
who will occupy seats in the even rows, which are limited to the right or left sides of
the plane only. The second group includes all the passengers who will sit on the
unoccupied side of the plane. The third and fourth groups consist of passengers oc-
cupying seats in the odd rows on each side of the plane [5] (see Figure 1g).
(a) (b) (c)
(d) (e) (f)
(g)
Figure 1. Illustration of the following boarding strategies [17]: (a) random; (b) back-to-front; (c) out-
side-in; (d) reverse pyramid; (e) blocks; (f) Steffen; and (g) modified optimal.
Several studies have already been carried out with a view to implement aircraft
boarding strategies. Different techniques have been used to address the problem, includ-
ing the following: (1) simulation [1,4,5,9,14,18,19], (2) analytical methods [2,3,20,21], and
(3) experiments in the aircraft [17,22]. The study developed by Bidanda et al. [8], for ex-
ample, reviews the literature dealing with the implementation of models aiming to opti-
mize boarding processes, thus achieving maximum efficiency. A more extensive compar-
ative study [6] considered previous and future research studies in this area. On analyzing
the results found in the research pertaining to boarding strategies, the authors Jaehn &
Neumann [6] concluded that simple methods such as random boarding are more effective
than the most commonly used back-to-front strategy. Nyquist & McFadden [2] demon-
strated that luggage restriction reduces boarding time. Qiang et al. [19] developed a sim-
ulation model in which passengers carrying more luggage are boarded first. Kisiel [18]
looked into the potentially problematic issues of generalized strategies, more specifically
Figure 1.
Illustration of the following boarding strategies [
17
]: (
a
) random; (
b
) back-to-front;
(c) outside-in; (d) reverse pyramid; (e) blocks; (f) Steffen; and (g) modified optimal.
Several studies have already been carried out with a view to implement aircraft board-
ing strategies. Different techniques have been used to address the problem, including the
following: (1) simulation [
1
,
4
,
5
,
9
,
14
,
18
,
19
], (2) analytical methods [
2
,
3
,
20
,
21
], and (3) ex-
periments in the aircraft [
17
,
22
]. The study developed by Bidanda et al. [
8
], for example,
reviews the literature dealing with the implementation of models aiming to optimize board-
ing processes, thus achieving maximum efficiency. A more extensive comparative study [
6
]
considered previous and future research studies in this area. On analyzing the results
found in the research pertaining to boarding strategies, the authors Jaehn & Neumann [6]
concluded that simple methods such as random boarding are more effective than the most
commonly used back-to-front strategy. Nyquist & McFadden [
2
] demonstrated that luggage
restriction reduces boarding time. Qiang et al. [
19
] developed a simulation model in which
passengers carrying more luggage are boarded first. Kisiel [
18
] looked into the potentially
problematic issues of generalized strategies, more specifically those which concern the
number of priority passengers involved. Ren & Xu (2018) [
22
] claimed that the absence
of music during boarding reduces the time required for this activity. A study conducted
Sustainability 2023,15, 16476 5 of 12
by Schultz [
20
] proposed changing the aircraft’s infrastructure to reduce the number of
interference events. Tang et al. [
21
] presented a boarding strategy that considers the charac-
teristics of individual passengers. This study was one of the first to discuss the correlation
between boarding time and the percentage of passengers carrying hand luggage and/or
the number of priority passengers, using seven different boarding strategies. Although
this study used the Airbus 320 aircraft in its analysis, this is simply a general example
which can be applied to different aircraft. Indeed, our chief objective is to enable airline
companies to implement better boarding methods. Another more recent study undertaken
by Kobbaey et al. [
11
] implements independent agent-based simulation in order to evaluate
the most widespread research pertaining to the boarding of individual passengers and
groups. The aspects considered include luggage, walking speed, and passengers’ disrespect
of required norms. The analysis also puts forward a new procedure to reduce delays in
boarding. The research results point to an improved performance of this new strategy
when compared to previously implemented ones, especially when there are greater levels
of seating and luggage capacity in an aircraft.
3. Methods
Computer simulation constitutes a critical tool for the study and analysis of complex
processes and systems [
23
]. Simulation makes it possible to design a model that anchors
on a real or hypothetical system, which can predict events from prior data, as well as
analyzing areas of potential improvement and evaluating the impact of different operating
strategies [
24
]. Discrete event simulation allows for the modeling of complex systems
for which analytical models are not available, see, e.g., Milne and Kelly [
25
], Steffen [
26
],
Tang et al. [
21
], Briel et al. [
27
], among others. To identify the best boarding strategies, a
discrete event simulation model was developed using the Arena
®
14.0 software. Arena
allows for flowchart modeling, performance metrics and dashboards, and realistic 2D and
3D animation, including a complete range of statistical distribution options to accurately
model process variability. The developed model includes not only logic and animation, but
also a graphical interface, which allows the user to parameterize the logical model.
3.1. Model Assumptions and Performance Measures
Different parameters have been considered in the simulation model to implement
the previously mentioned boarding strategies, namely, random, back-to-front, outside-in,
reverse pyramid, blocks, Steffen, and modified optimal. The main parameters considered
are the following:
•
Inter-arrival time: the time-lapse between two passengers arriving at the boarding gate.
•
Hand luggage delay: the time required for a passenger to stow his hand baggage in
the designated compartment.
•Response time: the response time of all involved passengers.
•Type 1 seat delay: the time caused by a type 1 seat interference.
•Type 2 seat delay: the time caused by a type 2 seat interference.
•Types 3 and 4 seat delay: the time caused by type 3 and type 4 seat interferences.
Table 1presents the various parameters adopted in the simulation model with their
respective values.
According to Schultz [
28
], the time each passenger needs to take his seat depends on
the hand luggage delay, the seat delay, and the response time of all the involved passen-
gers. These times in our study are modelled with stochastic probabilities distributions,
as indicated in Table 1. For the hand luggage delay we follow Schultz [
29
] and use the
Weibull distribution, while the seat delay is determined, as in Schultz [
28
,
29
], as the sum
of the required movement times using the proposed probability distribution for a single
movement, i.e., triangular (1.8, 2.4, 3) seconds. Finally, concerning the inter-arrival time
between passengers we follow Schultz [
29
], while passenger speed was adopted from
Schultz [28].
Sustainability 2023,15, 16476 6 of 12
Table 1. Simulation parameters and values.
Parameter Value
Passenger speed 0.8 m/s
Inter-arrival time between passengers Exponential (3.7) s
Hand luggage delay Weibull α= 1.7 and β= 16.0 s
Seat access without any disturbance Triangular (min = 1.8, mode = 2.4, max = 3) s
Response time of involved passengers Triangular (min = 6, mode = 9, max = 20) s
Type 1 seat delay Nine movements required
Type 2 seat delay Five movements required
Types 3 and 4 seat delay Four movements required
3.2. Simulation Model
The graphical interface for the simulation model was developed on Visual Basic
for Applications (VBA). This allows the user to configure the boarding strategies and
boarding parameters in a simple and intuitive manner; the user does not need to have prior
knowledge of simulation modeling techniques to manipulate this graphical interface. The
operation of the graphical interface is presented in detail in the flowchart in Figure 2, while
the graphical interface is presented in Figure 3. This interface allows for the automatic
generation of different boarding strategy models according to the user’s needs.
Sustainability 2023, 15, x FOR PEER REVIEW 6 of 13
Table 1. Simulation parameters and values.
Parameter Value
Passenger speed 0.8 m/s
Inter-arrival time between passengers Exponential (3.7) s
Hand luggage delay Weibull α = 1.7 and β = 16.0 s
Seat access without any disturbance Triangular (min = 1.8, mode = 2.4, max = 3) s
Response time of involved passengers Triangular (min = 6, mode = 9, max = 20) s
Type 1 seat delay Nine movements required
Type 2 seat delay Five movements required
Types 3 and 4 seat delay Four movements required
According to Schul [28], the time each passenger needs to take his seat depends on
the hand luggage delay, the seat delay, and the response time of all the involved passen-
gers. These times in our study are modelled with stochastic probabilities distributions, as
indicated in Table 1. For the hand luggage delay we follow Schul [29] and use the
Weibull distribution, while the seat delay is determined, as in Schul [28,29], as the sum
of the required movement times using the proposed probability distribution for a single
movement, i.e., triangular (1.8, 2.4, 3) seconds. Finally, concerning the inter-arrival time
between passengers we follow Schul [29], while passenger speed was adopted from
Schul [28].
3.2. Simulation Model
The graphical interface for the simulation model was developed on Visual Basic for
Applications (VBA). This allows the user to configure the boarding strategies and board-
ing parameters in a simple and intuitive manner; the user does not need to have prior
knowledge of simulation modeling techniques to manipulate this graphical interface. The
operation of the graphical interface is presented in detail in the flowchart in Figure 2, while
the graphical interface is presented in Figure 3. This interface allows for the automatic
generation of different boarding strategy models according to the user’s needs.
Figure 2. Flowchart for the graphical interface developed.
Figure 2. Flowchart for the graphical interface developed.
Sustainability 2023, 15, x FOR PEER REVIEW 7 of 13
Figure 3. Graphical interface—initial page.
The animation of the simulation model aims to generate its dynamic animated rep-
resentation, showing the boarding of passengers on the aircraft during the execution time.
It is, thus, possible to obtain feedback from the constructed system, verifying whether it
corresponds to what was initially envisioned. Figure 4 illustrates the developed animation
of the model, which presents a simplified version of an aircraft layout.
The Airbus A320 aircraft is used as a case study and boarding is carried out starting
from the front of the aircraft using a jet bridge. The arrangement of the cabin in question
consists of 30 passenger rows and one hundred and fifty-six seats, as follows: rows 1 to 6
have four seats, where first-class passengers are located; rows 7 and 8 do not have any
seats, thus forming a division between the classes; and the remaining rows have six seats,
where the economy class passengers are located. Seat numbering is in accordance with
the rows and follows a leering sequence of A–F, from left to right.
Figure 4. Example of the animated model developed (partly adapted from [30]).
At the beginning of the simulation, the passengers are organized in boarding groups
depending on the boarding strategy. Each boarding group has seats in a specific location.
The first boarding group to embark refers to the first class, followed by the priority pas-
sengers, and then by the groups defined for each boarding strategy.
Once the boarding process starts, the first passenger leaves the boarding gate and
walks thought the jet bridge followed by the other passengers. Upon entering the aircraft,
Figure 3. Graphical interface—initial page.
The animation of the simulation model aims to generate its dynamic animated repre-
sentation, showing the boarding of passengers on the aircraft during the execution time.
Sustainability 2023,15, 16476 7 of 12
It is, thus, possible to obtain feedback from the constructed system, verifying whether it
corresponds to what was initially envisioned. Figure 4illustrates the developed animation
of the model, which presents a simplified version of an aircraft layout.
Sustainability 2023, 15, x FOR PEER REVIEW 7 of 13
Figure 3. Graphical interface—initial page.
The animation of the simulation model aims to generate its dynamic animated rep-
resentation, showing the boarding of passengers on the aircraft during the execution time.
It is, thus, possible to obtain feedback from the constructed system, verifying whether it
corresponds to what was initially envisioned. Figure 4 illustrates the developed animation
of the model, which presents a simplified version of an aircraft layout.
The Airbus A320 aircraft is used as a case study and boarding is carried out starting
from the front of the aircraft using a jet bridge. The arrangement of the cabin in question
consists of 30 passenger rows and one hundred and fifty-six seats, as follows: rows 1 to 6
have four seats, where first-class passengers are located; rows 7 and 8 do not have any
seats, thus forming a division between the classes; and the remaining rows have six seats,
where the economy class passengers are located. Seat numbering is in accordance with
the rows and follows a leering sequence of A–F, from left to right.
Figure 4. Example of the animated model developed (partly adapted from [30]).
At the beginning of the simulation, the passengers are organized in boarding groups
depending on the boarding strategy. Each boarding group has seats in a specific location.
The first boarding group to embark refers to the first class, followed by the priority pas-
sengers, and then by the groups defined for each boarding strategy.
Once the boarding process starts, the first passenger leaves the boarding gate and
walks thought the jet bridge followed by the other passengers. Upon entering the aircraft,
Figure 4. Example of the animated model developed (partly adapted from [30]).
The Airbus A320 aircraft is used as a case study and boarding is carried out starting
from the front of the aircraft using a jet bridge. The arrangement of the cabin in question
consists of 30 passenger rows and one hundred and fifty-six seats, as follows: rows 1 to
6 have four seats, where first-class passengers are located; rows 7 and 8 do not have any
seats, thus forming a division between the classes; and the remaining rows have six seats,
where the economy class passengers are located. Seat numbering is in accordance with the
rows and follows a lettering sequence of A–F, from left to right.
At the beginning of the simulation, the passengers are organized in boarding groups
depending on the boarding strategy. Each boarding group has seats in a specific loca-
tion. The first boarding group to embark refers to the first class, followed by the priority
passengers, and then by the groups defined for each boarding strategy.
Once the boarding process starts, the first passenger leaves the boarding gate and
walks thought the jet bridge followed by the other passengers. Upon entering the aircraft,
the passengers make their way to find their assigned seats. The aisle is divided into cells,
one per row of seats, and the passengers move from cell to cell along the aisle until they
reach their assigned seat row. Before entering a cell, we check for possible blocking; if
the cell in front of the passenger is occupied by another passenger we have a blocking
situation, and the passenger has to wait. At each cell, we can have two passengers at a time.
Once a passenger reaches his seat, the time to stow their hand luggage in the overhead
compartment and to take his seat is generated, blocking the aisle for all the other passengers
that are behind him, creating an aisle interference. For the passengers that reach their seats,
a seat delay is generated depending on the type of seat interference. After the passenger is
seated, the aisle is unblocked for the passengers waiting behind. This process is repeated
for each one of the passengers, whenever necessary, until the last passenger is seated.
4. Simulation Results
To compare the performance of the strategies implemented, the total boarding time
and the boarding time per passenger were recorded as outputs of the simulation. Each
experimental scenario was replicated 100 times. We also considered the seating rate, which
is the inverse of the mean time between the seating of two passengers. To replicate a real-life
situation, data incorporating 24 first-class passengers was also acquired and analyzed.
Figure 5presents the results for the average total boarding times of each boarding
strategy using the maximum number of passengers seated in the aircraft. A simulation
was carried out under the following two main scenarios: (1) the continuous arrival of pas-
sengers during the boarding process following an exponential of (3.7) seconds; and (2) the
availability of all passengers at boarding time. The aircraft’s (maximum) capacity, 75% of
passengers carrying hand luggage, and no priority passengers were assumed. According
Sustainability 2023,15, 16476 8 of 12
to the results obtained, the Steffen strategy provides a reference point, constituting the
“fastest” boarding method. This is true for both scenarios, while performing relatively
better when all passengers are available at the beginning of the boarding process. However,
this strategy is rather impractical as it may cause enormous queues at the boarding gate.
The procedure ensures that passengers enter the cabin one by one, in accordance with seat
numbers in decreasing order (except for first-class passengers). The strategies that were
closest to this reference point were achieved using the outside-in and reverse pyramid
strategies. The back-to-front boarding and blocks strategies presented the worst results. A
slightly better performance was observed in the random and modified optimal strategies;
yet, these were not as good as the outside-in and reverse pyramid strategies.
Sustainability 2023, 15, x FOR PEER REVIEW 8 of 13
the passengers make their way to find their assigned seats. The aisle is divided into cells,
one per row of seats, and the passengers move from cell to cell along the aisle until they
reach their assigned seat row. Before entering a cell, we check for possible blocking; if the
cell in front of the passenger is occupied by another passenger we have a blocking situa-
tion, and the passenger has to wait. At each cell, we can have two passengers at a time.
Once a passenger reaches his seat, the time to stow their hand luggage in the overhead
compartment and to take his seat is generated, blocking the aisle for all the other passen-
gers that are behind him, creating an aisle interference. For the passengers that reach their
seats, a seat delay is generated depending on the type of seat interference. After the pas-
senger is seated, the aisle is unblocked for the passengers waiting behind. This process is
repeated for each one of the passengers, whenever necessary, until the last passenger is
seated.
4. Simulation Results
To compare the performance of the strategies implemented, the total boarding time
and the boarding time per passenger were recorded as outputs of the simulation. Each
experimental scenario was replicated 100 times. We also considered the seating rate,
which is the inverse of the mean time between the seating of two passengers. To replicate
a real-life situation, data incorporating 24 first-class passengers was also acquired and an-
alyzed.
Figure 5 presents the results for the average total boarding times of each boarding
strategy using the maximum number of passengers seated in the aircraft. A simulation
was carried out under the following two main scenarios: (1) the continuous arrival of pas-
sengers during the boarding process following an exponential of (3.7) seconds; and (2) the
availability of all passengers at boarding time. The aircraft’s (maximum) capacity, 75% of
passengers carrying hand luggage, and no priority passengers were assumed. According
to the results obtained, the Steffen strategy provides a reference point, constituting the
“fastest” boarding method. This is true for both scenarios, while performing relatively
beer when all passengers are available at the beginning of the boarding process. How-
ever, this strategy is rather impractical as it may cause enormous queues at the boarding
gate. The procedure ensures that passengers enter the cabin one by one, in accordance
with seat numbers in decreasing order (except for first-class passengers). The strategies
that were closest to this reference point were achieved using the outside-in and reverse
pyramid strategies. The back-to-front boarding and blocks strategies presented the worst
results. A slightly beer performance was observed in the random and modified optimal
strategies; yet, these were not as good as the outside-in and reverse pyramid strategies.
(a) (b)
Figure 5. Total boarding time for each one of the boarding strategies. (a) Continuous arrival of pas-
sengers during boarding; and (b) all passengers available at boarding time.
Figure 5.
Total boarding time for each one of the boarding strategies. (
a
) Continuous arrival of
passengers during boarding; and (b) all passengers available at boarding time.
Tables 2and 3present the average boarding time per passenger (p.p.) and seating rate
for the scenarios of continuous arrival of passengers during boarding and for all passengers
available, respectively. These measures are of considerable importance as they point to the
amount of interference that aisle and seat passengers experience before being able to take
their seats. Among the various strategies, the greatest difference in individual boarding
time lies in those that include seat interferences (random, back-to-front, block, and modified
optimal), as well as those that do not (outside-in, reverse pyramid, and Steffen). When
compared to the back-to-front and blocks strategies, the difference between the random
and modified optimal strategies relates to the amount of passenger congestion in the same
area of the plane.
Table 2. Boarding time per passenger and seating rate for the continuous arrival of passengers.
Boarding Strategy Boarding Time p.p. (min.) *
Boarding Time p.p.
with Hand Luggage
(min.) *
Boarding Time p.p.
without Hand
Luggage (min.) *
Seating Rate
(Passengers/min.)
Random 1.73 ±0.097 1.79 ±0.095 1.57 ±0.107 8.83
Back-to-front 2.99 ±0.151 3.05 ±0.150 2.82 ±0.155 7.70
Outside-in 1.12 ±0.053 1.17 ±0.053 0.96 ±0.055 9.78
Reverse Pyramid 1.07 ±0.038 1.13 ±0.038 0.88 ±0.040 9.90
Blocks 2.65 ±0.086 2.71 ±0.085 2.48 ±0.102 7.55
Steffen 0.73 ±0.020 0.79 ±0.020 0.56 ±0.021 10.26
Modified Optimal 1.76 ±0.098 1.82 ±0.098 1.59 ±0.099 8.99
* 95% confidence interval on the mean.
Sustainability 2023,15, 16476 9 of 12
Table 3. Boarding time per passenger and seating rate for all passengers available at boarding time.
Boarding Strategy Boarding Time p.p. (min.) *
Boarding Time p.p.
with Hand Luggage
(min.) *
Boarding Time p.p.
without Hand
Luggage (min.) *
Seating Rate
(Passengers/min.)
Random 2.70 ±0.035 2.75 ±0.035 2.52 ±0.051 9.29
Back-to-front 4.19 ±0.066 4.25 ±0.069 4.02 ±0.086 7.92
Outside-in 2.11 ±0.030 2.17 ±0.030 1.93 ±0.037 11.71
Reverse Pyramid 2.24 ±0.033 2.30 ±0.034 2.03 ±0.036 11.90
Blocks 3.39 ±0.053 3.44 ±0.055 3.23 ±0.077 8.27
Steffen 1.44 ±0.019 1.50 ±0.020 1.25 ±0.021 15.91
Modified Optimal 2.65 ±0.040 2.72 ±0.043 2.45 ±0.049 9.59
* 95% confidence interval on the mean.
When comparing the results from Table 2(continuous arrival of passengers) with
those from Table 3(all passengers available at boarding time), we can observe a higher
boarding time per passenger in the latter, as passengers, on average, arrive earlier to the
boarding gate. We also can see that the relative performance of the strategies is maintained
concerning the boarding time per passenger and the seating rate. However, all passengers
being available at boarding time results in a higher seating rate across the strategies, as
could be expected.
Figures 6and 7refer to the situation of the continuous arrival of passengers during
boarding time. Figure 6presents a graph which reveals potential issues arising from
each boarding strategy, associated with the number of passengers carrying hand luggage.
For any of the procedures adopted, the chart indicates that there is a positive correlation
between the percentage of passengers with carry-on luggage and the total boarding time.
What can be observed is that, as the percentage of these passengers increases, so does the
total boarding time, regardless of which strategy is implemented. However, this rate of
escalation may vary, depending on the strategy chosen. The Steffen strategy indicates an
escalation rate close to zero due to the virtual inexistence of interference. The outside-in
and reverse pyramid strategies tend to perform closer to an optimal level. This is chiefly
attributed to the elimination of seat interference at boarding. Performance deterioration
is moderate in the random and modified optimal strategies. The highest performance
deterioration occurs in the back-to-front and blocks strategies, where the aircraft is parted
into blocks, five in our case. This performance deterioration is due to the increase in aisle
and seat interference within each block (for the back-to-front strategy) and within and
between blocks (for the blocks strategy) when a higher percentage of passengers is carrying
hand luggage. When a scenario of the absence of luggage is contemplated, there are
virtually no differences between the various boarding strategies. As can be seen in Figure 7,
when all passengers carry hand baggage, there is a greater disparity in the boarding times
for the different strategies.
Figure 7presents a graph that indicates the possible differences in each boarding
strategy when associated with the number of priority passengers on the aircraft. The
chart shows a positive correlation between the number of priority passengers and the
total boarding time for the seven strategies. The random and modified optimal strategies
reveal no change when priority passengers are added. The outside-in, reverse pyramid,
and Steffen strategies tend towards lengthier boarding times as the number of priority
passengers increases. This is explained by the fact that these strategies are designed to
eliminate seat interference; it follows that, when priority passengers are included, these
interferences emerge once again. On the other hand, the back-to-front and blocks strategies
show an improved performance as the number of priority passengers increases. This is due
to a reduction in passenger congestion in the same area of the aircraft. Despite the better
performance of these strategies, they are unable to surpass those of the outside-in, reverse
Sustainability 2023,15, 16476 10 of 12
pyramid, and Steffen strategies, even when the second group is less efficient, and the first
group reveals an improved performance. Were the number of priority passengers equal to
the number of seats available for the economy class (132 seats), any of the strategies would
result in the same boarding times as the random strategy. This resides in the fact that their
behavior is identical; namely, there is only one boarding group.
Sustainability 2023, 15, x FOR PEER REVIEW 10 of 13
escalation rate close to zero due to the virtual inexistence of interference. The outside-in
and reverse pyramid strategies tend to perform closer to an optimal level. This is chiefly
aributed to the elimination of seat interference at boarding. Performance deterioration is
moderate in the random and modified optimal strategies. The highest performance dete-
rioration occurs in the back-to-front and blocks strategies, where the aircraft is parted into
blocks, five in our case. This performance deterioration is due to the increase in aisle and
seat interference within each block (for the back-to-front strategy) and within and between
blocks (for the blocks strategy) when a higher percentage of passengers is carrying hand
luggage. When a scenario of the absence of luggage is contemplated, there are virtually
no differences between the various boarding strategies. As can be seen in Figure 7, when
all passengers carry hand baggage, there is a greater disparity in the boarding times for
the different strategies.
Figure 6. Impact of the number of passengers carrying hand luggage on the total boarding time.
Figure 7 presents a graph that indicates the possible differences in each boarding
strategy when associated with the number of priority passengers on the aircraft. The chart
shows a positive correlation between the number of priority passengers and the total
boarding time for the seven strategies. The random and modified optimal strategies reveal
no change when priority passengers are added. The outside-in, reverse pyramid, and Stef-
fen strategies tend towards lengthier boarding times as the number of priority passengers
increases. This is explained by the fact that these strategies are designed to eliminate seat
interference; it follows that, when priority passengers are included, these interferences
emerge once again. On the other hand, the back-to-front and blocks strategies show an
improved performance as the number of priority passengers increases. This is due to a
reduction in passenger congestion in the same area of the aircraft. Despite the beer per-
formance of these strategies, they are unable to surpass those of the outside-in, reverse
pyramid, and Steffen strategies, even when the second group is less efficient, and the first
group reveals an improved performance. Were the number of priority passengers equal
to the number of seats available for the economy class (132 seats), any of the strategies
would result in the same boarding times as the random strategy. This resides in the fact
that their behavior is identical; namely, there is only one boarding group.
Figure 6. Impact of the number of passengers carrying hand luggage on the total boarding time.
Sustainability 2023, 15, x FOR PEER REVIEW 11 of 13
Figure 7. Impact of priority passengers on the total boarding time.
5. Conclusions
A study of the efficiency of passenger boarding strategies on an Airbus A320 was
carried out using discrete event simulation and the Arena software. By resorting to the
simulation, seven strategies were evaluated when boarding is carried out starting from
the front of the aircraft using a jet bridge, namely: random, back-to-front, outside-in, re-
verse pyramid, blocks, Steffen, and modified optimal.
The study was carried out under two main scenarios, the continuous arrival of pas-
sengers during the boarding process and the availability of all passengers at boarding
time. The relative performance of the boarding strategies considered in the study seems
to be independent of the arrival process of the passengers to the boarding gate. We, there-
fore, focused the study on one of the scenarios—the continuous arrival of passengers dur-
ing the boarding process. Concerning the relative performance of the boarding strategies
in this scenario, the outside-in and the reverse pyramid led to the shortest boarding time,
while the back-to-front and blocks strategies proved to be inefficient. Assuming that 75%
of passengers carried hand luggage, the reverse pyramid strategy achieved an improve-
ment of 11% over the random strategy. Compared to the back-to-front strategy, the reverse
pyramid method indicated a 22% improvement under the same conditions. For this rea-
son, one can conclude that the back-to-front strategy implemented by several airlines is
inefficient. When virtually all passengers carry hand luggage, the most effective boarding
strategies are those of the reverse pyramid and outside-in. A comparison with the random
strategy leads to the conclusion that the boarding time is improved by up to 15%. If one
were to compare the best scenario (reverse pyramid) with the worst (blocks), there is a
29% reduction in boarding time.
Following this study, we intend to analyze the most cost-effective boarding scenario
for airline companies, allowing them to make informed decisions about their boarding
procedures and improve operational efficiency. Additionally, the impact of late passen-
gers on boarding strategies will be tested.
Author Contributions: Conceptualization, H.M., L.P.F. and P.Á.; Methodology, H.M., L.P.F., A.L.R.
and P.Á.; Software, H.M., L.P.F., N.O.F. and A.L.R.; Validation, H.M., L.P.F., N.O.F. and P.Á.; Formal
analysis, A.L.R.; Investigation, H.M., L.P.F. and N.O.F.; Resources, P.Á.; Data curation, A.L.R.; Writ-
ing—original draft, H.M., L.P.F. and P.Á.; Writing—review & editing, H.M., L.P.F., N.O.F., A.L.R.
and P.Á.; Supervision, L.P.F. and P.Á. All authors have read and agreed to the published version of
the manuscript.
Funding: This research received no external funding.
Data Availability Statement: Data is contained within the article.
Conflicts of Interest: The authors declare no conflict of interest.
Figure 7. Impact of priority passengers on the total boarding time.
5. Conclusions
A study of the efficiency of passenger boarding strategies on an Airbus A320 was
carried out using discrete event simulation and the Arena software. By resorting to the
simulation, seven strategies were evaluated when boarding is carried out starting from the
front of the aircraft using a jet bridge, namely: random, back-to-front, outside-in, reverse
pyramid, blocks, Steffen, and modified optimal.
The study was carried out under two main scenarios, the continuous arrival of passen-
gers during the boarding process and the availability of all passengers at boarding time.
The relative performance of the boarding strategies considered in the study seems to be
independent of the arrival process of the passengers to the boarding gate. We, therefore,
focused the study on one of the scenarios—the continuous arrival of passengers during the
boarding process. Concerning the relative performance of the boarding strategies in this
scenario, the outside-in and the reverse pyramid led to the shortest boarding time, while
the back-to-front and blocks strategies proved to be inefficient. Assuming that 75% of pas-
sengers carried hand luggage, the reverse pyramid strategy achieved an improvement of
11% over the random strategy. Compared to the back-to-front strategy, the reverse pyramid
method indicated a 22% improvement under the same conditions. For this reason, one
can conclude that the back-to-front strategy implemented by several airlines is inefficient.
Sustainability 2023,15, 16476 11 of 12
When virtually all passengers carry hand luggage, the most effective boarding strategies are
those of the reverse pyramid and outside-in. A comparison with the random strategy leads
to the conclusion that the boarding time is improved by up to 15%. If one were to compare
the best scenario (reverse pyramid) with the worst (blocks), there is a 29% reduction in
boarding time.
Following this study, we intend to analyze the most cost-effective boarding scenario
for airline companies, allowing them to make informed decisions about their boarding
procedures and improve operational efficiency. Additionally, the impact of late passengers
on boarding strategies will be tested.
Author Contributions:
Conceptualization, H.M., L.P.F. and P.Á.; Methodology, H.M., L.P.F., A.L.R.
and P.Á.; Software, H.M., L.P.F., N.O.F. and A.L.R.; Validation, H.M., L.P.F., N.O.F. and P.Á.; For-
mal analysis, A.L.R.; Investigation, H.M., L.P.F. and N.O.F.; Resources, P.Á.; Data curation, A.L.R.;
Writing—original draft, H.M., L.P.F. and P.Á.; Writing—review & editing, H.M., L.P.F., N.O.F., A.L.R.
and P.Á.; Supervision, L.P.F. and P.Á. All authors have read and agreed to the published version of
the manuscript.
Funding: This research received no external funding.
Data Availability Statement: Data is contained within the article.
Conflicts of Interest: The authors declare no conflict of interest.
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