Field Trial Measurements to Validate a Stochastic Aircraft Boarding Model

Abstract

Efficient boarding procedures have to consider both operational constraints and the individual passenger behavior. In contrast to the aircraft handling processes of fueling, catering and cleaning, the boarding process is more driven by passengers than by airport or airline operators. This paper delivers a comprehensive set of operational data including classification of boarding times, passenger arrival times, times to store hand luggage, and passenger interactions in the aircraft cabin as a reliable basis for calibrating models for aircraft boarding. In this paper, a microscopic approach is used to model the passenger behavior, where the passenger movement is defined as a one-dimensional, stochastic, and time/space discrete transition process. This model is used to compare measurements from field trials of boarding procedures with simulation results and demonstrates a deviation smaller than 5%.

Full text

aerospace
Article
Field Trial Measurements to Validate a Stochastic
Aircraft Boarding Model
Michael Schultz ID
Department of Air Transportation, German Aerospace Center (DLR), Lilienthalplatz 7,
38108 Braunschweig, Germany; michael.schultz@dlr.de
Received: 2 February 2018; Accepted: 5 March 2018; Published: 7 March 2018
Abstract:
Efficient boarding procedures have to consider both operational constraints and the
individual passenger behavior. In contrast to the aircraft handling processes of fueling, catering and
cleaning, the boarding process is more driven by passengers than by airport or airline operators.
This paper delivers a comprehensive set of operational data including classification of boarding
times, passenger arrival times, times to store hand luggage, and passenger interactions in the aircraft
cabin as a reliable basis for calibrating models for aircraft boarding. In this paper, a microscopic
approach is used to model the passenger behavior, where the passenger movement is defined
as a one-dimensional, stochastic, and time/space discrete transition process. This model is used
to compare measurements from field trials of boarding procedures with simulation results and
demonstrates a deviation smaller than 5%.
Keywords:
aircraft boarding validation; stochastic behavior model; simulation; field trials;
operational improvements
1. Introduction
Operational air transportation processes have to be efficient in both cost and operational strategies.
The passenger handling at airports mainly aims at reliable on-time performance for the boarding
process. For aircraft boarding, a specific amount of passenger trajectories (individual path along
handling stations, such as check-in or security control, and corresponding timestamps [
1
]) and the
associated 4D aircraft trajectory [
2
,
3
] are brought together in one point of space and time. Thus,
boarding holds a significant potential for influencing the whole aircraft trajectory over the day
of operations.
The aircraft trajectory consists of an air and a ground part. The aircraft ground handling processes
to prepare the outbound flight are defined as the aircraft turnaround and take place between the in-block
(arrival) and off-block (departure) at the apron/gate position [
4
–
6
]. From an operational point of view,
passenger boarding becomes more important if an aircraft demands a short turnaround time, since the
operational buffers become smaller and boarding will be on the critical path of the turnaround [
7
].
For the
air traffic management, the turnaround has to provide a reliable basis for the operational procedures
on the day of operations. From the airline perspective, the boarding process allows the provision of
specific airline products (e.g., priority boarding and loyalty program), which results in a dedicated airline
revenue management for further improving the economic revenue of a flight.
Whereas the turnaround processes are controlled by the operational personnel from the airport,
airline, and ground handling agents, boarding is mainly influenced by individual passenger behavior,
which includes the willingness and ability to follow the designated boarding processes in an efficient
manner. The passenger behavior is characterized by individual attributes, such as late arrival at the
gate, amount of hand luggage, physical constraints (e.g., reduced mobility [
8
,
9
]), group constellations,
travel purpose (business or leisure), as well as time needed for orientation in the cabin or for storing
the hand luggage (cf. [10]).
Aerospace 2018,5, 27; doi:10.3390/aerospace5010027 www.mdpi.com/journal/aerospace

Aerospace 2018,5, 27 2 of 20
1.1. Status quo
In the following section, a short overview concerning scientific research on aircraft boarding
problems is given. Comprehensive overviews are provided for aircraft turnaround [
11
], boarding [
12
],
and corresponding economic impact [
13
–
15
]. Relevant studies include, but are not limited to, the
following current examples.
A common goal of simulation-based approaches is to minimize the time that is required for
passengers to board the aircraft. A study [
16
] investigated the efficiency of different boarding strategies,
considering specific boarding patterns. A similar approach focused particularly on disturbances to
the boarding sequence caused by early or late arrivals of passengers [
17
]. The results showed faster
boarding times for the commonly used back-to-front boarding in the case of passengers not boarding
in their previously assigned boarding block. This fact indicated that a back-to-front policy is not an
optimal solution for the boarding problem. Picking up the idea of block boarding, a study based on
an analytical model [
18
] showed significantly improved boarding times for block policies compared
to the back-to-front policy. In contrast, research contributions supported the back-to-front policy in
comparison to the random boarding strategy (cf. [
19
]). A stochastic cellular automaton model [
20
]
demonstrated that back-to-front boarding is most efficient if two boarding blocks are used, which was
confirmed using a 1 + 1 polynuclear growth model with concave boundary conditions [
21
]. In [
22
],
a cellular Discrete-Event System Specification (Cell-DEVS) is used to provide evaluation of aircraft
boarding strategies.
A minimum interference of passengers during the seating process was focused by using a mixed
integer linear program for optimization [
23
]. A stochastic approach [
20
] covered individual passenger
behavior (e.g., passenger conformance to the proposed boarding strategy, and individual hand luggage
amount and distribution) and aircraft/airline operational constraints of aircraft/airlines (e.g., seat
load factor and arrival rates). Using a Markov Chain Monte Carlo optimization algorithm, a boarding
strategy was developed [
24
] assuming that the handling of the hand luggage is a major impact factor
for the boarding time and a model based on fundamental statistical mechanics was provided [
25
].
A power
law rule was identified [
26
], where the boarding time scales with the number of passengers
to board, which allowed the prediction of back-to-front boarding strategy, and was extended to large
numbers of passengers [27].
A boarding model was developed, which considers passengers’ individual physique (maximum
speed), quantity of hand luggage, and individually preferred distance [
28
]. Based on a specific
boarding strategy [
24
], a method assigned passengers to seats so that their luggage is distributed
evenly throughout the cabin [
29
], assuming a less time-consuming process for finding available storage
in the overhead bins. The prioritization of passengers with a high number of hand luggage items
to board first was focused by [
30
]. The impact of hand luggage was investigated further [
31
] and
passengers were assigned to seats according to the number of hand luggage items proposing that
passengers with few pieces should be seated close to the entry. To minimize individual interference,
effects of passenger groups during boarding were analyzed [32].
An analytical approach demonstrated [
33
] that the efficiency of boarding strategies is linked
to the aircraft interior design (seat pitch and passengers per row). Furthermore, different aircraft
seating layouts and alternative designs could significantly reduce the boarding time for both single
and twin-aisle configuration [
7
,
34
]. The aircraft design and, in particular, the impact of aircraft
cabin modifications with regard to the boarding efficiency was analyzed by [
35
], while studies
evaluated novel aircraft layout configurations and seating concepts for single and twin-aisle aircraft
with 180–300 seats [36,37].
1.2. Objectives and Document Structure
In the context of input data for boarding models, there are only limited datasets available to
provide reliable input for boarding models. These datasets are from experimental mock-ups [
38
],
observations during boarding operations [
39
,
40
], and small scale experiments [
41
,
42
]. Therefore, this

Aerospace 2018,5, 27 3 of 20
paper provides a reliable dataset for calibrating models for aircraft boarding and covers a broad range
of input factors. In recent years data from more than 400 flights were manually recorded with a different
focus and level of details: passenger processes (e.g., time to store hand luggage or time needed to take
the seat), arrival rates at the aircraft, and boarding time using different boarding strategies. After a
brief introduction of the stochastic boarding model, the recorded data are systematically analyzed and
used to calibrate the boarding model [
7
,
20
]. In the next stage, data from two airline field trials are used
as a reference to demonstrate the reliability of the stochastic approach. For this reason, the observed
operational constraints (e.g., boarding procedures and arrival rates) are implemented in the existing
simulation environment and the simulation results are compared against the field measurements.
Finally, the conclusion provides an overview concerning the achieved results and an outlook on future
research activities.
2. Stochastic Boarding Model
Scientific approaches often not consider the operational conditions in the context of aircraft
boarding, such as seat load and passenger’s ability or willingness to follow the proposed procedure
(conformance). In addition, the non-deterministic nature of the accompanied handling processes and
input parameter is rarely considered (e.g., amount and distribution of hand luggage). Furthermore,
there is a clear lack of reliable data from the aircraft operations and the passenger handling.
Assumptions regarding the inner processes are often derived from simplified research environments
or gathered in less realistic test setups. To bridge this gap, data from the field are manually recorded
during the day of operations to calibrate the sub-processes of a stochastic aircraft boarding model [
7
,
20
].
The used dynamic model for the boarding simulation is based on an asymmetric simple exclusion
process (ASEP [
43
]). The ASEP was successfully adapted to model the dynamic passenger behavior
in the airport terminal environment [
1
,
10
,
44
]. In this context, passenger boarding is assumed to be a
stochastic, forward-directed, one-dimensional and discrete (time and space) process. To provide both
an appropriate set of input data and an efficient simulation environment, the aircraft seat layout is
transferred into a regular grid with aircraft entries, the aisle(s) and the passenger seats as shown in
Figure 1. In this context, the Airbus 320 with 29 seat rows (single aisle, 174 seats) is used as a common
reference aircraft to allow efficient comparisons of achieved results within the research community.
The regular grid consists of equal cells with a size of 0.4 m
×
0.4 m, whereas a cell can either be free or
contain exactly one passenger.
Aerospace 2018, 5, x FOR PEER REVIEW 3 of 20
observations during boarding operations [39,40], and small scale experiments [41,42]. Therefore, this
paper provides a reliable dataset for calibrating models for aircraft boarding and covers a broad range
of input factors. In recent years data from more than 400 flights were manually recorded with a
different focus and level of details: passenger processes (e.g., time to store hand luggage or time
needed to take the seat), arrival rates at the aircraft, and boarding time using different boarding
strategies. After a brief introduction of the stochastic boarding model, the recorded data are
systematically analyzed and used to calibrate the boarding model [7,20]. In the next stage, data from
two airline field trials are used as a reference to demonstrate the reliability of the stochastic approach.
For this reason, the observed operational constraints (e.g., boarding procedures and arrival rates) are
implemented in the existing simulation environment and the simulation results are compared against
the field measurements. Finally, the conclusion provides an overview concerning the achieved results
and an outlook on future research activities.
2. Stochastic Boarding Model
Scientific approaches often not consider the operational conditions in the context of aircraft
boarding, such as seat load and passenger’s ability or willingness to follow the proposed procedure
(conformance). In addition, the non-deterministic nature of the accompanied handling processes and
input parameter is rarely considered (e.g., amount and distribution of hand luggage). Furthermore,
there is a clear lack of reliable data from the aircraft operations and the passenger handling.
Assumptions regarding the inner processes are often derived from simplified research environments
or gathered in less realistic test setups. To bridge this gap, data from the field are manually recorded
during the day of operations to calibrate the sub-processes of a stochastic aircraft boarding model
[7,20].
The used dynamic model for the boarding simulation is based on an asymmetric simple
exclusion process (ASEP [43]). The ASEP was successfully adapted to model the dynamic passenger
behavior in the airport terminal environment [1,10,44]. I n this c ontext , passenger boardi ng is assumed
to be a stochastic, forward-directed, one-dimensional and discrete (time and space) process. To
provide both an appropriate set of input data and an efficient simulation environment, the aircraft
seat layout is transferred into a regular grid with aircraft entries, the aisle(s) and the passenger seats
as shown in Figure 1. In this context, the Airbus 320 with 29 seat rows (single aisle, 174 seats) is used
as a common reference aircraft to allow efficient comparisons of achieved results within the research
community. The regular grid consists of equal cells with a size of 0.4 m × 0.4 m, whereas a cell can
either be free or contain exactly one passenger.
Figure 1. Grid-based simulation environment—Airbus A320 as reference.
The boarding progress consists of a simple set of rules for the passenger movement: (a) enter the
aircraft at the assigned door (based on the current boarding scenario); (b) move forward from cell to
cell along the aisle until reaching the assigned seat row; and (c) store the hand luggage (aisle is
blocked for other passengers) and take the seat. The movement process only depends on the state of
the next cell (free or occupied). The storage of the hand luggage is a stochastic process and depends
on the individual amount of hand luggage. The seating process is stochastically modelled as well,
whereas the time to take the seat depends on the already used seats in the corresponding row. The
stochastic nature of the boarding process requires a minimum of simulation runs for each selected
scenario to derive reliable simulation results. In this context, a simulation scenario is mainly defined
by the underlying seat layout, the number of passengers to board (seat load factor, default: 85%), the
arrival frequency of the passengers at the aircraft (default: 14 passengers per minute), the number of
Figure 1. Grid-based simulation environment—Airbus A320 as reference.
The boarding progress consists of a simple set of rules for the passenger movement: (a) enter the
aircraft at the assigned door (based on the current boarding scenario); (b) move forward from cell to
cell along the aisle until reaching the assigned seat row; and (c) store the hand luggage (aisle is blocked
for other passengers) and take the seat. The movement process only depends on the state of the next
cell (free or occupied). The storage of the hand luggage is a stochastic process and depends on the
individual amount of hand luggage. The seating process is stochastically modelled as well, whereas
the time to take the seat depends on the already used seats in the corresponding row.
The stochastic
nature of the boarding process requires a minimum of simulation runs for each selected scenario
to derive reliable simulation results. In this context, a simulation scenario is mainly defined by the
underlying seat layout, the number of passengers to board (seat load factor, default: 85%),
the arrival
frequency of the passengers at the aircraft (default: 14 passengers per minute), the number of available
doors (default: 1 door), the specific boarding strategy (default: random) and the conformance of

Aerospace 2018,5, 27 4 of 20
passengers in following the current strategy (default: 85%). The default values are used to define
the reference boarding scenario, which is the benchmark to evaluate boarding performance. In this
context,
the conformance
of passengers only impacts non-random boarding strategies. Further details
regarding the model and the simulation environment are provided by [7,20].
In the simulation environment, the boarding process is implemented as follows. Depending on the
seat load, a specific number of randomly chosen seats are used for boarding. For each seat, a passenger
(agent) is created. The agent contains individual parameters, such as number of hand luggage items,
maximum walking speed in the aisle (set for all agents to 0.8 m/s), seat coordinates, time to store
the hand luggage and arrival time at the aircraft door. Further, several process characteristics could
be saved during the simulation runs (e.g., waiting times, number of interactions). To create the time
needed to store the hand luggage, a triangular distribution provides a stochastic time value depending
on the number of items (see [
7
,
20
]). The agents are sorted with regard to their seats and the current
boarding strategy. From this sequence, a given percentage of agents (conformance rate) are taken out
of the sequence and inserted into a position, which contradicts the current strategy (e.g., inserted into
a different boarding block). According to the arrival time distribution (e.g., linear or exponential) and
the boarding sequence, each agent gets a timestamp to appear on the aircraft door queue. When the
simulation starts, the first agent of the queue always enters the aircraft by moving from the queue
to the entry cell of the aisle grid (aircraft door), if this cell is free. In each simulation step, all agents
located in the row are moved to the next cell, if possible (free cell and not arrived at the seat row),
using a shuffled sequential update procedure (emulating parallel update behavior, cf. [
10
,
43
]). If the
agent arrives at the assigned seat row, he waits on the aisle cell according to the time needed to store
the hand luggage. Depending on the seat row condition (e.g., blocked aisle or middle seat or both),
an additional
time is stochastically generated to wait in the aisle to perform the seat shuffle. During
the whole waiting process, no other agent can pass. If the waiting process finally finishes, the agent is
set to the seat and the aisle cell is set free. Each boarding scenario is simulated 100,000 times, to derive
statistically relevant results defined by average boarding time (start with first passenger arrives the
aircraft and finished, when last passenger is seated) and standard deviation of boarding time.
To model different boarding strategies, the grid-based approach enables both the individual
assessment of seats and classification/aggregation according to the intended strategy. In Figure 2,
the seats
are color-coded (grey-scale) and aggregated to a structure with three blocks of seats (
per row
and per designation). The boarding takes place in the order of the grey-scale value, from the back to the
front (back-to-front sequence I-II-III) in the first example and from the outer to the inner seat designation
(window to aisle, outside-in) in the second example. In this context, random boarding means that all
passengers possess a seat, but the chronological order of the arrival of passengers is not defined. Block
boarding stands for an optimized block sequence, which is, in the case of six equal blocks (numbered
from the back to the front by I, II, III, IV, V, and VI), II-IV-VI-I-III-V. Finally, the back-to-front policy is
only favorable for a two-block configuration [20,21].
Aerospace 2018, 5, x FOR PEER REVIEW 4 of 20
available doors (default: 1 door), the specific boarding strategy (default: random) and the conformance
of passengers in following the current strategy (default: 85%). The default values are used to define
the reference boarding scenario, which is the benchmark to evaluate boarding performance. In this
context, the conformance of passengers only impacts non-random boarding strategies. Further details
regarding the model and the simulation environment are provided by [7,20].
In the simulation environment, the boarding process is implemented as follows. Depending on
the seat load, a specific number of randomly chosen seats are used for boarding. For each seat, a
passenger (agent) is created. The agent contains individual parameters, such as number of hand
luggage items, maximum walking speed in the aisle (set for all agents to 0.8 m/s), seat coordinates,
time to store the hand luggage and arrival time at the aircraft door. Further, several process
characteristics could be saved during the simulation runs (e.g., waiting times, number of
interactions). To create the time needed to store the hand luggage, a triangular distribution provides
a stochastic time value depending on the number of items (see [7,20]). The agents are sorted with
regard to their seats and the current boarding strategy. From this sequence, a given percentage of
agents (conformance rate) are taken out of the sequence and inserted into a position, which
contradicts the current strategy (e.g., inserted into a different boarding block). According to the
arrival time distribution (e.g., linear or exponential) and the boarding sequence, each agent gets a
timestamp to appear on the aircraft door queue. When the simulation starts, the first agent of the
queue always enters the aircraft by moving from the queue to the entry cell of the aisle grid (aircraft
door), if this cell is free. In each simulation step, all agents located in the row are moved to the next
cell, if possible (free cell and not arrived at the seat row), using a shuffled sequential update procedure
(emulating parallel update behavior, cf. [10,43]). If the agent arrives at the assigned seat row, he waits
on the aisle cell according to the time needed to store the hand luggage. Depending on the seat row
condition (e.g., blocked aisle or middle seat or both), an additional time is stochastically generated to
wait in the aisle to perform the seat shuffle. During the whole waiting process, no other agent can
pass. If the waiting process finally finishes, the agent is set to the seat and the aisle cell is set free.
Each boarding scenario is simulated 100,000 times, to derive statistically relevant results defined by
average boarding time (start with first passenger arrives the aircraft and finished, when last
passenger is seated) and standard deviation of boarding time.
To model different boarding strategies, the grid-based approach enables both the individual
assessment of seats and classification/aggregation according to the intended strategy. In Figure 2, the
seats are color-coded (grey-scale) and aggregated to a structure with three blocks of seats (per row
and per designation). The boarding takes place in the order of the grey-scale value, from the back to
the front (back-to-front sequence I-II-III) in the first example and from the outer to the inner seat
designation (window to aisle, outside-in) in the second example. In this context, random boarding
means that all passengers possess a seat, but the chronological order of the arrival of passengers is
not defined. Block boarding stands for an optimized block sequence, which is, in the case of six equal
blocks (numbered from the back to the front by I, II, III, IV, V, and VI), II-IV-VI-I-III-V. Finally, the
back-to-front policy is only favorable for a two-block configuration [20,21].
Figure 2. Example for back-to-front and outside-in boarding strategy (darker seats are boarded first,
block sequence is I-II-III) modelled in the simulation environment.
Figure 2.
Example for back-to-front and outside-in boarding strategy (darker seats are boarded first,
block sequence is I-II-III) modelled in the simulation environment.

Aerospace 2018,5, 27 5 of 20
The model does not address unruly behavior or counterflow passenger movements which may arise
from individual problems in finding the assigned seat or blocked overhead compartments.
In particular
,
the problem of blocked overhead compartments could not be solved by operational strategies, but with
increased compartment capacity or a more restrictive airline policy regarding the amount of allowed
hand luggage. If the airline does not react to high numbers of hand luggage items, a boarding approach
to allow for evenly distributed hand luggage throughout the cabin is provided by [29].
3. Measurements and Calibration
This section will provide an overview of boarding times, boarding/deboarding rates, and
measurements regarding the individual passenger behaviors inside the aircraft (seat interactions
and hand luggage storage). Addressing the bilateral agreements with the concerned airlines and
airports, the data sets are appropriately aggregated to be used in this research context. The data were
manually and specifically recorded addressing the specific process to calibrate. This results in a high
level of reliability, since each setup was controlled by the responsible examiner and contains additional
descriptions of progress, setup and comments.
3.1. Field Measurements and Airline Trials
The data were recorded at several field measurements during actual aircraft turnarounds of Airbus
A320 and Boeing B737/B738. Each measurement campaign aimed at different aspects of the individual
boarding behavior of passengers and was realized in close cooperation with the corresponding airlines,
ground handling agents, and airport operators. While passenger arrival/departure rates could be
measured from outside the cabin by recording the individual time stamps of passengers passing the
aircraft door, the hand luggage storage time and passenger interactions during the seating (seat shuffle)
were recorded from positions inside the narrow aircraft cabin. Particularly, the specific seat shuffles
required special attention and a close observation position, which results only in a limited number
of measurements.
The first field measurements aimed to record the passenger boarding time and determine the
correlation to the number of passengers boarded, which should be used as an input for an aircraft
turnaround model [
45
]. The boarding time was defined as time between first passengers enters the
aircraft (pass the aircraft door) and last passenger is seated. The boarding times were recorded at
different German airports with different airlines during the summer periods 2010–2015. The observer
cooperates closely with the ground handling companies and stands near the aircraft door, where the
(inter-arrival) times between the passengers during boarding and deboarding could be additionally
measured. The analysis of the boarding times shows a positive correlation (Section 3.2), but different
categories of boarding speed exists (slow, medium, fast boarding), which are not indicated by the
number of passengers. In the context of the aircraft turnaround, the boarding time consists of additional
dependencies, which are mainly driven by the individual passenger behavior.
To cover this expected individual behavior during the passenger boarding process, the existing
stochastic aircraft boarding model was planned to be calibrated with data from additional field trial
measurements. Since inter-arrival times of passengers are already covered by the prior measurements
(Section 3.3) passenger interactions are focused on, particularly the time to store the hand luggage
(Section 3.4) and time for the seating process (Section 3.5). The measurements were taken in the
summer period of 2012. For each flight, two observers were positioned inside the cabin to separately
cover the front and rear part of the aircraft cabin. Therefore, the observers stood near the first and the
last seat row or used unbooked seats.

Aerospace 2018,5, 27 6 of 20
To prove the reliability of the calibrated stochastic model, a third field measurement with a
German airline was setup, to compare simulated boarding times with the actual boarding times of
newly introduced boarding strategies (Section 4.1). Thus, the airline prepared an operational test
phase in summer 2014 with the developed boarding strategies and recorded both the boarding time
(
in accordance
to the definition above) and the number of passengers. The latest airline trials in 2015
and 2016 (Section 4.2) mainly focusses on the impact boarding strategies, operational configurations
(one door and two doors), seat load factor, transfer mode (walk, bus shuttle, and gate), and destination.
3.2. Boarding Times
In Figure 3, the measurements of 282 boarding events for single-aisle aircraft (Airbus A320 and
Boeing B737) are shown, with a minimum of 29 passengers (pax) and a maximum of 190 passengers.
Assuming a linear boarding progress, boarding time increases for each passenger by 4.5 s with an
additional offset of 2.3 min on average (bold regression line in Figure 3). In the simplest case, if the
boarding time only depends on the number of passengers (no offset), a rate of 5.5 s per passenger
has to be used (thin regression line in Figure 3). To derive a more sophisticated understanding of
boarding times, the boarding time t
B
is weighted by the amount of passengers n
p
, so the boarding rate
is rnB =tB/np.
Aerospace 2018, 5, x FOR PEER REVIEW 6 of 20
(one door and two doors), seat load factor, transfer mode (walk, bus shuttle, and gate), and
destination.
3.2. Boarding Times
In Figure 3, the measurements of 282 boarding events for single-aisle aircraft (Airbus A320 and
Boeing B737) are shown, with a minimum of 29 passengers (pax) and a maximum of 190 passengers.
Assuming a linear boarding progress, boarding time increases for each passenger by 4.5 s with an
additional offset of 2.3 min on average (bold regression line in Figure 3). In the simplest case, if the
boarding time only depends on the number of passengers (no offset), a rate of 5.5 s per passenger has
to be used (thin regression line in Figure 3). To derive a more sophisticated understanding of
boarding times, the boarding time tB is weighted by the amount of passengers np, so the boarding rate
is rnB = tB/np.
Figure 3. Boarding times of 282 measured flights with different number of passengers assuming a
linear correlation between passengers and boarding time with both defined offset (bold line) and no
offset (thin line).
In a descriptive statistic summary, rnB can be characterized by the following quantiles: Q.10, Q.25,
Q.50, Q.75 and Q.90 with values of 4.5 s/pax, 5.0 s/pax, 5.6 s/pax, 6.5 s/pax and 8.0 s/pax, respectively
(positive skew). This descriptive summary demonstrates that 80% of rnB is in the range of 4.5 s/pax
and 8.0 s/pax (between Q.10 and Q.90). According to the median (Q.50 = 5.6 s/pax), this is a spread of
the boarding time from −19% to +44%. For a detailed analysis, the linear boarding progress is
compared against the boarding measurements; a Q–Q plot is used (see Figure 4). In a Q–Q plot, the
probability functions of two distributions are compared against each other. In the case of similarity,
the data points converge to a diagonal line. Comparing the expected (linear function with tB = 5.5
s/pax × np) and the measured distribution of the boarding rate (boarding time weighted by number
of passengers), a constant linear correlation does not seem to be a valid assumption.
0
5
10
15
20
050100150200
boarding time (min)
passengers
Figure 3.
Boarding times of 282 measured flights with different number of passengers assuming a
linear correlation between passengers and boarding time with both defined offset (bold line) and no
offset (thin line).
In a descriptive statistic summary, r
nB
can be characterized by the following quantiles: Q.10,
Q.25, Q.50, Q.75 and Q.90 with values of 4.5 s/pax, 5.0 s/pax, 5.6 s/pax, 6.5 s/pax and 8.0 s/pax,
respectively (positive skew). This descriptive summary demonstrates that 80% of r
nB
is in the range
of 4.5 s/pax and 8.0 s/pax (between Q.10 and Q.90). According to the median (Q.50 = 5.6 s/pax),
this is a spread of the boarding time from −19% to +44%. For a detailed analysis, the linear boarding
progress is compared against the boarding measurements; a Q–Q plot is used (see Figure 4). In a Q–Q
plot, the probability functions of two distributions are compared against each other. In the case of
similarity, the data points converge to a diagonal line. Comparing the expected (linear function with
tB= 5.5 s/pax ×np
) and the measured distribution of the boarding rate (boarding time weighted by
number of passengers), a constant linear correlation does not seem to be a valid assumption.

Aerospace 2018,5, 27 7 of 20
Aerospace 2018, 5, x FOR PEER REVIEW 7 of 20
Figure 4. Q–Q plot of cumulative distribution functions (CDF) of boarding rate percentiles with
measured boarding rates against a linear boarding progress with rnB = 5.5 s/pax.
The Q–Q plot indicates a classification into three sectors: fast, medium and slow boarding
progress. In Figure 4, two prominent coordinates could be observed at 8.4 min and 12.1 min in the
measured distribution. At 8.4 min, the boarding time per passenger decreases after a section of a
nearly constant rate and at 12.1 min, an offset indicates a new section of boarding rate. If these values
are used as section dividers, three sections with different boarding rates can be introduced. In Figure
5, the result of the classification is shown.
Figure 5. Boarding time classification of field measurements: fast, medium, and slow progress.
On the left side, the observed boarding times are separated according to a fast, medium and
slow boarding progress. On the right side, the characteristics regarding the number of passengers
according to the classification are shown (95 measurements with fast, 78 with medium, and 109 with
slow boarding rates). Following the initial approach of linear correlation between the number of
passengers and the boarding time (defined by slope and constant offset), the accompanied slope
values are 1.0 s/pax, 1.2 s/pax, and 2.2 s/pax and the constant offsets are 12.3 min, 8.2 min, and 3.5
min for the slow, medium and fast classification respectively. In the following Table 1, the results of
the classification are summarized and exemplarily chosen to point out the consequence of using a
common average for scenarios with 80, 110, 140, and 170 passengers. According to Figure 5, these
scenarios consist of a chance to be classified as boarding with a fast, medium or slow progress.
Depending on both the scenario and the classification, the boarding time could accordingly deviate
within a corridor of ± 5.3 min (170 pax: 15.0 min in the slow category and 9.7 min in the fast category).
0
20
40
60
80
100
0 20406080100
linear distribution (CDF %)
measured distribution (CDF %)
fast medium slow
0
10
20
30
40
50
0 50 100 150 200
absolute frequency
passengers
fast medium slow
Figure 4.
Q–Q plot of cumulative distribution functions (CDF) of boarding rate percentiles with
measured boarding rates against a linear boarding progress with rnB = 5.5 s/pax.
The Q–Q plot indicates a classification into three sectors: fast, medium and slow boarding progress.
In Figure 4, two prominent coordinates could be observed at 8.4 min and 12.1 min in the measured
distribution. At 8.4 min, the boarding time per passenger decreases after a section of a nearly constant
rate and at 12.1 min, an offset indicates a new section of boarding rate. If these values are used as
section dividers, three sections with different boarding rates can be introduced. In Figure 5, the result
of the classification is shown.
Aerospace 2018, 5, x FOR PEER REVIEW 7 of 20
Figure 4. Q–Q plot of cumulative distribution functions (CDF) of boarding rate percentiles with
measured boarding rates against a linear boarding progress with rnB = 5.5 s/pax.
The Q–Q plot indicates a classification into three sectors: fast, medium and slow boarding
progress. In Figure 4, two prominent coordinates could be observed at 8.4 min and 12.1 min in the
measured distribution. At 8.4 min, the boarding time per passenger decreases after a section of a
nearly constant rate and at 12.1 min, an offset indicates a new section of boarding rate. If these values
are used as section dividers, three sections with different boarding rates can be introduced. In Figure
5, the result of the classification is shown.
Figure 5. Boarding time classification of field measurements: fast, medium, and slow progress.
On the left side, the observed boarding times are separated according to a fast, medium and
slow boarding progress. On the right side, the characteristics regarding the number of passengers
according to the classification are shown (95 measurements with fast, 78 with medium, and 109 with
slow boarding rates). Following the initial approach of linear correlation between the number of
passengers and the boarding time (defined by slope and constant offset), the accompanied slope
values are 1.0 s/pax, 1.2 s/pax, and 2.2 s/pax and the constant offsets are 12.3 min, 8.2 min, and 3.5
min for the slow, medium and fast classification respectively. In the following Table 1, the results of
the classification are summarized and exemplarily chosen to point out the consequence of using a
common average for scenarios with 80, 110, 140, and 170 passengers. According to Figure 5, these
scenarios consist of a chance to be classified as boarding with a fast, medium or slow progress.
Depending on both the scenario and the classification, the boarding time could accordingly deviate
within a corridor of ± 5.3 min (170 pax: 15.0 min in the slow category and 9.7 min in the fast category).
0
20
40
60
80
100
0 20406080100
linear distribution (CDF %)
measured distribution (CDF %)
fast medium slow
0
10
20
30
40
50
0 50 100 150 200
absolute frequency
passengers
fast medium slow
Figure 5. Boarding time classification of field measurements: fast, medium, and slow progress.
On the left side, the observed boarding times are separated according to a fast, medium and
slow boarding progress. On the right side, the characteristics regarding the number of passengers
according to the classification are shown (95 measurements with fast, 78 with medium, and 109 with
slow boarding rates). Following the initial approach of linear correlation between the number of
passengers and the boarding time (defined by slope and constant offset), the accompanied slope values
are 1.0 s/pax, 1.2 s/pax, and 2.2 s/pax and the constant offsets are 12.3 min, 8.2 min, and 3.5 min
for the slow, medium and fast classification respectively. In the following Table 1, the results of the
classification are summarized and exemplarily chosen to point out the consequence of using a common
average for scenarios with 80, 110, 140, and 170 passengers. According to Figure 5, these scenarios
consist of a chance to be classified as boarding with a fast, medium or slow progress. Depending on
both the scenario and the classification, the boarding time could accordingly deviate within a corridor
of ±5.3 min (170 pax: 15.0 min in the slow category and 9.7 min in the fast category).

Aerospace 2018,5, 27 8 of 20
Table 1.
Boarding time using different classifications of linear behavior (slow, medium, fast, and average).
Boarding
Classification
Boarding Time (min)
Boarding Rate
rnB (pax/s)
Offset
(min)
Passengers
80 110 140 170
slow 1.0 12.3
13.6 14.0 14.5
15.0
medium 1.2 8.2 9.9
10.5 11.1
11.7
fast 2.2 3.5 6.4 7.5 8.6 9.7
average—no offset
5.5 0 7.3
10.1 12.8
15.6
average—best fit 4.5 2.3 8.3
10.5 12.7
15.0
To emphasize the different boarding progresses, three boarding real boarding events are selected
from the recorded data. These events reflect a single specific flight with nearly the same number of
passengers: 99, 104 and 100 for Scenarios A, B, and C, with fast, medium and slow arrival behavior,
respectively (see Figure 6).
Aerospace 2018, 5, x FOR PEER REVIEW 8 of 20
Table 1. Boarding time using different classifications of linear behavior (slow, medium, fast, and
average).
Boarding
Classification
Boarding Time (min)
Boarding Rate
rnB (pax/s)
Offset
(min)
Passengers
80 110 140 170
slow 1.0 12.3 13.6 14.0 14.5 15.0
medium 1.2 8.2 9.9 10.5 11.1 11.7
fast 2.2 3.5 6.4 7.5 8.6 9.7
average—no offset 5.5 0 7.3 10.1 12.8 15.6
average—best fit 4.5 2.3 8.3 10.5 12.7 15.0
To emphasize the different boarding progresses, three boarding real boarding events are
selected from the recorded data. These events reflect a single specific flight with nearly the same
number of passengers: 99, 104 and 100 for Scenarios A, B, and C, with fast, medium and slow arrival
behavior, respectively (see Figure 6).
Figure 6. Progress of different boarding events measured in the field.
Due to the different passengers’ arrival times, boarding is completed after 7 min in Scenario A,
after 11 min in Scenario B and after 15 min in Scenario C. Obviously, late passengers will significantly
extend the boarding process (Scenario C). However, a (constant) lower arrival rate of passengers at
the aircraft also affects the boarding progress adversely. The arrival rate of passengers at the aircraft
is mainly triggered by the presence of passengers at the boarding gate and the service rate at boarding
card control. Consequently, an airline should balance the effort/benefit ratio between introducing
new boarding procedures and faster dispatch/ higher availability of passengers at the boarding gate.
3.3. Arrival Rates and Deboarding Rates
The arrival rate of passengers at the aircraft is a significant input factor for the boarding model
to reliably simulate the final boarding time. In the recorded data, 188 flights are available for an
analysis rate at boarding and 186 flights for the departure rate at deboarding. Figure 7 demonstrates
that the arrival rate (arrival at aircraft door or at corresponding queue) is not constant over the time:
the arrival rate decreases during the boarding progress. This behavior is shown by using the 25%, 50%
and 75% quantiles (Q.25, median and Q.75), the expected value (μ) and the number of covered flights
(right scale). After 10 min, approximately 50% of flights already completed their boarding and
provide no values for arrival rates after this timestamp. In the first minute, passengers arrive at the
aircraft door at a rate of 14 pax/min (median value) with Q.25 = 12 pax/min and Q.75 = 18 pax/min.
These rates decrease to 3 pax/min, 6 pax/min and 11 pax/min in the 17th min for Q.25, median and
Q.75 respectively. At this time, the boarding is finished in 91% of all recorded flights. The remaining
data possess only a limited significance (only a few samples per period) and are not included in
Figure 7.
0
5
10
15
20
25
123456789101112131415
passengers per minute
boarding time (min)
scenario A (fast) scenario B (medium) scenario C (slow)
Figure 6. Progress of different boarding events measured in the field.
Due to the different passengers’ arrival times, boarding is completed after 7 min in Scenario A,
after 11 min in Scenario B and after 15 min in Scenario C. Obviously, late passengers will significantly
extend the boarding process (Scenario C). However, a (constant) lower arrival rate of passengers at the
aircraft also affects the boarding progress adversely. The arrival rate of passengers at the aircraft is
mainly triggered by the presence of passengers at the boarding gate and the service rate at boarding
card control. Consequently, an airline should balance the effort/benefit ratio between introducing new
boarding procedures and faster dispatch/higher availability of passengers at the boarding gate.
3.3. Arrival Rates and Deboarding Rates
The arrival rate of passengers at the aircraft is a significant input factor for the boarding model to
reliably simulate the final boarding time. In the recorded data, 188 flights are available for an analysis
rate at boarding and 186 flights for the departure rate at deboarding. Figure 7demonstrates that
the arrival rate (arrival at aircraft door or at corresponding queue) is not constant over the time: the
arrival rate decreases during the boarding progress. This behavior is shown by using the 25%, 50%
and 75% quantiles (Q.25, median and Q.75), the expected value (
µ
) and the number of covered flights
(
right scale
). After 10 min, approximately 50% of flights already completed their boarding and provide
no values for arrival rates after this timestamp. In the first minute, passengers arrive at the aircraft
door at a rate of 14 pax/min (median value) with Q.25 = 12 pax/min and Q.75 = 18 pax/min. These
rates decrease to 3 pax/min, 6 pax/min and 11 pax/min in the 17th min for Q.25, median and Q.75
respectively. At this time, the boarding is finished in 91% of all recorded flights. The remaining data
possess only a limited significance (only a few samples per period) and are not included in Figure 7.

Aerospace 2018,5, 27 9 of 20
Aerospace 2018, 5, x FOR PEER REVIEW 9 of 20
Figure 7. Passenger arrival rates decrease during aircraft boarding (arrival at aircraft door or at
corresponding queue). Coverage of flights (green dashes) is indicated on secondary y-axis.
The straight lines of the Q.25, median, and Q.75 values in Figure 7 emphasize a declining trend
and the increasing spread of the arrival rates. If the median is used as a reference with a linear
behavior, the arrival rate decreases by 0.45 pax/min per minute starting at 14.1 pax/min.
An in-depth analysis of inter-arrival times (the times between successive arrivals) indicates an
exponential distribution of these time values. The cumulative distribution function of the exponential
distribution is given by Equation (1) where λ is the rate parameter defined by λ = 1/μinter-arrival time.
,=1− ,≥0,
0,<0.
(1)
The results of the evaluation are shown in Figure 8. An appropriate fitting of the measured
number of passengers is achieved with an exponential distribution assuming μinter-arrival time = 3.7 s,
which results in a chi-squared test value of 0.64 (acceptance level of 14.07, using significance level of
5% and 7 degrees of freedom).
Figure 8. Inter-arrival times clustered in 5 s intervals and exponential distributed values.
The exponential distributed inter-arrival times also indicate a Poisson process. The
corresponding cumulative distribution function of the Poisson distribution is given by Equation (2)
where, in this case, the rate parameter λ is defined as the reciprocal value of the average amount of
passengers expected in a given time interval.
,=

!

 (2)
Using this strong fitting result for the inter-arrival times as a basis, the corresponding Poisson
distribution is shown in Figure 9. The field measurements are categorized by a 5 s interval. According
0
100
200
300
400
500
0
5
10
15
20
25
0481216
flights covered (%)
pax per minute
boarding time (min)
Q.25 median Q.75 exp. value flights
^^ ^
^
0
25
50
75
100
0-5 5-10 10-15 15-20 20-25 25 -30 30-35 35-40 40-45
amount of passengers
arrival time intervals (s)
field measurements
exponential distribution
Figure 7.
Passenger arrival rates decrease during aircraft boarding (arrival at aircraft door or at
corresponding queue). Coverage of flights (green dashes) is indicated on secondary y-axis.
The straight lines of the Q.25, median, and Q.75 values in Figure 7emphasize a declining trend
and the increasing spread of the arrival rates. If the median is used as a reference with a linear behavior,
the arrival rate decreases by 0.45 pax/min per minute starting at 14.1 pax/min.
An in-depth analysis of inter-arrival times (the times between successive arrivals) indicates an
exponential distribution of these time values. The cumulative distribution function of the exponential
distribution is given by Equation (1) where λis the rate parameter defined by λ= 1/µinter-arrival time.
F(x,λ)=(1−e−λx,x≥0,
0 , x<0. (1)
The results of the evaluation are shown in Figure 8. An appropriate fitting of the measured
number of passengers is achieved with an exponential distribution assuming
µinter-arrival time
= 3.7 s,
which results in a chi-squared test value of 0.64 (acceptance level of 14.07, using significance level of
5% and 7 degrees of freedom).
Aerospace 2018, 5, x FOR PEER REVIEW 9 of 20
Figure 7. Passenger arrival rates decrease during aircraft boarding (arrival at aircraft door or at
corresponding queue). Coverage of flights (green dashes) is indicated on secondary y-axis.
The straight lines of the Q.25, median, and Q.75 values in Figure 7 emphasize a declining trend
and the increasing spread of the arrival rates. If the median is used as a reference with a linear
behavior, the arrival rate decreases by 0.45 pax/min per minute starting at 14.1 pax/min.
An in-depth analysis of inter-arrival times (the times between successive arrivals) indicates an
exponential distribution of these time values. The cumulative distribution function of the exponential
distribution is given by Equation (1) where λ is the rate parameter defined by λ = 1/μinter-arrival time.
,=1− ,≥0,
0,<0.
(1)
The results of the evaluation are shown in Figure 8. An appropriate fitting of the measured
number of passengers is achieved with an exponential distribution assuming μinter-arrival time = 3.7 s,
which results in a chi-squared test value of 0.64 (acceptance level of 14.07, using significance level of
5% and 7 degrees of freedom).
Figure 8. Inter-arrival times clustered in 5 s intervals and exponential distributed values.
The exponential distributed inter-arrival times also indicate a Poisson process. The
corresponding cumulative distribution function of the Poisson distribution is given by Equation (2)
where, in this case, the rate parameter λ is defined as the reciprocal value of the average amount of
passengers expected in a given time interval.
,=

!

 (2)
Using this strong fitting result for the inter-arrival times as a basis, the corresponding Poisson
distribution is shown in Figure 9. The field measurements are categorized by a 5 s interval. According
0
100
200
300
400
500
0
5
10
15
20
25
0481216
flights covered (%)
pax per minute
boarding time (min)
Q.25 median Q.75 exp. value flights
^^ ^
^
0
25
50
75
100
0-5 5-10 10-15 15-20 20-25 25 -30 30-35 35-40 40-45
amount of passengers
arrival time intervals (s)
field measurements
exponential distribution
Figure 8. Inter-arrival times clustered in 5 s intervals and exponential distributed values.
The exponential distributed inter-arrival times also indicate a Poisson process. The corresponding
cumulative distribution function of the Poisson distribution is given by Equation (2) where, in this case,
the rate parameter
λ
is defined as the reciprocal value of the average amount of passengers expected
in a given time interval.
F(x,λ)=e−λk
∑
i=0
λi
i!(2)
Using this strong fitting result for the inter-arrival times as a basis, the corresponding Poisson
distribution is shown in Figure 9. The field measurements are categorized by a 5 s interval. According

Aerospace 2018,5, 27 10 of 20
to the average inter-arrival time of 3.7 s, it is expected that 1.35 passengers will arrive on average
in this 5 s interval. Thus, the
λ
value for the Poisson distribution will be 0.74. As Figure 9already
qualitatively emphasizes, the associated Poisson distribution with a chi-squared test value of 67.2
is not an appropriate candidate for describing the measured field data (acceptance level of 11.07
using significance level of 5% and 5 degrees of freedom). Whereas the probability of 0 arrivals and
2 per
interval corresponds to the Poisson distribution, the arrival of 1 pax per interval shows a much
higher probability and lower probabilities for more than 2 arrivals with regard to the recorded dataset.
Figure 9supports the observation of group arrivals in the airport environment (cf. [
1
,
10
]). Finally,
the arrival process will be modeled by exponential distributed inter-arrival times.
Aerospace 2018, 5, x FOR PEER REVIEW 10 of 20
to the average inter-arrival time of 3.7 s, it is expected that 1.35 passengers will arrive on average in
this 5 s interval. Thus, the λ value for the Poisson distribution will be 0.74. As Figure 9 already
qualitatively emphasizes, the associated Poisson distribution with a chi-squared test value of 67.2 is
not an appropriate candidate for describing the measured field data (acceptance level of 11.07 using
significance level of 5% and 5 degrees of freedom). Whereas the probability of 0 arrivals and 2 per
interval corresponds to the Poisson distribution, the arrival of 1 pax per interval shows a much higher
probability and lower probabilities for more than 2 arrivals with regard to the recorded dataset.
Figure 9 supports the observation of group arrivals in the airport environment (cf. [1,10]). Finally, the
arrival process will be modeled by exponential distributed inter-arrival times.
Figure 9. Expected amount arriving passengers in 5 s interval considering field measurement data
and Poisson distribution (λ = 0.74).
The analysis of deboarding with regard to outflow rates (measured at aircraft door) focuses only
on the aggregated flow rate. In contrast to the arrival rates, the outflow rates (deboarding) are
significantly higher (first minute: 18 pax/min, 23 pax/min and 29 pax/min for Q.25, median and Q.75
values, respectively, see Figure 10). The outflow rate increases during the first three minutes. After 8
min, for 91% of the recorded flights deboarding is finished (this level was reached after 17 min for
boarding, so deboarding is 53% faster than boarding). In the context of deboarding, the seat
interference disappears and only the interference of passengers in the aisle is important for an
efficient process [42,46]. A study of deplaning strategies [47] used stochastic optimization methods
and assumed a deboarding time of between 9 and 4.8 min, depending on the structure of the
deboarding procedure.
Figure 10. Deboarding outflow rates of passengers during the deboarding progress (measured at
aircraft door). Coverage of flights (green dashes) is indicated on secondary y-axis.
0
10
20
30
40
50
0123456
relative frequency (%)
amount of arriving passengers (s)
field measurement
Poisson distribution
0
100
200
300
400
0
10
20
30
40
048
flights covered (%)
pax per minute
deboarding time (min)
Q.25 median Q.75 exp. value flights
^^ ^
^
Figure 9.
Expected amount arriving passengers in 5 s interval considering field measurement data and
Poisson distribution (λ= 0.74).
The analysis of deboarding with regard to outflow rates (measured at aircraft door) focuses
only on the aggregated flow rate. In contrast to the arrival rates, the outflow rates (deboarding) are
significantly higher (first minute: 18 pax/min, 23 pax/min and 29 pax/min for Q.25, median and
Q.75 values, respectively, see Figure 10). The outflow rate increases during the first three minutes.
After 8 min,
for 91%
of the recorded flights deboarding is finished (this level was reached after
17 min
for boarding, so deboarding is 53% faster than boarding). In the context of deboarding, the seat
interference disappears and only the interference of passengers in the aisle is important for an efficient
process [
42
,
46
]. A study of deplaning strategies [
47
] used stochastic optimization methods and assumed
a deboarding time of between 9 and 4.8 min, depending on the structure of the deboarding procedure.
Aerospace 2018, 5, x FOR PEER REVIEW 10 of 20
to the average inter-arrival time of 3.7 s, it is expected that 1.35 passengers will arrive on average in
this 5 s interval. Thus, the λ value for the Poisson distribution will be 0.74. As Figure 9 already
qualitatively emphasizes, the associated Poisson distribution with a chi-squared test value of 67.2 is
not an appropriate candidate for describing the measured field data (acceptance level of 11.07 using
significance level of 5% and 5 degrees of freedom). Whereas the probability of 0 arrivals and 2 per
interval corresponds to the Poisson distribution, the arrival of 1 pax per interval shows a much higher
probability and lower probabilities for more than 2 arrivals with regard to the recorded dataset.
Figure 9 supports the observation of group arrivals in the airport environment (cf. [1,10]). Finally, the
arrival process will be modeled by exponential distributed inter-arrival times.
Figure 9. Expected amount arriving passengers in 5 s interval considering field measurement data
and Poisson distribution (λ = 0.74).
The analysis of deboarding with regard to outflow rates (measured at aircraft door) focuses only
on the aggregated flow rate. In contrast to the arrival rates, the outflow rates (deboarding) are
significantly higher (first minute: 18 pax/min, 23 pax/min and 29 pax/min for Q.25, median and Q.75
values, respectively, see Figure 10). The outflow rate increases during the first three minutes. After 8
min, for 91% of the recorded flights deboarding is finished (this level was reached after 17 min for
boarding, so deboarding is 53% faster than boarding). In the context of deboarding, the seat
interference disappears and only the interference of passengers in the aisle is important for an
efficient process [42,46]. A study of deplaning strategies [47] used stochastic optimization methods
and assumed a deboarding time of between 9 and 4.8 min, depending on the structure of the
deboarding procedure.
Figure 10. Deboarding outflow rates of passengers during the deboarding progress (measured at
aircraft door). Coverage of flights (green dashes) is indicated on secondary y-axis.
0
10
20
30
40
50
0123456
relative frequency (%)
amount of arriving passengers (s)
field measurement
Poisson distribution
0
100
200
300
400
0
10
20
30
40
048
flights covered (%)
pax per minute
deboarding time (min)
Q.25 median Q.75 exp. value flights
^^ ^
^
Figure 10.
Deboarding outflow rates of passengers during the deboarding progress (measured at
aircraft door). Coverage of flights (green dashes) is indicated on secondary y-axis.

Aerospace 2018,5, 27 11 of 20
3.4. Hand Luggage Storage
The hand luggage storage process is parameterized by the time to store one piece and the
individual amount of luggage pieces. The prior approach to modelling the time needed to store the
hand luggage was based on both a triangular distribution (Equation (3)) with time values for the
minimum, maximum, and mode time value for storing one piece of hand luggage as well as the
distribution of the hand luggage per passenger [7,16,20].
F(t)=






(t−tmin)2
(tmax−tmin )(tmode−tmin ),tmin ≤t≤tmode,
1−(tmax−t)2
(tmax−tmin )(tmax−tmode ),tmode <t≤tmax.
. (3)
During the field trials, 323 values are manually recorded. The recording starts at the time the
passenger reaches his seat row and ends when the passenger enters the seat row. To mathematically
fit the measurements, the Weibull distribution is used (Equation (4)) with the scale parameter
α
and
the shape parameter
β
. Since the minimum time x
min
to store the hand luggage is zero, no offset is
required to derive the distribution parameter (xmin = 0).
F(x,α,β,xmin)=1−e−(x−xmin
β)α
(4)
With the parameter
α
= 1.7 and
β
= 16.0 s, the Weibull distribution demonstrates an appropriate
level of correlation with a chi-squared test value of 3.65 (acceptance level of 12.6. using significance level
of 5% and six degrees of freedom). Although the previously used triangular distribution qualitatively
describes the shape of the recorded data, it clearly over-estimates the time for the hand luggage storage
(see Figure 11). The expected average time for storing the hand luggage is 13.9 s for the recorded
field data and 17.5 s for the initial triangular distribution. In the first section (0–5 s), the triangular
distribution indicates no values, whereas the field data indicate a probability of 12%. The sections
10–15 s, 20–25 s and 25–30 s exhibit a deviation of 5% on average. As a result of this analysis, further
simulations will use the derived Weibull distribution with the parameter set
α
= 1.7 and
β
= 16.0 s.
An empirical analysis by [40] also provides time values for hand luggage and outerwear storage into
the overhead compartments, which qualitatively confirms measured times.
Aerospace 2018, 5, x FOR PEER REVIEW 11 of 20
3.4. Hand Luggage Storage
The hand luggage storage process is parameterized by the time to store one piece and the
individual amount of luggage pieces. The prior approach to modelling the time needed to store the
hand luggage was based on both a triangular distribution (Equation (3)) with time values for the
minimum, maximum, and mode time value for storing one piece of hand luggage as well as the
distribution of the hand luggage per passenger [7,16,20].
=




 −min
max−minmode−min,
min ≤≤mode,

1− max−
max−minmax−mode,
mode <≤max. (3)
During the field trials, 323 values are manually recorded. The recording starts at the time the
passenger reaches his seat row and ends when the passenger enters the seat row. To mathematically
fit the measurements, the Weibull distribution is used (Equation (4)) with the scale parameter α and
the shape parameter β. Since the minimum time xmin to store the hand luggage is zero, no offset is
required to derive the distribution parameter (xmin = 0).
,,,=1−min

(4)
With the parameter α = 1.7 and β = 16.0 s, the Weibull distribution demonstrates an appropriate
level of correlation with a chi-squared test value of 3.65 (acceptance level of 12.6. using significance
level of 5% and six degrees of freedom). Although the previously used triangular distribution
qualitatively describes the shape of the recorded data, it clearly over-estimates the time for the hand
luggage storage (see Figure 11). The expected average time for storing the hand luggage is 13.9 s for
the recorded field data and 17.5 s for the initial triangular distribution. In the first section (0–5 s), the
triangular distribution indicates no values, whereas the field data indicate a probability of 12%. The
sections 10–15 s, 20–25 s and 25–30 s exhibit a deviation of 5% on average. As a result of this analysis,
further simulations will use the derived Weibull distribution with the parameter set α = 1.7 and β =
16.0 s. An empirical analysis by [40] also provides time values for hand luggage and outerwear
storage into the overhead compartments, which qualitatively confirms measured times.
Figure 11. Time needed to store the individual amount of hand luggage.
3.5. Seat Interactions
The chronological order of occupying the seat rows affects the boarding time, due to the required
coordination of position changes (seat shuffle, cf. [20,23]). In the worst case, the aisle and the middle
seats are already occupied and the arriving passenger wants to sit in the window seat. For this
constellation, nine movements are necessary for stepping out of the row, (re-)entering the row and
unblocking the aisle. The other seat occupation patterns demand four (aisle seat blocked) and five
movements (middle seat is blocked and window seat is the target). If the passenger can enter his seat
0
10
20
30
40
0-5 5-10 10-15 15-20 20-25 25-30 30-35 35-40 40-45
probability (%)
time (s)
triangular distribution (old model)
Weibull distribution
field measurement
Figure 11. Time needed to store the individual amount of hand luggage.

Aerospace 2018,5, 27 12 of 20
3.5. Seat Interactions
The chronological order of occupying the seat rows affects the boarding time, due to the required
coordination of position changes (seat shuffle, cf. [
20
,
23
]). In the worst case, the aisle and the middle
seats are already occupied and the arriving passenger wants to sit in the window seat. For this
constellation, nine movements are necessary for stepping out of the row, (re-)entering the row and
unblocking the aisle. The other seat occupation patterns demand four (aisle seat blocked) and five
movements (middle seat is blocked and window seat is the target). If the passenger can enter his
seat without any interference, the time for entering the seat row is defined with one movement.
The characteristics
of the accompanied time required to finally unblock the aisle are shown in Figure 12,
where the blue color represents the field measurement and the red color represents the results of the
modelled distribution of time needed. Furthermore, the colored boxes represent 50% of all values
(measured or calculated) bounded by the accompanied upper and lower quantiles (Q.25 and Q.75).
Around these colored areas, additional areas are defined by bars to cover 80% of all values (with Q.10
and Q.90).
Aerospace 2018, 5, x FOR PEER REVIEW 12 of 20
without any interference, the time for entering the seat row is defined with one movement. The
characteristics of the accompanied time required to finally unblock the aisle are shown in Figure 12,
where the blue color represents the field measurement and the red color represents the results of the
modelled distribution of time needed. Furthermore, the colored boxes represent 50% of all values
(measured or calculated) bounded by the accompanied upper and lower quantiles (Q.25 and Q.75).
Around these colored areas, additional areas are defined by bars to cover 80% of all values (with Q.10
and Q.90).
Figure 12. Seat interference: measurement vs. simulation.
During the field trials, only a minor quantity of specific movements could be recorded (between
10 and 15 measurements per category). This is mainly caused by the observation position at the
front/back door of the aircraft, the unpredictable seating progress of a specific row and the ability to
clearly define start and end of the seating process. Consequently, the observers could only
concentrate on a limited set of seat rows. However, the recorded measurements qualitatively confirm
the proposed model as regards calculating the time required to unblock the aisle. As a side note, the
cabin crews approve the order of magnitude of the gathered data as well, but point out that specific
events during boarding regularly disturb the progress. These events are not covered in the model.
Considering both the minor quantity of measurements and the same order of magnitude of the
results, the initial distribution of the seat shuffle would appear to be an acceptable approach and will
be used in the following simulations.
3.6. Simulation-Validation of Prior Results
Since the field measurements of the specific sub-processes of boarding are analyzed in detail and
used to calibrate the simulation environment, the validity of the prior simulation results will be
checked (see [7]). For this purpose, the additional input parameters are seat load factor (85%) and
passenger conformance rate according to the assigned seat (85%). The random strategy is used as
baseline with both the non-calibrated and calibrated input values to evaluate the average boarding
time and the accompanied standard deviation. Table 2 demonstrates the differences in the boarding
times between non-calibrated and calibrated simulation runs are not significant (<1.5%).
As all strategies show a minor improvement, the relative order of the strategies is still valid.
However, the calibrated random strategy is 8.4% faster accompanied with a 5.9% lower standard
deviation against the non-calibrated random strategy. As was expected, the standard deviations of
the boarding strategies increase, caused by a higher bandwidth of the hand luggage distribution and
the non-constant arrival distribution observed in the field.
0
5
10
15
20
25
time (s)
number of seat shuffles
field measurement
simulated distribution
14 59
Figure 12. Seat interference: measurement vs. simulation.
During the field trials, only a minor quantity of specific movements could be recorded (
between 10
and 15 measurements per category). This is mainly caused by the observation position at the front/back
door of the aircraft, the unpredictable seating progress of a specific row and the ability to clearly define
start and end of the seating process. Consequently, the observers could only concentrate on a limited
set of seat rows. However, the recorded measurements qualitatively confirm the proposed model as
regards calculating the time required to unblock the aisle. As a side note, the cabin crews approve the
order of magnitude of the gathered data as well, but point out that specific events during boarding
regularly disturb the progress. These events are not covered in the model. Considering both the minor
quantity of measurements and the same order of magnitude of the results, the initial distribution of the
seat shuffle would appear to be an acceptable approach and will be used in the following simulations.
3.6. Simulation-Validation of Prior Results
Since the field measurements of the specific sub-processes of boarding are analyzed in detail
and used to calibrate the simulation environment, the validity of the prior simulation results will be
checked (see [
7
]). For this purpose, the additional input parameters are seat load factor (85%) and
passenger conformance rate according to the assigned seat (85%). The random strategy is used as
baseline with both the non-calibrated and calibrated input values to evaluate the average boarding
time and the accompanied standard deviation. Table 2demonstrates the differences in the boarding
times between non-calibrated and calibrated simulation runs are not significant (<1.5%).
As all strategies show a minor improvement, the relative order of the strategies is still valid.
However, the calibrated random strategy is 8.4% faster accompanied with a 5.9% lower standard

Aerospace 2018,5, 27 13 of 20
deviation against the non-calibrated random strategy. As was expected, the standard deviations of the
boarding strategies increase, caused by a higher bandwidth of the hand luggage distribution and the
non-constant arrival distribution observed in the field.
Table 2. Comparison of simulated aircraft boarding strategies using real data for calibration.
Boarding Scenario Boarding Strategies
1 door/2 doors random outside-in back-to-front block
Boarding time (%)
1 door, non-calibrated 100 (reference) 80.9 110.5 96.2
1 door, calibrated 100 (reference) 79.5 109.2 95.3
2 doors, non-calibrated
74.2 63.8 75.3 76.2
2 doors, calibrated 74.1 62.5 75.0 76.2
Standard deviation (%)
1 door, non-calibrated 7.1 5.5 7.9 6.6
1 door, calibrated 7.3 5.7 8.1 6.9
2 doors, non-calibrated
4.6 2.9 4.8 5.3
2 doors, calibrated 5.9 5.5 5.9 5.8
4. Field Trials, Validation of Simulation Results
The previous section was aimed at the calibration of the stochastic passenger boarding model. In a
next step, the calibrated model is used to simulate boarding scenarios, which were set up in operational
field trials of an airline, to validate the passenger boarding model. The airline provides all information
about the test setup and the measured boarding times. The first airline trial evaluates the performance
of two advanced boarding scenarios as a proof of concept. The second field trial extends the initial
concept and integrates the boarding scenarios into the airline operations, which cover different seat
loads, the use of one/two doors, gate/apron position, destination, amount of pre-boarding passengers,
and transfer mode (bus, gate, walk).
4.1. Airline Trials 1
To ensure convenient and fast boarding progress airline operates employed new strategies, which
were tested in field. These strategies were also simulated with the calibrated modeled and compared
against data collected from the field (provided by the airline). Beside the common approach of group
boarding (back-to-front with four blocks, validation Scenario 1 in Figure 13), a new outside-in strategy
was tested (validation Scenario 2 in Figure 13) to determine potential operational benefits. In the
boarding validation Scenario 2, the aircraft cabin is divided into a rear/front section (rows) as well as
a window and middle/aisle section. The rear window seats are boarded first, followed by the front
window seats, the rear middle/aisle seats, and the front middle/aisle seats.
Aerospace 2018, 5, x FOR PEER REVIEW 13 of 20
Table 2. Comparison of simulated aircraft boarding strategies using real data for calibration.
Boarding Scenario Boarding Strategies
1 door/2 doors random outside-in back-to-front block
Boarding time (%)
1 door, non-calibrated 100 (reference) 80.9 110.5 96.2
1 door, calibrated 100 (reference) 79.5 109.2 95.3
2 doors, non-calibrated 74.2 63.8 75.3 76.2
2 doors, calibrated 74.1 62.5 75.0 76.2
Standard deviation (%)
1 door, non-calibrated 7.1 5.5 7.9 6.6
1 door, calibrated 7.3 5.7 8.1 6.9
2 doors, non-calibrated 4.6 2.9 4.8 5.3
2 doors, calibrated 5.9 5.5 5.9 5.8
4. Field Trials, Validation of Simulation Results
The previous section was aimed at the calibration of the stochastic passenger boarding model.
In a next step, the calibrated model is used to simulate boarding scenarios, which were set up in
operational field trials of an airline, to validate the passenger boarding model. The airline provides
all information about the test setup and the measured boarding times. The first airline trial evaluates
the performance of two advanced boarding scenarios as a proof of concept. The second field trial
extends the initial concept and integrates the boarding scenarios into the airline operations, which
cover different seat loads, the use of one/two doors, gate/apron position, destination, amount of pre-
boarding passengers, and transfer mode (bus, gate, walk).
4.1. Airline Trials 1
To ensure convenient and fast boarding progress airline operates employed new strategies,
which were tested in field. These strategies were also simulated with the calibrated modeled and
compared against data collected from the field (provided by the airline). Beside the common
approach of group boarding (back-to-front with four blocks, validation Scenario 1 in Figure 13), a new
outside-in strategy was tested (validation Scenario 2 in Figure 13) to determine potential operational
benefits. In the boarding validation Scenario 2, the aircraft cabin is divided into a rear/front section
(rows) as well as a window and middle/aisle section. The rear window seats are boarded first,
followed by the front window seats, the rear middle/aisle seats, and the front middle/aisle seats.
Figure 13. Airline boarding strategies for validation trials: Scenario 1 and Scenario 2.
These field measurements were conducted in 2014, aiming at business routes with the following
restrictions: families were not separated, the aircraft stands at gate position, and an A320/B738 aircraft
is used. The average seat load factor (SLF) of the 13 recorded flights was 76%. Since the test is based
on non-operational strategies, the boarding progress and group assignment were directly supported
by the airline ground staff. For reasons of comparability to the past and current airline boarding
operations, all measured boarding times were linearly extrapolated (based an average of 76%) to a
Figure 13. Airline boarding strategies for validation trials: Scenario 1 and Scenario 2.

Aerospace 2018,5, 27 14 of 20
These field measurements were conducted in 2014, aiming at business routes with the following
restrictions: families were not separated, the aircraft stands at gate position, and an A320/B738 aircraft
is used. The average seat load factor (SLF) of the 13 recorded flights was 76%. Since the test is based on
non-operational strategies, the boarding progress and group assignment were directly supported by the
airline ground staff. For reasons of comparability to the past and current airline boarding operations,
all measured boarding times were linearly extrapolated (based an average of 76%) to a reference seat
load factor of 90%. This approach contradicts the fact that the impact of seat load factor for the block
boarding strategies (including back-to-front) shows a nonlinear behavior [
7
,
20
,
33
]. To allow a reliable
comparison of the field trials with the simulation results, two approaches are used.
The first
simulation
trial starts with the reference seat load factor of 90% and the second trial starts with the average
76% SLF (measured in the field) with an equal distributed variation of
±
5% to cover the expected
deviation from the average load. All simulations use calibrated values for arrival times, seat interaction,
and hand luggage storage (see Section 3). The results of the simulation runs are listed in Table 3,
where expected values of the boarding time as well the quantiles of the boarding time distribution are
shown (10%, 25%, 75%, and 90%). In the first scenario with 90% SLF, the baseline boarding strategy
(random) exhibits only minor differences (
−
1%) and the validation
Scenario S2
strategy also indicates a
reliable simulation approach (
−
3% difference from the field trials).
A different
picture is given for the
validation Scenario S1 strategy, where the simulated boarding times are 11% higher than the measured
times at the field trials. The observed differences could also be caused by the linear up-scaling for the
reference boarding scenario (seat load factor of 90%). This linear scaling results in an underestimation
of the boarding time. Since the airline could not provide the full details of the tests, the measured
boarding times were linearly scaled back to reflect the reported average SLF of 76%. To cover the
operational bandwidth of seat load, the simulation considers an additional variation of SLF within a
range of
±
5% (equally distributed). With these adjustments,
the absolute
differences of the random
and validation Scenario S2 strategies are slightly increased,
but now
the validation Scenario S1 strategy
shows only a difference of 3.9%. As a side note, simulation results show additional time savings of 3%,
if in validation Scenario S2 the defined four boarding blocks are aggregated to three blocks (
Scenario S2*
,
see Figure 13, combining the window seats in the front and middle/aisle seats in the back to one
single block).
Finally, the results of simulation runs with the calibrated values cover the observed boarding
times at the field with an accuracy of
±
5%. The observed boarding times are within a
±
25% range
(between Q.25 and Q.75), which additionally emphasizes the validity of the calibrated stochastic
boarding model.
Table 3. Comparison of boarding progress using data from airline trials.
Boarding
Strategies
Boarding Time (%)
Field
Measurements
Simulation
Results Difference Quantiles
Q.10 Q.25 Q.75 Q.90
Seat load factor 90%
random 101.4
100 (reference)
−1.4 −8.6 −4.6 4.9 9.5
Scenario S1 93.7 104.5 10.8 −9.3 −5.1 5.2 10.2
Scenario S2 87.0 83.8 −3.2 −7.4 −4.0 4.4 8.4
Scenario S2* 80.5
Seat load factor 76% ±5%
random 102.6 100.0 −2.6 −
10.6
−5.7 6.2 11.8
Scenario S1 94.8 98.7 3.9 −
11.5
−6.3 6.6 12.7
Scenario S2 88.0 83.4 −4.6 −8.9 −4.8 5.2 10.2
Scenario S2* 80.8

Aerospace 2018,5, 27 15 of 20
4.2. Airline Trials 2
During the second airline trial, 64 additional boarding events were recorded, aiming at a deeper
understanding on how passengers and their individual behavior influence the boarding process,
beyond the already considered input parameters. These particular validation trials mainly focused on
two boarding scenarios: Scenario S1 (four blocks back-to-front) and outside-in (cf. Figure 2). Furthermore,
two operational configurations (one door and two doors) were chosen and single aisle aircraft with
180–210 seats (A320/B738) were used. Figure 14 demonstrates that the ability of the rear door for
boarding does not necessarily result in an efficient operational use (not even in a field trial environment).
Thus, a boarding event will be defined as a one-door scenario (37 flights), if at least 75% of the
passengers are using the front door. All operational relevant information for a specific flight was
recorded, such as amount of pre-boarding passengers, aircraft position at apron and additional flight
categorization (tourist, EU, Germany). It is suggested that all these parameters will substantially
influence the boarding progress. As an example, an apron position near the gate enables walk boarding
(passengers walk across the apron directly to the aircraft).
Aerospace 2018, 5, x FOR PEER REVIEW 15 of 20
75% of the passengers are using the front door. All operational relevant information for a specific
flight was recorded, such as amount of pre-boarding passengers, aircraft position at apron and
additional flight categorization (tourist, EU, Germany). It is suggested that all these parameters will
substantially influence the boarding progress. As an example, an apron position near the gate enables
walk boarding (passengers walk across the apron directly to the aircraft).
Figure 14. Usage of the front door at the field trial.
If all recorded field data from airline trial 2 are used as an input for a flight classification, only a
few flights will be in one category. In Table 4, the transfer mode to aircraft and destination of flights
are used for categorization. The different positions of aircraft at the apron determine the mode of
passenger transfer: bus shuttle (apron position), terminal gangway (gate position) or walk boarding
(near gate or apron position).
Table 4. Flight categorization.
Seat Load Factor Transfer Mode Destination
Bus Gate Walk Tourist EU Germany No Tag
60–80% 1 14 13 7 7 12 2
80–90% 0 4 16 6 5 6 4
90–100% 0 7 10 6 5 5 1
It is necessary to reduce the amount of input parameters to analyze the field data in the context
of boarding model validation. For the analysis, flights are separated by seat load factor in three
groups: SLF 60–80% (27 flights), SLF 80–90% (20 flights) and with SLF 90–100% (17 flights). These
groups are mainly chosen to reflect the initial operational assumption of the stochastic boarding
model, which uses a reference value for seat load factor of 85% with ±5% deviation. Figure 15 exhibits
the distribution of pre-boarded passengers. These passengers are allowed to board first because of
their membership in loyalty programs (e.g., frequent traveler status), reduced mobility or specific
group constellations (e.g., families with small children). In the stochastic boarding model,
pre-boarding is also considered indirectly by passenger’s conformance to the current strategy, which
is set to 85% (cf. Section 2).
40
60
80
100
120
140
50 60 70 80 90 100
boarding time (%)
usage of front door (%)
outside-in (field) block (field)
Figure 14. Usage of the front door at the field trial.
If all recorded field data from airline trial 2 are used as an input for a flight classification, only a
few flights will be in one category. In Table 4, the transfer mode to aircraft and destination of flights
are used for categorization. The different positions of aircraft at the apron determine the mode of
passenger transfer: bus shuttle (apron position), terminal gangway (gate position) or walk boarding
(near gate or apron position).
Table 4. Flight categorization.
Seat Load
Factor
Transfer Mode Destination
Bus Gate Walk Tourist EU Germany No Tag
60–80% 1 14 13 7 7 12 2
80–90% 0 4 16 6 5 6 4
90–100% 0 7 10 6 5 5 1
It is necessary to reduce the amount of input parameters to analyze the field data in the context of
boarding model validation. For the analysis, flights are separated by seat load factor in three groups:
SLF 60–80% (27 flights), SLF 80–90% (20 flights) and with SLF 90–100% (17 flights). These groups are
mainly chosen to reflect the initial operational assumption of the stochastic boarding model, which uses
a reference value for seat load factor of 85% with
±
5% deviation. Figure 15 exhibits the distribution
of pre-boarded passengers. These passengers are allowed to board first because of their membership
in loyalty programs (e.g., frequent traveler status), reduced mobility or specific group constellations

Aerospace 2018,5, 27 16 of 20
(e.g., families with small children). In the stochastic boarding model, pre-boarding is also considered
indirectly by passenger’s conformance to the current strategy, which is set to 85% (cf. Section 2).
Aerospace 2018, 5, x FOR PEER REVIEW 16 of 20
Figure 15. Amount of pre-boarding passengers.
While the first airline trials where strictly focused on specific flights with nearly identical
operational conditions (input factors are covered by the stochastic boarding model), the second trial
is characterized by a high range of different (new) impact factors (not covered by the model).
Consequently, the simulation results exhibit higher deviations from the operational measurements
for both average boarding time and corresponding standard deviation.
In Figure 16, the simulation results are marked with circles with an error bar indicating the 10%
and 90% quantile. The red crosses mark the block strategy (Scenario S1 with four blocks, back-to-front)
and the green plus signs mark the outside-in strategy separated by one-door/two-door configuration.
In particular, the outside-in strategy does not show the expected benefit. Since the simulation results
in shorter boarding times, it is expected that the amount of pre-boarding passengers and the
operational procedures to handle these passengers will mainly cause this effect.
Figure 16. Comparison of simulation results and measured boarding times using the block strategy
(validation Scenario S1) and the standard outside-in boarding strategy.
Several (measured) input factors influence aircraft boarding, such as aircraft position or flight
destination. Unfortunately, the recorded data are insufficient for a comparison between simulation
results and the field data from airline trial 2 with regards to a specific input factor. To cover significant
operational constraints, these factors have to be considered in future boarding models.
5. Conclusions and Outlook
This paper provides a comprehensive set of operational data as a reliable basis for the calibration
of a stochastic boarding model, including classification of boarding times, arrival and departure rates
of passengers at the aircraft door, individual durations to store hand luggage, and timestamps for
passenger interactions during seating. The data were recorded at several field measurements during
0
2
4
6
8
10
12
14
16
pre-boarded passengers (%)
SLF 60% - 80% SLF 80% - 90% SLF 90% - 100%
40
60
80
100
120
140
boarding time (%)
outside-in (field) block (field) simulation
1door | 2doors
SLF 60% - 80%
1door | 2doors
SLF 80% - 90%
1door | 2doors
SLF 90% - 100%
Figure 15. Amount of pre-boarding passengers.
While the first airline trials where strictly focused on specific flights with nearly identical
operational conditions (input factors are covered by the stochastic boarding model), the second
trial is characterized by a high range of different (new) impact factors (not covered by the model).
Consequently, the simulation results exhibit higher deviations from the operational measurements for
both average boarding time and corresponding standard deviation.
In Figure 16, the simulation results are marked with circles with an error bar indicating the 10%
and 90% quantile. The red crosses mark the block strategy (Scenario S1 with four blocks, back-to-front)
and the green plus signs mark the outside-in strategy separated by one-door/two-door configuration.
In particular, the outside-in strategy does not show the expected benefit. Since the simulation results in
shorter boarding times, it is expected that the amount of pre-boarding passengers and the operational
procedures to handle these passengers will mainly cause this effect.
Aerospace 2018, 5, x FOR PEER REVIEW 16 of 20
Figure 15. Amount of pre-boarding passengers.
While the first airline trials where strictly focused on specific flights with nearly identical
operational conditions (input factors are covered by the stochastic boarding model), the second trial
is characterized by a high range of different (new) impact factors (not covered by the model).
Consequently, the simulation results exhibit higher deviations from the operational measurements
for both average boarding time and corresponding standard deviation.
In Figure 16, the simulation results are marked with circles with an error bar indicating the 10%
and 90% quantile. The red crosses mark the block strategy (Scenario S1 with four blocks, back-to-front)
and the green plus signs mark the outside-in strategy separated by one-door/two-door configuration.
In particular, the outside-in strategy does not show the expected benefit. Since the simulation results
in shorter boarding times, it is expected that the amount of pre-boarding passengers and the
operational procedures to handle these passengers will mainly cause this effect.
Figure 16. Comparison of simulation results and measured boarding times using the block strategy
(validation Scenario S1) and the standard outside-in boarding strategy.
Several (measured) input factors influence aircraft boarding, such as aircraft position or flight
destination. Unfortunately, the recorded data are insufficient for a comparison between simulation
results and the field data from airline trial 2 with regards to a specific input factor. To cover significant
operational constraints, these factors have to be considered in future boarding models.
5. Conclusions and Outlook
This paper provides a comprehensive set of operational data as a reliable basis for the calibration
of a stochastic boarding model, including classification of boarding times, arrival and departure rates
of passengers at the aircraft door, individual durations to store hand luggage, and timestamps for
passenger interactions during seating. The data were recorded at several field measurements during
0
2
4
6
8
10
12
14
16
pre-boarded passengers (%)
SLF 60% - 80% SLF 80% - 90% SLF 90% - 100%
40
60
80
100
120
140
boarding time (%)
outside-in (field) block (field) simulation
1door | 2doors
SLF 60% - 80%
1door | 2doors
SLF 80% - 90%
1door | 2doors
SLF 90% - 100%
Figure 16.
Comparison of simulation results and measured boarding times using the block strategy
(validation Scenario S1) and the standard outside-in boarding strategy.

Aerospace 2018,5, 27 17 of 20
Several (measured) input factors influence aircraft boarding, such as aircraft position or flight
destination. Unfortunately, the recorded data are insufficient for a comparison between simulation
results and the field data from airline trial 2 with regards to a specific input factor. To cover significant
operational constraints, these factors have to be considered in future boarding models.
5. Conclusions and Outlook
This paper provides a comprehensive set of operational data as a reliable basis for the calibration
of a stochastic boarding model, including classification of boarding times, arrival and departure
rates of passengers at the aircraft door, individual durations to store hand luggage, and timestamps
for passenger interactions during seating. The data were recorded at several field measurements
during actual aircraft turnarounds of Airbus A320 (short-medium haul, single aisle) and comparable
Boeing B737/B738. These aircraft are mainly used as a reference layout for boarding research.
Each measurement
campaign aimed at different aspects of individual boarding behavior of passengers
and realized in close cooperation with the corresponding airlines, ground handling agents, and airport
operators. While passenger arrival/departure rates could be measured from outside the cabin by
recording the individual time stamps of passengers passing the aircraft door, the hand luggage storage
time and passenger interactions during the seating (seat shuffle) were recorded from positions inside
the narrow aircraft cabin. Particularly, the specific seat shuffles are required special attention and a
close observation position, which results only in a limited number of measurements.
The analyzed boarding times, defined as time between first passengers enters the aircraft and last
passenger is seated, demonstrate three different characteristics of boarding progress: fast, medium,
and slow boarding. This result emphasizes the demand for a more comprehensive investigation into
the passenger boarding process to enable a reliable boarding time prediction. Since arrival at the
aircraft, storage of hand luggage, and interactions during the seating process are identified as major
input factors for the individual passenger behavior, specific field trials provide a fundamental database
to calibrate these factors. As a result, the measurements show a non-constant arrival rate,
a Weibull
distribution for the time needed to store the hand luggage, and support the initial assumptions
about the interactions during the seat shuffle (taking a seat, while other seats already occupied).
The comparison
between prior simulations (non-calibrated input) and current simulations (calibrated
input) shows only minor relative differences (smaller 2%) with regard to the corresponding boarding
time (random boarding non-calibrated/calibrated as a reference).
The calibrated boarding model was then used to simulate the different boarding scenarios,
which were also operationally implemented during a field trial campaign (controlled environment).
The comparison
of simulation results and measured boarding times showed deviations smaller than
±
5%. Additionally, measurements from a less controlled operational environment demonstrate that
the boarding is also driven by external factors, which are currently not covered by the stochastic
boarding model. Thus, measurements show a much higher deviation than the simulation results.
It is
expected that future cooperation between researchers and operators will enable new insights into
passenger boarding processes. As a necessary first step, this paper provides a comprehensive set of
data to calibrate the input parameter of boarding models.
The simulation environment and the aircraft boarding model are being continuously developed
to enable both scientific and operational assessments of aircraft boarding scenarios. In the context of
specific research projects, the simulation environment is extended with evolutionary algorithms to
search for optimal strategies under certain airline requirements and operational conditions [
48
,
49
].
Starting with the implemented basic boarding strategies, new boarding strategies will emerge to enable
new infrastructural approaches (e.g., combination of block +alternation patterns for the Side-Slip Seat
implementation, see Figure 17).

Aerospace 2018,5, 27 18 of 20
Aerospace 2018, 5, x FOR PEER REVIEW 17 of 20
actual aircraft turnarounds of Airbus A320 (short-medium haul, single aisle) and comparable Boeing
B737/B738. These aircraft are mainly used as a reference layout for boarding research. Each
measurement campaign aimed at different aspects of individual boarding behavior of passengers and
realized in close cooperation with the corresponding airlines, ground handling agents, and airport
operators. While passenger arrival/departure rates could be measured from outside the cabin by
recording the individual time stamps of passengers passing the aircraft door, the hand luggage
storage time and passenger interactions during the seating (seat shuffle) were recorded from
positions inside the narrow aircraft cabin. Particularly, the specific seat shuffles are required special
attention and a close observation position, which results only in a limited number of measurements.
The analyzed boarding times, defined as time between first passengers enters the aircraft and
last passenger is seated, demonstrate three different characteristics of boarding progress: fast,
medium, and slow boarding. This result emphasizes the demand for a more comprehensive
investigation into the passenger boarding process to enable a reliable boarding time prediction. Since
arrival at the aircraft, storage of hand luggage, and interactions during the seating process are
identified as major input factors for the individual passenger behavior, specific field trials provide a
fundamental database to calibrate these factors. As a result, the measurements show a non-constant
arrival rate, a Weibull distribution for the time needed to store the hand luggage, and support the
initial assumptions about the interactions during the seat shuffle (taking a seat, while other seats
already occupied). The comparison between prior simulations (non-calibrated input) and current
simulations (calibrated input) shows only minor relative differences (smaller 2%) with regard to the
corresponding boarding time (random boarding non-calibrated/calibrated as a reference).
The calibrated boarding model was then used to simulate the different boarding scenarios,
which were also operationally implemented during a field trial campaign (controlled environment).
The comparison of simulation results and measured boarding times showed deviations smaller than
±5%. Additionally, measurements from a less controlled operational environment demonstrate that
the boarding is also driven by external factors, which are currently not covered by the stochastic
boarding model. Thus, measurements show a much higher deviation than the simulation results. It
is expected that future cooperation between researchers and operators will enable new insights into
passenger boarding processes. As a necessary first step, this paper provides a comprehensive set of
data to calibrate the input parameter of boarding models.
The simulation environment and the aircraft boarding model are being continuously developed
to enable both scientific and operational assessments of aircraft boarding scenarios. In the context of
specific research projects, the simulation environment is extended with evolutionary algorithms to
search for optimal strategies under certain airline requirements and operational conditions [48,49].
Starting with the implemented basic boarding strategies, new boarding strategies will emerge to
enable new infrastructural approaches (e.g., combination of block + alternation patterns for the Side-
Slip Seat implementation, see Figure 17).
Figure 17. Combination of boarding strategies block + alternation to support the implementation of the
Side-Slip Seat [49,50].
Figure 17.
Combination of boarding strategies block +alternation to support the implementation of the
Side-Slip Seat [49,50].
After introducing a stochastic approach to consider the individual passenger behavior during
aircraft boarding [
7
,
20
], the field measurements to calibrate the stochastic model, and investigations
into procedural/infrastructural changes [
48
,
49
], two new topics in the context of aircraft boarding
will be focused upon: the real-time prediction of the boarding time [
51
,
52
] using sensor information
from a connected aircraft cabin [
53
,
54
] and the seatNow concept [
55
]. The seatNow concept addresses
operational improvements if the current standard call-in boarding procedure is replaced by a dynamic
seat allocation process. The seatNow concept has already been successfully tested with Eurowings
at Cologne/Bonn airport and will be a promising approach towards further improvement in both
passenger convenience and efficient airport/airline operations.
Conflicts of Interest: The author declares no conflicts of interest.
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