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An Effort-Based Model for Pedestrian Route Choice
Behaviour
By
Fatma Saleh Salem Al-Widyan
Thesis submitted as a requirement for the degree of
Doctor of Philosophy
School of Electrical, Mechanical and Mechatronic Systems
Faculty of Engineering and Information Technology
University of Technology Sydney (UTS)
July 2018
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Certificate
I certify that the work in this thesis has not previously been submitted for a degree nor
has it been submitted as part of requirements for a degree except as fully acknowledged
within the text.
I also certify that the thesis has been written by me. Any help that I have received in my
research work and the preparation of the thesis itself has been acknowledged.
Also, I certify that all information sources and literature used are indicated in the thesis.
Signature of Student
Fatma Saleh Al-Widyan
Date: 27/8/2018
Production Note:Signature removed prior to publication.
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ACKNOWLEDGEMENT
I would like to thank my supervisor, A/Prof Robert Fitch, for supporting my research with
admirable enthusiasm. Being critical, but at the same time ready to help me find solutions
to topical issues in my research. The wise direction and generosity, you showed during
my research made the dissertation more than I could have done by myself. Secondly, I
wish to acknowledge my sincere appreciation to my project supervisor Dr Nathan
Kirchner for his personal, mathematical, and scientific support.
I also would like to extend my gratitude to the team members of the transportation project,
Dr Alen Alempijevic, Dr Michelle Zeibots, Julien Collart and Alexander Virgona, who
had a great effect in achieving the benefit and taking the time to provide very useful
suggestions for improvement.
Finally, a special thanks and love go to my beloved family and friends for their unfailing
support, being there for me when I needed them.
Fatma Saleh Al-Widyan
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To my beloved son, Yamen
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People choose the paths that grant them the greatest rewards for the least
amount of effort
David shore
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ABSTRACT
This research proposes a novel effort-based theoretical framework for the
pedestrian route choice problem to discover principles that pedestrians use to select their
routes. A pedestrian chooses their route by optimising certain criteria, such as distance,
time, and effort. Several possible criteria that could be used to predict the route choices
of a pedestrian are re-assessed. In most cases, the common criteria of a pedestrian route
choice are route length and travel time. Effort is proposed as an additional criterion, which
indicates metabolic energy expenditure.
The basic principle and a methodology are proposed for route choice based on the
least effort that a pedestrian may consume during travel between destinations. The
followed deterministic approach assumes that the perceived utility of a route is
deterministic and that pedestrians will only choose the route that features minimum
average cost.
A mathematical formulation for solving the pedestrian route choice problem
utilising the concept of physical effort is introduced. We compare our effort-based model
against time and distance based models and validate against the Brisbane dataset. We
demonstrate that our method has higher performance efficiency than the models that exist
in the state-of-the-art and thereby the model justifies optimal pedestrian behaviour when
choosing a route in a congested environment.
Our discussion concludes with an overview of how our approach could be used by
rail service providers to optimise operations and improve customer experience. It is
contended that the entire behaviour of an individual is subject to effort minimization.
Hence, the pedestrian route choice problem is formulated as a constrained non-linear
optimization problem whose objective function is the effort consumed while moving from
current position to destination over the route.
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This doctoral research is a part of research project entitled “Integrated Passenger
Behaviour, Train Operations Diagnostics, and Vehicle Condition Monitoring System”,
which aims to consolidate foundation technology for the sensing and perception functions
of a system that can monitor passenger behaviour and operational characteristics of
passenger trains as they arrive at crowded stations using low-cost multi-sensor network.
The Brisbane Central Rail Train Station is selected for a case study for validation of the
developed model.
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ACRONYMS AND ABBREVIATION
PLE: Principle of least effort
PRC: Pedestrian route choice
SHP: Sensing Hardware Platform
MTC: Minimum time criteria
MDC: Minimum distance criteria
MEC: Minimum effort criteria
V: The walking speed (m/s)
P: Metabolic power (Watts)
L: Length of the route (m)
X: The external load (N)
W: The individual weight (N): The terrain factor defined as 1 for free walking
G: The grade (%)
s0: Initial position
sf: Final position
t0: Initial time (s)
tf: Final time (s)
x0: Initial point at x-axis
xf: The final point at x-axis
y0: Initial point at y-axis
yf: The final point at the y-axisv : The magnitude of velocity (m/s)
T: Time (s)
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D: Distance (m)
O: Origin
D: DestinationE: Energy rate (Watt)x: X Component of the velocity (m/s)y: Y Component of the velocity (m/s)
E: Energy (Joul)p: Position vector(x , y ): Initial coordinate, Origin(x , y ): Final coordinate, Destination
q(t): Number of passengers in the queue
n(t): The rate of passengers existing from the bottleneck
m(t): Passenger rate departing from the train at a time, t
C: Escalator capacity (Ped/s)
O-D pair: Origin-destination
M: metabolic rate (Watts)
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CONTENTS
CHAPTER 1 ................................................................................................................................................................ 1 INTRODUCTION ....................................................................................................................................................... 1
1.1 SCOPE AND MOTIVATION .................................................................................................................................................. 3 1.2 RESEARCH OBJECTIVE ....................................................................................................................................................... 4 1.3 RESEARCH CONTRIBUTIONS ............................................................................................................................................. 4 1.4 RESEARCH METHODOLOGY .............................................................................................................................................. 5 1.5 ORGANIZATION OF THE DISSERTATION .......................................................................................................................... 6 1.6 PUBLICATIONS ARISING DIRECTLY FROM THE PHD RESEARCH ................................................................................ 9
CHAPTER 2 ............................................................................................................................................................. 10 LITERATURE REVIEW OF PEDESTRIAN BEHAVIOUR ............................................................................. 10
2.1 ROUTE CHOICE ................................................................................................................................................................. 11 2.1.1 Route Choice Definition .................................................................................................................................... 11 2.1.2 Route Choice Models.......................................................................................................................................... 13 2.1.3 Factors Influencing Route Choice ................................................................................................................ 15
2.2 WALKING BEHAVIOUR .................................................................................................................................................... 18 2.2.1 Walking Behavior Models ............................................................................................................................... 18
2.3 CONGESTION ..................................................................................................................................................................... 19 2.3.1 Influence of Congestion Occurrence on Route Choice .......................................................................... 21 2.3.2 Pedestrian Bottleneck ................................................................................................................................ 28
2.4 PRINCIPLE OF LEAST EFFORT ........................................................................................................................................ 29 2.4.1 Metabolic Energy ................................................................................................................................................ 32
2.5 CONCLUSIONS.................................................................................................................................................................... 35 CHAPTER 3 ............................................................................................................................................................. 36 EFFORT-BASED THEORETICAL FRAMEWORK FOR PEDESTRIAN ROUTE CHOICE ...................... 36
3.1 PROBLEM STATEMENT .................................................................................................................................................... 39 3.2 EFFORT-BASED FORMULATION OF PRC PROBLEM ................................................................................................... 42
3.2.1 The Euler-Lagrange Equations ..................................................................................................................... 43 3.2.2 Constraint -Free Pedestrian Walk ............................................................................................................... 44
3.3 EVALUATION OF THE PROPOSED EFFORT FORMULATION; CLIMBING STAIRS VS RIDING ESCALATOR ............. 48 3.4 EVALUATION OF THE PROPOSED EFFORT FORMULATION; ESCALATOR WITH DIFFERENT LEVELS OF CONGESTION ............................................................................................................................................................................. 51 3.5 CONCLUSIONS.................................................................................................................................................................... 53
CHAPTER 4 ............................................................................................................................................................. 54 COMPARISON BETWEEN DIFFERENT CRITERIA FOR PEDESTRIAN ROUTE CHOICE .................. 54
4.1 ROUTE COST IN TERMS OF DISTANCE, TIME AND PHYSICAL EFFORT ..................................................................... 54 4.1.1 Route Cost in Terms of Distance ................................................................................................................... 55 4.1.2 Route Cost in Terms of Time .......................................................................................................................... 56 4.1.3 Route Cost in Terms of Physical Effort ....................................................................................................... 56
4.2 A COMPARISON BETWEEN CRITERIA ............................................................................................................................. 57 4.3 EXAMPLE 1: ....................................................................................................................................................................... 60 4.4 EXAMPLE 2: ....................................................................................................................................................................... 64 4.5 CONCLUSIONS.................................................................................................................................................................... 68
CHAPTER 5 ............................................................................................................................................................. 69 EXPERIMENTAL RESULTS OF A BOTTLENECK INVESTIGATION AT THE BRISBANE CENTRAL TRAIN STATION ................................................................................................................................................... 69
5.1 DATA COLLECTION TECHNIQUES .................................................................................................................................. 69 5.2 CASE STUDY 1: STAIRS OR ESCALATOR ........................................................................................................................ 71 5.3 CASE STUDY 2: ESCALATOR ENTRY BOTTLENECK ..................................................................................................... 79
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5.3.1 Bottleneck and Queuing ................................................................................................................................... 80 5.3.2 Bottleneck Capacity ........................................................................................................................................... 81 5.3.3 Model Formulation Escalator Entry Bottleneck .................................................................................... 82 5.3.4 Experimental Results ........................................................................................................................................ 86
5.4 CONCLUSIONS.................................................................................................................................................................... 87 CHAPTER 6 ............................................................................................................................................................. 90 CONCLUSIONS AND FUTURE WORK .............................................................................................................. 90
6.1 SUMMARY .......................................................................................................................................................................... 90 6.2 MAIN FINDINGS ................................................................................................................................................................ 91 6.3 FUTURE WORK ................................................................................................................................................................. 93
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LIST OF FIGURES
Figure 2.1 Levels of pedestrian behaviour 10Figure 2.2 A route as a chain of nodes from origin to destination 11Figure 2.3 Congestion at the Brisbane central rail train station 20Figure 2.4 Comparison between two routes (with and without
congestion)24
Figure 2.5 Illustration of the key direction of moving congestion 25Figure 2.6 Human beings utilise a path of least effort 31Figure 3.1 Possible routes between two destinations 40Figure 3.2 Route description 41Figure 3.3 A characteristic curve of power P 45Figure 3.4 Trajectories ( ) ( ) 48Figure 3.5 Route choice between the platform and concourse 49Figure 4.1 The shortest route between points A and B 55Figure 4.2 Shows the surface of effort E versus the time T and the
length L58
Figure 4.3 The relation between the velocity V and the effort E 59Figure 4.4 Comparison between two routes 61Figure 4.5 Illustration of the key direction of route choice possibilities 61Figure 4.6 The relation between route length and time 62Figure 4.7 The relation between effort and time 63Figure 4.8 Comparison between two Routes 65Figure 4.9 Comparison between walk through mud path (more
resistance) and least resistance path at the right side in real life.
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Figure 5.1 Queensland rail field layout for Brisbane central rail station Feb-2015, (Box 4)
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Figure 5.2 Escalator and stairs, in Brisbane central rail station 72Figure 5.3 Our SHP located at Brisbane central rail station 72Figure 5.4 Number of pedestrians over time on the escalator at
Queensland rail for Brisbane central station Feb-201573
Figure 5.5 Percentage of passengers walking up escalator/stairs without congestion
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Figure 5.6 Route choice behaviour passengers’ based on the congestionstate
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Figure 5.7 Congestion occurrence prediction with numbers and percentages of passengers who travelling over stairs and escalator
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Figure 5.8 Train station layout 83Figure 5.9 Case A, no congestion 84Figure 5.10 Case B, the number of passengers travelling over an
escalator equal escalator capacity84
Figure 5.11 Case C, high- level congestion occurs 85Figure 5.12 The sensing (SHP) located at Brisbane central rail station. 86Figure 5.13 Bottlenecks in a peak hour situation at Brisbane central rail
station.87
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LIST OF TABLES
Table 1.1 Overview of the dissertation organisations 8Table 2.1 Summary of metabolic energy formula proposed in literature 34Table 3.1 Route cost in terms of length, time and effort without considering
the congestion 50
Table 3.2 Route O-B with different terrain and velocities in congested infrastructure
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Table 4.1 Route cost in terms of time, distance and effort 63Table 4.2 An overview of route usage 67Table 5.1 A comparison of effort with a different state of congestion 78
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Chapter 1
Introduction
The modelling of pedestrian behaviour, especially the modelling of pedestrian route
choice has become very important in recent years. This is due to the fact that crowding
events are getting larger at all times. Furthermore, the density of population is increasing.
This implies that in the preparation and design of public transport facilities, airports,
shopping centres, etc., it is essential to understand pedestrian behaviour. Additionally,
theoretical models can help infrastructure designers as well as transport designers to
optimize their plans. Furthermore, the controlling of pedestrian flows requires an
understanding of both the collective pedestrian flows as well as the individual pedestrian
behaviour in the flow. Therefore, it is essential to optimise a route choice of the
pedestrian.
Passengers that use public transport networks may require making pedestrian route
choices within public transport environments. For instance, in rail station precincts,
pedestrian route choices may occur in concourse and platform areas. Such route choices
become more complicated as public transport stations become more complex, especially
when they are integrated with retail activities and have access to other transport services.
This increases the number of activities that may be performed in a station and can
complicate the route choice process for individuals.
Predicting pedestrian flows and route choice is a requirement for the operation,
planning, and design of public transport facilities. The provided egress options may
influence the emergence of congestion within facilities if every passenger chooses the
same route. In real-time practice, there are usually multiple egress options, and so the
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question arises as to how people make decisions when choosing between them, for
example between escalators and stairs, and further, how the emergence of congestion may
affect route choice.
Pedestrians usually enjoy a high-degree of movement freedom even in a highly-
congested area. Accordingly, several alternative paths are favoured by pedestrians
between any origin-destination (O-D) pair. This thesis presents a methodology for
predicting the preferred route by passengers during their egress. This is achieved by
proposing a basic principle and a methodology for route choice based on the concept of
least effort that a passenger may put during his/her travel between destinations. The
methodology proposed takes into consideration the movement of passengers and
congestion state. The principle of least effort is formulated in terms of metabolic energy,
and congestion state.
Brisbane central railway station is one of the busiest railway stations in Queensland,
which is the central business district, Australia. The traffic demand exerts a serious stress
on the station that was designed. The study of pedestrian behaviour within Brisbane
central train station during rush hours is essentially important, as there are a high number
of pedestrian and restricted capacities of the pedestrian transport facility. However, a
major improvement and reconstruction of the central train station are expensive.
Accordingly, the need for the proper design of an underground station and transport
facilities is crucial for the maximum realisation of the station capacity. Our model is
applicable for any other station; the factors that are to be considered when applying it to
other stations include width of the escalator, length of the escalator, staircase width, and
escalator entry area.
Our approach uses a new mathematical model for representing effort expended for
each path, based on a formulation that minimises the total amount of metabolic energy
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used when moving on a trajectory. Using results from an empirical study at Brisbane
Central rail station, we show our approach correlates well with real patterns of passenger
egress.
1.1 Scope and Motivation
This dissertation is a theoretical and experimental framework mainly developed for
the planning of transportation facilities with intensive pedestrian crowds. The research
work describes the pedestrian behaviour walking and passenger route choice (PRC) in
public transportation facilities.
In general, public transportation facilities are designed mainly for practice and
common sense. However, the increase of the passenger use of these facilities will lead
to lower efficiency of the design and to get more crowded. Planning of such a public
transportation facilities required real experimental and theoretical studies that can be
performed to predict the increase of passenger each year.
Crowding at egress points and waiting for areas in public transport environments
during peak periods can potentially impede passenger movements, which in turn may
cause delays to scheduled services. Passenger modelling is a complex task. There are
relatively few models able to simulate the complex behavioural characteristics of large
volumes of a passenger walking through confined public transport environments such as
rail station concourse and platform areas. With the aid of sensing technology, however,
rich data can be acquired to provide high-quality inputs on which passenger behaviour
models can be based upon.
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1.2 Research Objective
The objective of this work is to contribute a solution to the challenging problem of
predicting the route a passenger selects while walking. Such a problem is crucial and
highly demanded in transportation fields and their applications. According to the scope of
this research, the following can be identified as the major research objectives:
i. To formulate a new mathematical model for representing effort expended by each
passenger, based on a biomechanical formulation that minimises the total amount
of metabolic energy used when walking on a trajectory from origin to destination.
ii. To test the feasibility of route choice modelling based on the least effort principle
to quantify the perceived utility of the passenger environment as revealed by
passengers’ actual behaviours. The focus is on developing better route choice models
and understanding of the passenger environment and walking behaviour.
iii. To quantify the relation based on the least effort between the congestion presence
and pedestrian route choice behaviour.
1.3 Research Contributions
The main scientific contributions described in this dissertation exploits the
Principle of Least Effort, applied to pedestrian route choice, which postulates that credible
behaviours emerge as a function of the organism’s propensity to minimise metabolic
energy expenditure with respect to task, environment dynamics, and an organism’s
constraints to action. The path of least effort is also used to describe certain human
behaviours, although with much less specificity than in the strict physical sense in these
cases, least effort is often used as a metaphor for personal effort; a person taking the path
of least effort avoids obstacles. Additionally, the design of a methodology to assess the
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relation between the pedestrian route choice and congestion based on least effort is
proposed.
Besides, this work presents the least effort principle for passenger route choice, a
novel principle for computing a biomechanically energy-efficient trajectory. Our
mathematical formulation is based on the least effort principle and navigates passengers
along the optimal route to the destination while simultaneously avoiding congestion,
reducing the amount of effort, and maintaining the preferred speed.
1.4 Research Methodology
In this research, we follow the deterministic approach, which assumes that the
perceived utility of a route is deterministic and that pedestrians will only choose the
route that has minimum average cost.
Our approach uses a new mathematical model for representing effort expended for
each path, based on a formulation that minimizes the total amount of metabolic
energy used when moving on a trajectory. Using results from an empirical study at
Brisbane Central rail station, we show our approach collates well with real patterns
of passenger egress.
This research presents a methodology for predicting the preferred route selected by
passengers during their egress. Proposed in this research are a basic principle and a
methodology for route choice based on the least effort that a passenger may consume
during their travel between destinations. The methodology proposed takes into
consideration the movement based on passenger and congestion state. We employ
the principle of least effort, formulated in terms of metabolic energy, and congestion
states.
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The main research question is:
What is the preferred route selected by passengers during their egress within public
transport environments, and what is its influence at Brisbane central rail station?
Final results of the experiments conducted :
Experiment 1 shows that pedestrians change their route choice with perceived
congestion, and anticipate different route choice behaviour during congestion and
without congestion. Data suggest that part of the population has a habit to avoid
congestion routes even when no congestion is present. The analysis shows that the
number of passengers avoiding escalator increases when congestion occurs.
In experiment 2, pedestrian behaviour and the escalator, entry bottleneck was
studied. Show that the route choice is significantly influenced by the presence of
congestion; this shows that route choice is influenced by the escalator entry
bottleneck. The escalator entry bottleneck on route selection has a cost in a real
world (using real data from a field study), and that passenger route models can
exploit this to describe behaviour.
1.5 Organization of the Dissertation
The overview remainder of the dissertation is organised as follows.
Chapter 1: Provides an introduction to the proposed study. In this Chapter, the
motivation for the research is introduced. In Section 1.1 scope and the objective are
explained. Then, the research contribution is introduced in Section1.3. This chapter is
concluded in Section 1.6 with the publications arising directly from the PhD research.
Chapter 2: Presents a review of relevant literature about the general background of
techniques and models. Section 2.1 route choice is first defined, then route choice
models and factors influencing route choice are represented. Walking behaviour and
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models are addressed in Section 2.2. Then, a congestion, influence of congestion, and
pedestrian bottleneck are introduced and described in Section 2.3. Research on the
principle of least effort and metabolic energy for pedestrian movement is presented in
Section 2.4.
Chapter 3: The main theoretical framework and foundations for the formulation of the
pedestrian route choice based on the concept of physical are included in this Chapter.
In Section 3.1 the problem at hand is formally stated. The mathematical formulation
of the research problem based on the concept of effort is derived in Section 3.2.
Climbing stairs vs escalator effort formulation in Evaluated in Section 3.3. Then
escalator with different level of congestion is evaluated in section 3.5. This chapter is
concluded in section 3.5.
Chapter 4: This chapter includes the comparison between route choice criteria. Section
4.1 discusses route cost in term of distance, time, and effort. A comparison of three
criteria is conducted in section 4.2. Insightful examples are included to explain the
main concept and fundamental idea pertinent to the dissertation research in Sections
4.3 and 4.4. The conclusion of the chapter is included in section 4.5.
Chapter 5: Summarises the experimental research. Section 5.1 presents an overview
of different data collection technique, consisting of observation in Brisbane central rail
station. In section 5.2 experiments are performed in route choice between stairs or
escalator. Respectively, section 5.3 concerns new data collection for escalator entry
bottleneck in Brisbane central rail station. This chapter is concluded in Section 5.4.
Chapter 6: Provides conclusions, a summary of the dissertation, and suggestions for
future research directions.
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Overview of the dissertation organisations is presented in Table 1.1.
Problem Definition
Model formulation
Case studies and Validation
1. Introduction
: Escalator Entry Bottleneck
Literature review - Route choice - Walking behaviour - Congestion - Principle of least effort
Stairs or Escalator
Effort-Based Formulation of PRC
Problem
Route Cost in Terms of Distance, Time and
Effort
Research Outline - Motivation - Scope and Objective - Contribution - Publication arising
Conclusions and Future Work
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1.6 Publications Arising Directly from the PhD Research
1. F. Al-Widyan, N. Kirchner, M. Zeibots, (2015), An empirically verified
Passenger Route Selection Model based on the principle of least effort for
monitoring and predicting passenger walking paths through congested rail
station environments. Australasian Transport Research Forum 2015 Proceedings.
2. F. Al-Widyan, A. Al-Ani, N. Kirchner, M. Zeibots, (2017). An Effort-Based
Evaluation of Pedestrian Route Choice Behaviour Scientific Research and
Essays journal 2017.
3. F. Al-Widyan, N. Kirchner, A. Al-Ani, M. Zeibots, (2016). A Bottleneck
investigation on escalator entrance at the Brisbane Central Train Station.
Australasian Transport Research Forum 2015 Proceedings.
4. F. Al-Widyan, A. Alani, N. Kirchner, M. Zeibots, (2017). A Comparison between
different criteria for pedestrian route choice behaviour. IEEE Proceedings
(ICIEA 2017) Siem Reap, Cambodia.
5. F. Al-Widyan, A. Al-Ani, N. Kirchner, M. Zeibots, (2017). An Effort-Based
Formulation of Pedestrian Route Choice. Journal of Intelligent Transportation
Systems: Technology, Planning, and Operations (under review).
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Chapter 2
Literature Review of Pedestrian Behaviour
This chapter will present an overview of existing literature about the general
background and models that are associated with pedestrian behaviour as route choice and
influence of pedestrian with the transport facilities.
Pedestrian behaviour is described at three levels: strategic level, tactical level, and
operation level, as described by Daamen (2004), and illustrated in Figure 2.1.
At the strategic level, pedestrians have determined many activities they like to
perform at train station; those include activities and the activity order. The set of activity
choice concerns the choice of optimum locations to perform an activity by each
passenger. Only a small literature exists on the choice of activity locations (Helbing,
Keltsch and Molnár, 1997), (Borgers & Timmermans 1986).
Route choice is a very important process at the tactical level, justifying why much
literature is found on a related topic (Guo and Loo, 2013, Ramming, 2002). Route choice
behaviour has been considered in different research fields such as psychology, transport
engineering, and geography.
At the operational level, most of the passenger decisions concern their walking
behaviour and the interaction with the public transport (Timmermans, 2009). Much
literature has been found on pedestrian moment behaviour, although less were dedicated
Strategic - Activity set
choice
Operational - Walking - Influance with transport facilities
Tactical - Route choice
Figure 2.1: Levels of pedestrian behaviour
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to transportation environment. Pedestrian travel purposes, the type of infrastructure,
culture and physical characteristic influenced pedestrian walking behaviour.
2.1 Route Choice
Route choice is an important behaviour in passenger models at public transport
facilities, explaining why a lot of literature involves the route choice problem. Route
choice has been considered in a variety of research fields such as psychology,
geography, and traffic engineering.
2.1.1 Route Choice Definition
A route is defined as a chain of nodes, connecting consecutive parts of walking
infrastructure, starting from the origin of the pedestrian and ending at pedestrian’s
destination between which multiple route alternatives exist, as shown in Figure 2.2. A
trajectory is a graphical representation of the walked path over time. In fact, trajectories
provide an efficient and clear summary of passenger movement in the walking direction
of the passenger (Daamen, 2004, Bovy & E. Stern 1990).
Route choice decision may affect the infrastructure used within the train station
facilities, as an example, the route choice between the escalator and the stairs or between
Figure 2.2: A route as a chain of nodes from origin to destination
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the right or lift passing of a shop (Voskamp, 2012). Since pedestrians enjoy a high degree
of movement freedom even in heavily congested areas, the graphical representation is
complicated for the passenger trajectories in both lateral and longitudinal direction.
Route choice can be a complex process by which a pedestrian chooses among path
alternatives given the infrastructure configuration. Often stations are designed to limit
path alternatives and information guides related to way-finding are provided to
passengers in an attempt to consolidate egress. Nevertheless, personal preferences and
perceptions can cause egress to fluctuate at key points along path alternatives, and lead
to a subsequent cascade of effects.
In fact, the routes that a passenger might choose can be clear and predictable to
transport experts. Some existing alternatives may, however, be unfamiliar. On the other
hand, passengers make choices depending on the changing conditions they encounter
while they are on their way. A choice set is a group of possible route alternative between
an origin and a given destination from that passengers will choose their route (Daamen,
2004, Hoogendoorn and Bovy, 2004).
Within the research on the environment and active travel, pedestrian route choice
has not been deeply studied. Challenges exist for examining pedestrian route choice,
especially the difficulty of collecting data on the routes taken by pedestrians. Generally,
pedestrian route choice data had to be gathered first-hand through monitoring individual
behaviour or through surveys, which can be unreliable (Guo and Loo, 2013), (Rodríguez
et al., 2015). This is because privacy considerations are paramount in tracking
pedestrians. Furthermore, and in contrast to the literature on the environment and active
travel, most considerations of pedestrian route choices focused on the frequently used
business district areas, which represent only a small fragment of the built environment.
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Hoogendoorn & Bovy (2004) claimed that the basis of passengers’ route choice
behaviour is that passengers individually choose optimal routes and influenced by
personal taste as well as conditions on the other routes. Rodriguez (2015) sets a route
choice as a high order spatial ability that comes above activities to walk, but he also
defines that passenger’s self-understanding of their route choice shapes does not appear
mainly deep. Accordingly, it is hard to reveal the preferred route choice, and a challenge
to observe all route alternatives.
2.1.2 Route Choice Models
Route choice models have been proposed to predict pedestrian behaviour on the
transport facilities. Most route models found in literature estimate complete alternatives
of the route from the given origin to a given destination of which passenger will choose
one of the alternatives. Many researchers have investigated the route choice problem, and
consequently, several pedestrian route choice modelling approaches have been proposed
and empirically validated.
In 1985, Gipps & Marksjö described algorithms to predict pedestrian flows within
and around constructed facilities. The model uses a physical layout to generate several
nodes that a pedestrian can walk between (Gipps and Marksjö, 1985b).
In 1986, Borgers & Timmermans formulated a model that gives a satisfactory
description of pedestrian route choice and allocation behaviour within an inner-city
shopping area ( Borgers & Timmermans 1986b). In 1998, Cheung & Lam investigated
the pedestrian choice between escalators and staircase in the Hong Kong stations. It is
assumed that the travel time functions for escalators and staircase form an important
factor in estimating the pedestrian split between the two options (Cheung and Lam, 1998).
In 2000, Hughes stated that pedestrians seek to minimise their estimated travel time, but
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temper this behaviour to avoid extremely high densities. The psychological state of
pedestrians can completely change the behaviour (Hughes, 2000).
Hoogendoorn & Bovy have developed a model that pedestrians schedule their
activities to maximise the benefit of their walking (Hoogendoorn and Bovy, 2004). Other
researchers further pointed out that a pedestrian walks from origin to destination moves
in a straight line (Liu, Bunker and Ferreira, 2010). The choice is limited to those that are
visible from the present pedestrian position and may vary from one pedestrian to another
(Burgess 1983). Some studies have shown that a pedestrian chose the route depends on
the minimum time from origin to destination; this route often is the shortest route
(Seneviratne and Morrall 1985, Guy et al. 2010).
More recently, some researchers attempted to investigate the principle of least
effort to the pedestrian route choice problem. Silder et al. (2012) provided an
experimental study to determine which measured variable best predict metabolic cost.
However, this study did not determine the direct relationship between each measure
variables and metabolic cost. Farris and Sawicki n.d (2012) investigated the effect of
walking and running speed on the total average power; this study lakes a measure for
muscle fascicle behaviour over a range of speed. Kramer veloand Sylvester (2011)
establish the degree to which the various method of calculating the mechanical energy is
related to the characterisation of the relationship of the effective method with measure
energy expenditure. A drawback of this study is that the choice of a predictive method is
dependent on the data available for use as inputs, and no method is intrinsically better or
worse than another.
The model proposed in (Guy et al. 2010) is very simple and lacks any real
considerations like friction and resistance in walking. McNeill Alexander (2002) reported
based on his experimental observations that we may plan our routes over soft ground and
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over a hill to minimise energy cost. Route choice models such as those developed by
(Daamen et al., 2005), may create clear deep understanding in the route choice problem
by estimating factors are influencing the choice from detecting aggregated passenger flow
in different routes.
We propose in this dissertation a more comprehensive model that attempts to
overcome the limitations of existing models. Details of the proposed model are presented
in Chapter three.
2.1.3 Factors Influencing Route Choice
This section will present existing factors influencing route choice behaviour, of
which walking distance or walking time performed most important.
For traffic in general, pedestrians only enjoy a high degree of movement freedom
even in heavily congested areas. Even though pedestrians move more slowly than
vehicles, they are more aware of and sensitive to their surroundings. Consequently, there
are more alternative links available to pedestrians between a given origin and destination
(Seneviratne and Morrall 1985).
Factors identified from the literature that has been found to influence pedestrian
route selection include:
1. Walking distance. The most straightforward route choice is the shortest
distance. Pedestrians with information choose the shortest route. Many
route choice studies assume that pedestrians always choose the shortest
route to minimise distance and time. Pedestrians select the quickest route,
although they are rarely aware that they minimize distance as a primary
method of route choice (Ciolek, 1978, Seneviratne and Morrall, 1985,
16
Daamen, 2004, AlGadhi, Saad AH and Mahmassani, 1991, Verlander and
Heydecker, 1997, Helbing D., P. Molnár, 2001, (Lsva, 1994).
2. Walking time. This route factor is the estimation of minimizing travel time.
The quickest path is generally considered the most significant route choice
factor, even though the rest of factors cannot be ignored, a significant
number of studies have also found that the shortest distance is not always
the dominant factor (Bovy & E. Stern, 1990, Verlander and Heydecker,
1997). Most of the pedestrians choose the route with the shortest route, but
also that choice may relate to the complexity of routes. Both research
mention that route choice is influenced by more than a simple factor like
time or distance (Seneviratne and Morrall, 1985, Daamen, 2004).
3. Effort. The pedestrian does not only consider the quickest route and shortest
route, but also the effort involves in the vertical dimension in the transport
facilities (over stairs, escalator or climbing a grade), (Daamen and
Hoogendoorn, 2004). Sometimes passengers choose stairs to move upwards
(Cheung and Lam, 1998, Kinsey, Galea and Lawrence, 2009) Energy
expenditure due to walking at a certain speed for a certain period describes
the cost along the trajectory (Hoogendoorn and Bovy, 2005, Cotes and
Meade, 1960).
4. Pleasantness. (Daamen and Hoogendoorn, 2004), (Seneviratne & Morrall
1985a) (Bovy & E. Stern, 1990) as a route becomes more attractive, walking
time, distance and effort become less important factors; but here
crowdedness may be perceived by a ‘tourist’ as an indication of a route’s
potential saliency and in such actually increase its attractiveness. Again, this
is an example where the co-variant congestion has a nonlinear effect on its
17
co-variant that is dependent on the individual pedestrian’s perception (in
this case route attractiveness).
5. Crowding. Is commonly experienced on buses, subways and waiting
platforms (Palma and Lindsey, 2001). Senevirantne & Morrall (1985)
showed that even if the progress on a direct route is relatively slow until
approximately 0.75 of flow capacity is reached, the choice of a longer route
still rarely happens and is considered to be outlier behaviour. While
congestion is touched upon in the crowdedness models it is treated as an
isolated variable, and its notable influence as a co-variate is not captured. It
is shown however to have value as an isolated variable.
6. Familiarity (always use). Pedestrians also choose a route for no apparent
reason. They usually choose the route they have always used, presumably
originally chosen because it was the shortest, or choose the route out of habit
or because they always use it. This is an indication that even unintentionally,
people always tend to minimise their walking distance (Seneviratne and
Morrall, 1985, Saneinejad 2010).
7. Person characteristics, (Bovy & E. Stern, 1990, Seneviratne and Morrall,
1985) showed that the individual passenger takes decisions based on the
purpose of the trip ( Borgers & Timmermans 1986). Gender (Verlander and
Heydecker, 1997), (Seneviratne and Morrall, 1985). The choice of route has
not found to be much influenced by gender. According to (Seneviratne and
Morrall, 1985, Daamen, 2004, (Barbier et al., 2010) most pedestrians of all
age groups considered the quickest route when selecting a route. However,
the proportion of pedestrian route choice follows up to a given factor
changes slightly between the eminent groups of age.
18
2.2 Walking Behaviour
Walking is a means of experiencing and interacting with the environment and
society in a way not possible when using other forms of transportation. In many cases,
the pedestrian may move freely in the space which results in inflows in various directions.
Walking is considered as a most efficient mode of transport for shorter routes as it
requires minimal energy, and costs nothing.
This section defines an overview of the walking behaviour, followed by walking
behaviour models and characteristics. Hughes (2002) describes the optimum walking
route to the given destination (in terms of travel time) as a function of the current point x
of the pedestrian. However, the method excludes many route factors, such as the walking
distance or the environment. Main microscopic variables depend on individual
pedestrians and external conditions, such as trajectories, while the main macroscopic
parameters are speed, density, and flow (Seyfried et al., 2009).
2.2.1 Walking Behavior Models
This subsection describes existing pedestrian walking behaviour models. These
models are listed below:
Microscopic models
Microscopic models for evaluating and describe the individual pedestrian
behaviour. Pedestrian behaviour is defined by a set of rules in an exact situation
on an exact aspect such as route choice behaviour and walking behaviour. Many
microscopic models have been developed that includes the social forces model
(Helbing, Keltsch and Molnár, 1997), Nomad (Hoogendoorn and Bovy, 2005),
and Legion (Still 2000).
19
Cellular automata models
In cellular automata models, both time and space are course- grained. Herein, it is
assumed that particles move in a single direction, stopping and starting depending
on the others particles in front of them (Lachapelle and Wolfram, 2011, Burstedde
et al., 2001).
Queuing models
These models describe how pedestrian moves from one node of the network to
another, where each pedestrian is treated as an individual (Helbing 1997). In
general, these models have used to describe evacuation passenger behaviour from
shopping malls, hospitals, and buildings.
Gas kinetic models
Gas kinetic models describe the dynamics of the velocity distribution functions of
pedestrians in the pedestrian flow. The phase-space density can be considered as
a macroscopic generalisation of the macroscopic traffic density (Daamen and S.
P. Hoogendoorn, 2003).
According to the above, many models have been found in the literature relating to
walking behaviour. On the other hand, only a few of these models can be applied to
pedestrian movement in the transport facilities and train stations.
2.3 Congestion
Congestion is an important concept in pedestrian traffic, which is simply defined as
the state of being overcrowd especially with traffic or people. The number of train
commuters increases every year, an issue that needs to be considered by transport
authorities. Otherwise, increased levels of congestion can cause tremendous economic
loss and train delays (Ivon et al. 2011) as shown in Figure 2.3.
20
In urban transportation systems, a pedestrian congestion phenomenon exists due to
current oversaturated flow state or inefficient use of capacity. The current research on
pedestrian congestion has been focused on congestion pricing, which requires the
optimisation of limited route allocation and routes alternative capacities among travellers
by their need to travel (Celikoglu and Dell’Orco, 2008). Congestion is an important
concept in transport analysis as its presence can change the behaviour of people’s
movement and travel choices. Over time, congestion levels can rise this is particularly the
case when the general demand for train travel rises. This can create significant challenges
for public transport authorities and service providers by potentially causing delays to train
movements, destabilising schedules and ultimately restricting the number of train paths
that might be supported by a rail network (Palma & Lindsey 2001), (Voskamp, 2012).
Congestion has been studied extensively by transportation researchers that occur
when a passenger’s traffic demand exceeds the infrastructure capacity (Bandini et al.
2014, Tajima et al. 2001, Tabuchi 1993). Palma and Lindsey (2001) studied congestion
Figure 2.3: Congestion at the Brisbane Central Rail Train Station
21
that imposes a wide range of problem on passengers like delay in travel time, rescheduling
train, and crowded confusion. Delays in passenger travel are a paramount component of
people congestion on platforms and trains, and hence it is highly important to measure
the precise cost of travel time, which is known as the Value of Time. Congestions in train
travel invoke unpleasant experiences for the passengers mainly because of pushing and
shoving (Souza. 2010, Baumberger. 1986, Bertrand. 1978, Palma and Lindsey. 2001).
Lachapelle and Wolfram (2011) presented an approach to model crowd motion. It
is called mean field games (MFG). This model differentiates itself from other models
mainly in the combination of two points and treats the pedestrians as real individuals who
have preferences and strategical interactions within the crowd.
Voskamp, (2012) presented a practical method of measuring the influence of
bottlenecks on route choice behaviour from combining Bluetooth and CCB tools and
measurement of video to provide more precise peak time estimation of the congestion
occurrence.
2.3.1 Influence of Congestion Occurrence on Route Choice
In assessing transport facility design, it is important to predict the routes taken by
the passengers effectively, since it is one of the key factors affecting the occurrence of
congestion. Route choice is defined as the process by which a passenger chooses amongst
path alternatives of infrastructure within a station. Typically, these stations are
intentionality designed with limited path alternatives and information systems present
wayfinding to direct egress. Nevertheless, personal preferences and perceptions cause
egress to fluctuate at these path alternatives and lead to the subsequent egress cascade.
22
There is a need for a descriptive model for planning that captures these aspects; a model
that can describe this real-world route choice behaviour.
Every year the cost of congestion increases and so too does the number of
commuters depending on train travel. For that, we need to improve our knowledge of
factors influencing passenger route choice behaviour and focus on the route choice
process and influencing factors both from environmental and social aspects. Typically,
passenger research focuses on factors that may affect the route choice of a passenger,
which are related to the passenger, the environment, travel time, or a combination thereof
and forego the including social influencing factors, or treat them as isolated variables
rather than integrated co-variant (Al-widyan F, Kirchner N, Zeibots M, 2015).
In this research, the factors that involve congestion are studied, and their influence
on passenger route choice is analysed. The research motive is addressed by empirical
observations of revealed choices of train users under varying conditions concerning route
choice factors, especially types of route alternatives (stairs, and escalators).
The factors identified from the literature that influences a passenger route
selection are summarised in subsection 2.2.3. If congestion is included, it is typically
considered crowdedness and treated somewhat like an independent variable. However,
the influencing social factor of congestion is a co-variant with these factors; and as such
its potential effect is significant but perhaps non-obvious (non-linear). The modelling
complexity of treating congestion as a co-variant arises from interpersonal differences
that drive perception – different passengers will potentially have different levels of
congestion at which significant influence on their route selection occurs.
Consider approaching a particular egress point around the station. Crowdedness
may have a relatively less influencing effect in the typically busy concourse where
passengers’ perception of this will tamper with factors such as ‘of course it is busy here’.
23
Conversely, it may have a relatively larger effect on the typical quieter platform and
perception may align more with ‘why is everyone standing in the same spot?’. Finally,
the associated threshold level of route selection due to congestion for each passenger is a
personal perception.
More specifically, when considering walking distance (Ciolek, 1978)
(Seneviratne & Morrall 1985a) passengers tend to choose the shortest route, although
they are infrequently aware that they are minimising distance as a primary strategy in
route choice. Figure 2.4 shows two paths options: Fig. 2.4 a) without a point of
congestion, and Fig. 2.4 b) with a point of congestion. Referring to Fig 2.4a), using the
shortest distance approach probably the passenger will choose path 1. However, if we
consider congestion Fig. 2.4b), it’s reasonable that at least some passengers, due to their
personal perceptions of congestion, will choose path 2. Clearly here congestion is a co-
variant, this model would benefit from the inclusion of congestion at the time of decision.
Likewise, walking time (Cheung and Lam. 1998, Daamen et al., 2005) where passengers
choose the path with the shortest length, but congestion on this path will probably change
the time it takes. This effect of retarding passenger is likely to vary considerably between
passengers.
For instance, a ‘footballer’ may push straight through the congestion with no
retardation whereas an ‘old lady’ may be severely retarded by the crowd. The key point
is that these individual passengers will have an awareness and appreciation of this prior
to the route selection point. In other words, the perception of crowdedness will weigh
differently for each passenger irrespectively of whether their underlying route selection
is based on the same factor (shortest time in this example).
24
a. Route choice without congestion
b. Route choice with congestion
This interplay between typically modelled factors and an individual’s perception
of the repercussion of congestion on their decision factors is apparent also in effort driven
models. Effort models tend to discriminate between path selections using a measure of
physical work required, such as that involved in climbing a grade or terrain versus
traversing flat terrain (Daamen and Hoogendoorn, 2004, Cheung and Lam, 1998, B.
Givoni 1971).
Congestion again is a notable co-variant with the derivation of a path’s effort.
For example, referring to Figure 2.5, if a hundred people are walking faster than you and
in the same direction as your intended travel, Figure 2.5a, then this would result in you
walk faster and effectually reduce the perceived effort of that path. Conversely, if a
hundred people are walking considerably slower than you or perhaps in less uniform
Figure 2.4: Comparison between two routes (with and without congestion)
25
direction; than your perception of required effort to traverse this path would likely
increase, Figure 2.5b). In both cases, the crowdedness will be the same, and hence, a
description of the crowd behaviour and the potential resulting perception actions of
surrounding passengers must be modelled to describe this. Accordingly, the same number
of people doing the same behaviour could consume a different amount of effort depending
on their behaviour, as shown in Figure 2.5. The distance from the origin to destination
does not change, the congestion is the same, but the time will change. Thus, congestion
is not only related to the number of people but also to their behaviour and how this
behaviour interacts with the other variables of the model.
a. Passengers walking the same direction
b. Passengers walking opposite or random direction
Figure 2.5: Illustration of key direction of moving congestion
26
Pleasantness or route attractiveness make walking time and distance less
important factors (Daamen and Hoogendoorn, 2004, Seneviratne & Morrall 1985a); Also,
crowdedness may be perceived by a tourist’ as an indication of a route’s potential saliency
and in such case increases its attractiveness. Again, this is an example where the co-
variant congestion has a non-linear effect on its co-variant that is dependent on the
individual passenger’s perception (in this case route attractiveness).
Crowding is commonly experienced on buses, subways and waiting platforms
(Palma and Lindsey, 2001). While congestion is touched upon in the crowdedness models
such as (Seneviratne and Morrall, 1985), it is treated as an isolated variable, and its
notable influence as a co-variate is not captured. It is shown however to have value as an
isolated variable. (Seneviratne and Morrall, 1985) showed that even if the progress on a
direct route is relatively slow (until reached approximately ¾ of flow capacity), still the
choice for a longer route is rarely happened and considers these to be outliers.
This result is indicative of the current trend in modelling towards group
modelling. Clearly, congestion is significant for route choice and can be considered as an
individual specific co-variant for key group factors such as walking distance, walking
time, or route attractiveness.
This work does not argue these models’ usefulness; rather this research suggests
that the outliers often discarded by the group were focused models can be modelled by
introducing an individual specific co-variant to interplay with these crowd generalised
variants.
One of the under-investigated factors in route choice research is the consumed
effort. As indicated in the literature, route choice models are inherently limited in that
they focus on shortest distance and minimum time whereas, in reality, other variants are
likely to exist. There is a need for a more comprehensive model that can describe
27
pedestrian route choice based on foreseeable variants such physical effort that pedestrians
may consume during their travel from origin to destination.
Two approaches can be followed to model pedestrian route choice problem
(PRC): deterministic or probabilistic. In this research, we follow the deterministic
approach, which assumes that the perceived utility of a route is deterministic and that
pedestrians will only choose the route that has minimum average cost. On the other hand,
probabilistic choice models assume that the perceived utility of a route is stochastic, and
express the probability that pedestrians will choose each of the available alternatives
(Borgers and Timmermans 1986).
Researchers proposed many different modelling approaches: microscopic versus
macroscopic description, deterministic versus stochastic, and discrete versus
continuous. In deterministic models, the output of the model is fully determined by the
parameter values and the initial conditions. On the other hand, stochastic models
possess some inherent randomness. The same set of parameter values and initial
conditions will lead to an ensemble of different outputs. Obviously, the natural world be
faced with stochastic. However, stochastic models are considerably more complicated.
Deterministic models provide a useful approximation to great effect on the real-world
process that is truly stochastic (Cascetta, 2009). Researchers proposed many different
modelling approaches: microscopic versus macroscopic description, deterministic
versus stochastic, and discrete versus continuous.
We propose in this research a more comprehensive model that incorporates the
route surface and surrounding into a newly proposed energy formulation. The model
represents the effort that pedestrians will put in when walking on different surfaces and
surrounding as a cost that is added to the energy function.
28
2.3.2 Pedestrian Bottleneck
When assessing the design of transport facilities, it is important to be able to
anticipate the attributes of pedestrian movement to the configuration of passable open
spaces and their visibility caused by the urban layout. The term configuration refers to
the way every space in the environment relates to every other (Hillier et al., 1993).
A bottleneck, as a physical condition that results in a reduction of the transport
facilities, is a result of a specific physical condition at public transport facilities, often
caused by the design of the station or badly timed pedestrian travel. They can also be
caused by temporary situations, such as an escalator entrance, narrow corridors or gates.
Bottlenecks impose a wide range of problems for passengers especially at escalator entry
in train stations. These problems include a delay in travel time, rescheduling train, and
unhappy experiences for passengers mainly because of pushing and shoving (Palma and
Lindsey, 2001). The ability to influence the movement of people could reduce collisions
on blind corners, or increase the efficiency of passenger flow through bottlenecks such as
passageways, stairs and escalator (Kirchner et al., 2015).
Congestion starts when a passenger’s demand exceeds the station infrastructure
capacity and has been studied extensively by transportation researchers (Bandini et al.
2014, Tajima et al. 2001, Tabuchi 1993). Bottleneck capacity is determined by some
factors, such as a wall surface, a width of the bottleneck, and interaction behaviour of
passengers walking through the bottleneck (Hoogendoorn and Daamen, 2005).
Capacity is certainly important in the design of the area around the escalator and
has a significant impact on the escalator performance. Lower passenger densities are
desirable in uncongested environments so that passengers may manoeuvre and pass each
other to maintain their desired speed (Kauffmann and Kikuchi, 2013). Conversely, in
congested environments, it is important to provide adequate queuing space under crush
29
loading conditions like train arrivals or emergency evacuations so that passenger safety
is assured.
Queues are developed when the arrival rate of passengers at the escalator entry
exceeds its capacity (Kauffmann and Kikuchi, 2013). For that, we need to improve our
knowledge of the escalator entry bottleneck and its influence on passenger selection
behaviour. Some empirical studies have been carried out on bottlenecks and focused on
the behaviour of passengers in a narrow bottleneck experiment (Shiwakoti1 et al. 2015,
Cepolina & Tyler. 2005, Fosgerau & de Palma. 2012, Davis & Dutta. 2002, Kinsey et al.
2014, Arnott et al. 1990, Laval and Daganzo, 2006). However, to our knowledge, none
of these empirical studies provides any data about the escalator entry bottleneck
phenomena, which is discussed in this research.
Most available research focuses on the relation between capacity and bottlenecks.
This issue is important to understand and monitor for passenger traffic management
(Seyfried et al., 2009), where there is a change in size of escalator which might give rise
to a change in capacity, and involve congestion with the influence on passenger route
choice, in instance train stations and emergency exits (Braid 1989, Fosgerau & de Palma
2012, Yang & Hai-Jun 1997, Still 2000, Hoogendoorn & Daamen 2005). Meanwhile, the
core of this research is to create a model of route choice behaviour on the escalator entry
bottleneck.
2.4 Principle of Least Effort
Modelling a human behaviour is a difficult task and models are often simplified
due to this difficulty as Zipf (1951) argued. To fill the gap between psychology and
physiology are often associated resulting in route choice models. Several modelling
30
techniques were presented by Timmermans (Borgers & Timmermans 1986a). It is
observed that people take routes that involve least efforts to reach their targets. This
observation has been later known as the principle of least effort (PLE) (Zipf 1951), which
explains and justifies the individual behaviours of human beings. This phenomenon has
been applied in many engineering applications that include passenger movements and
route selection. It assumes a general law ingrained in human brains, often referred to as a
psychological force that could be summarised as the law of the least effort where a person
will choose the option that can perform the task with the least effort. This has been
explored by several researchers (Silder, Besier and L, 2012, Guo and Hall, 2011, Guy S,
Chhugani J, Curtis S, Dubey P, Lin M, 2010, McNeill Alexander, 2002).
Some researchers have proposed the distance travelled as an indicator of the
effort. However, this indicator does not account for walking speed. Few other researchers
have proposed an effort metric — the time to reach the target destination. However, this
approach does not consider the optimal route and assumes individuals will walk at their
maximum speed. Others have suggested metabolic energy as a metric for effort
(Vieilledent et al., 2001, Guy S et al., 2010).
A human being movement is a complex process, involving psychological,
behavioural, crowd characteristics, and environmental characteristics. However, it has
long been observed that people tend to utilise a path of least effort, as shown below in
Figure 2.6.
31
Humans may walk in curved lines, creating paths around obstacles. We
understand that the shortest distance between two points is a straight line, but human
behaviour shows that this is not always the case. Obstacles, terrain, and weather are
important factors that guide human behaviour. They noticed that over time, even with a
designated route, a path that fits natural human behaviour could be created, e.g., paths
across streets and between bushes.
When walking freely, humans show some general characteristics (Kramer and
Sylvester, 2011):
Walking process is objectively-oriented. That is a person starts to form a
starting point and aims to reach a goal destination.
Travel time needed is not specified a priori.
Tends to perform the task with the least effort.
Prefers to select paths with reasonable path length.
Figure 2.6: Human beings utilise a path of least effort
32
Controls both direction and velocity.
Prefers a smooth motion, i.e., avoids an abrupt change in position, velocity,
and acceleration.
2.4.1 Metabolic Energy
Metabolic energy is defined as the energy cost of human locomotion, which can
be estimated from oxygen consumption. The metabolic energy common uses a proxy of
metabolic function that is the volumetric rate of oxygen consumption (VO2), which serves
as an estimate of ongoing cellular respiration and thus the bodies’ use of energy. At this
time, metabolic energy consumption approaches to the study of locomotors energy
expenditure are inherently empirical, and they employ statistical techniques to predict the
dependent variable oxygen consumption from independent covariates (Zipf, 1951),
(Cotes and Meade, 1960).
The metabolic rate of a fully activated muscle depends on the rate of shortening.
The metabolic rate is higher when the muscle is shortened, doing work, than when it is
isometrically contracted. Prefer to walk at speed close to the velocity of 1.4 m/s at which
the energy cost per unit distance is least. The speed threshold between walking and
running is about 2 m/s, where below this speed walking requires less energy than running,
while above 2 m/s running uses less energy than walking (McNeill Alexander 2002),
Kramer & Sylvester (2011).
In another study, Ralston (1958) developed a mathematical relationship between
energy expenditure and speed which is useful in the sense that it is simple and of
suggestive physical form. During level walking, the energy expenditure is a linear
function of the square of the speed. The relation is,
w = 29 + 0.0053V2
33
where Ew is energy expenditure in Cal/min/kg, and V is speed in meter/min
(calculate energy expenditure in term of distance walked)
Guy et al., (2010) present a mathematical model for representing effort expended
by each agent, based on a biomechanical formulation that minimises the total amount of
metabolic energy used when travelling on a trajectory to the goal. By measuring the
oxygen consumed, the instantaneous power (P) spent by a walking object can be modelled
as a function of the underlying speed.
P= es+ ew|v|2
where v is the instantaneous velocity, and es (measured in J/Kg/s) and ew
(measured in Js/Kg/m2) are per-agent constants.
The energy expenditure of walking may vary between individuals and also vary
for a given individual depending on some factors. Pandolf, Givoni, and Goldman (1976)
conducted a series of laboratory experiments to measure the metabolic rate (M) which
was measured during treadmill walking at different speeds and grades when carrying
different loads. An empirical predictive formula was derived for a metabolic rate as a
function of these factors.
M = 1.5W + 2.0(W + L) LW + (W + L)[1.5V + 0.35 VG]where M: metabolic rate in watts; W: subject weight in kg; L: load carried in kg,
V: speed of walking in m /s; G: grade in %, : terrain factor = 1.0 for the treadmill.
Because pedestrians move with numerous features in the physical and social
environment, an empirical equation was proposed for the prediction of the metabolic
energy costs of such activities (Givoni, 1971). The equation was examined and found to
be valid for walking speeds from 2.5 to 9 km/hr with grades up to 25 % and running
speeds from 8 to 17 km/hr with grades up to 10% with loads up to 70 kg.M = (W + L) 2.3 + 0.32 ( (V 2.5) . ) + G 0.2 + 0.07 (V 2.5)
34
A summary and a difference of metabolic energy formulas proposed in the
literature are included in Table 2.1.
Table 2.1: Summary of metabolic energy formula proposed in the literatureResearchers Formula Comments H.J.Ralston (1958) w = 29 + 0.0053V2 No consideration of the
impact of other parameters (weight, surface friction, terrain, grade)
Guy S et al., (2010) P= 2.23+ 1.26|V|2
B Givoni (1971) M = (W + L) 2.3+ 0.32 ( (V 2.5) . )+ G 0.2+ 0.07 (V 2.5) i. Valid for walking
speeds from 2.5 to 9 km/hr with grades to 25% and loads up to 70kg.
ii. Is not valid for standstill level
Researchers from the different backgrounds have tackled this problem from
numerous viewpoints and aspects. Several criteria have been proposed in the literature
for predicting the shape of walking human trajectories (Burgess, 1983). Indeed, some
researchers proposed the principle of minimum time (Vaziri et al., 1983); others
suggested the principle of minimum path length (Verlander and Heydecker, 1997). Some
researchers reported that not only do individuals generally choose a walking speed that
requires the least energy to travel a given distance (Ganem, 1998), but over the usual
range of walking speeds people also choose gait rates that minimise the rate of metabolic
energy expenditure (Zarrugh, Todd and Ralston, 1974).
A number of authors (Radcliffe, 1978), (Cotes and Meade, 1960), (B Givoni,
1971), (Farris and Sawicki, no date), (Holt, Hamill and Andres, 1991), (Kramer and
Sylvester, 2011), (Pandolf, Givoni, Goldman 1976), (Silder, Besier and L, 2012),
(Zarrugh, Todd and Ralston, 1974) to mention just a few have discussed the energy
expenditure per unit distance during walking, which was usually expressed as a function
of walking speed, step length and step rate. When people can adapt their step rate for a
35
given speed, they unconsciously select a unique step rate requiring the least energy
expenditure for the imposed speed.
Cheung & Lam (1998) found that the pedestrians are more sensitive to the relative
delays when using the vertical pedestrian facilities in a descending direction than in an
ascending one direction and reported an investigation on the behaviour of pedestrians in
choosing between escalators and stairways in Hong Kong mass transit railway stations
during peak hours.
2.5 Conclusions
The important finding of Chapter 2, is that a few of these models can be applied
to pedestrian movement, and model route choice behaviour in the transport facilities and
train stations. There is various factors effect pedestrian route choice, which is related to
the pedestrian, such as the environment around the individual, walking time, walking
distance, and effort consumption or a combination of all of these. Literature quantifying
congestion is just one of the factors associated with travel time to influence route choice
behaviour.
The aim of route choice modelling is to determine the entire route from a
pedestrian’s current position to the destination. Most researchers have formulated the
problem at stake as an optimisation problem while considering a single objective among
the ones mentioned above. However, a passenger usually makes a decision while
accounting for many aspects, by simultaneously evaluating the trade-off between many
objectives. In this work, we adopt the metabolic energy as a metric for the effort with a
more general formula accounting for many factors; the work presented in the dissertation
is to go beyond the objectives of the earlier research work and present a more focused
solution towards the route choice problem.
36
Chapter 3
Effort-Based Theoretical Framework for Pedestrian Route Choice
In this chapter, we present an effort-based framework where we evaluate the cost
of the pedestrian route between two points in space with different constraints. We justify
a choice made by comparing the cost in terms of metabolic energy. The environment
comprises of route alternatives such as escalator vs stairs.
As mentioned in Section 2.1, route choice is a critical theoretical and practical
problem for practitioners working in the field of pedestrian behaviour modelling. A key
challenge for researchers is to identify criteria or discover principles that pedestrians use
when selecting their walking routes. The number of possible routes between two given
destinations is, in theory, infinite. That is, among all admissible routes, people generally
prefer to select one specific route that we will here call the optimal route. Consequently,
there is scope for the development of a theoretical framework and models that describe
route choice.
It is essential to understand pedestrian route choice behaviour under normal
conditions before modelling pedestrian route choice in case of congestion. This research
puts forward a new formulation for the pedestrian route choice that uses the concept of
physical effort. The fundamental assumption is that pedestrians follow a route where a
set of criteria are optimised. These criteria can be time, distance or physical effort.
According to the literature, the two most common criteria are related to walking distance
and walking time. Here we adopt physical effort as a general criterion and formulate it
using a pedestrian’s metabolic energy expenditure.
37
The problem of pedestrian route choice (PRC) is of central importance to
pedestrian models used in the fields of transportation planning and engineering. PRC is a
complex activity that has psychological, behavioural and environmental dimensions that
potentially open it up to different interpretations, approaches and levels of sophistication.
Borgers & Timmermans (1986) formulated a model that describes PRC within an
inner-city shopping area. Cheung & Lam (1998) investigated PRC in relation to choices
between an escalator and set of stairs located in Hong Kong MTR stations where the
travel time functions for the escalator and stairs are assumed to form an important factor
in determining the split between the two. A model by Hughes (2000) contended that
pedestrians seek to minimise their travel time, but temper this behaviour to avoid
extremely high densities of pedestrians or congestion, and in the process highlights how
the psychological disposition of pedestrians can change behaviour. Hoogendoorn & Bovy
(2004) developed a model where pedestrians schedule their activities, the activity area,
and the paths between the activities simultaneously to maximise the utility of their effort
and walking.
In fact, some of the existing route choice models are based on the minimum
distance; that is, pedestrians tend to choose the shortest route (Ciolek 1978, Hewawasam
2013). Helbing and Molnár (2001) pointed out that pedestrians prefer the shortest route
even if that route is crowded. Similarly, Hill (1982) reported that the most influential
factor in PRC is the minimization of the distance travelled. Golledge (1997) found that
PRC based on shortest distance received the highest rating in empirical studies. Liu et al.
(2010) pointed out that a pedestrian walk from origin to destination moves in a straight
line.
Seneviratne & Morrall (1985) shown that pedestrians choose their routes to
minimise travel times from origin to destination, which often tends to be the shortest
38
routes. It has also been observed that people select routes that involve the least effort to
achieve their targets (Stephen et al. 2010), (Pinto & Keitt 2009), (Daamen 2004).
Zipf (1951) referred to this observation as the Principle of Least Effort (PLE) and
claimed that it explained key features of human movement and pedestrian behaviour in
general. This phenomenon has been incorporated into many engineering applications that
include pedestrian walking. More recently, several researchers have attempted to apply
the PLE to PRC problem (Al-widyan et al. 2015, Silder et al. 2012). The model proposed
by Guy et al. (2010) is relatively simple and does not incorporate many real
considerations like friction and resistance in walking. McNeill Alexander (2002) based
on his experimental observations, reported that people might select routes over a soft
ground for example or surface with various gradients to minimise energy cost.
In this work, we propose a more comprehensive model that incorporates route
surface and surrounding, weight, surface friction, and grade in estimating the amount
of physical effort required to move between two points.
Pedestrians choose among routes depending on their route cost that is determined
by factors such as time, distance travelled, and potentially physical effort expanded to
traverse the route. The physical effort has a cost in the real world, and so we have devised
a formula capable of encapsulating this. As indicated in the literature, most route choice
models are limited in that most focus on shortest distance and minimum time whereas
other factors also impact on PRC. There is a need for a more comprehensive model that
can describe PRC based on foreseeable variants such physical effort that pedestrians
expend during their travel from origin to destination.
39
3.1 Problem Statement
In principle, pedestrians usually move freely in their environment to choose a
route from an infinite set of alternatives, as shown in Figure 3.1. However, among all
admissible routes, people generally prefer to select one preferable route that we will call
the optimum route. We call it optimum as it minimizes certain quantities such as time
and/or distance. A route is the trajectory of a pedestrian that starts at the origin and ends
at a destination. A pedestrian trajectory is usually obtained by recording their coordinates
at each time step and finally connecting all the points.
The main behavioural assumption is that all movement of the pedestrian, let it be
performing an activity or walking along a certain route, will provide utility (or
equivalently, induce cost) to him. The pedestrian will predict and optimize this expected
cost, taking into account the environmental conditions. It is well known that normative
choice theory will not fully cover real-life human choice behaviour. It does, however,
offer a convenient framework for modelling human decision making (Van Berkum and
Van Der Mede, 1993). Moreover, several empirical studies have shown the applicability
of cost-based approaches to pedestrian route choice (Hill, 1982, Bovy and Stern, 1990).
The route a pedestrian takes should be a sufficiently smooth function of time, and
it should respect any environmental limits or constraints to avoid obstacles. Here, we
consider the route as a combination of paths, a purely geometric description of a sequence
of configurations achieved by the pedestrian, and a time scale that specifies the times
when these configurations are reached.
40
The location of a pedestrian, at any time t, can be described by a pair of coordinates ( ) and ( ) that define the position vector , namely:
( ) = ( )( ) (3.1)
The instance velocity ( ) of a pedestrian is defined as the time derivative of their
position vector (Hibbeler, 2010), that is:= = ( ) (3.2)
which can be written using Eq. (3.1) as
= ( )( ) (3.3a)
whose magnitude can be expressed as:
Figure 3.1 Possible routes between two destinations
41
= = + (3.3b)
where is the magnitude of vthe elocity , and is an infinitesimal distance
travelled along the route chosen as indicated in Figure 3.2.
The problem of PRC can be stated as: find a route, described by the set of two-
time dependents variable, {( ( ), ( ))}, that a pedestrian traces while travelling from
point A (the origin), specified by the coordinates ( , ), to point B (the destination),
specified likewise by the coordinates( , ), as shown in Figure 3.2.
Figure 3.2: Route Description
42
3.2 Effort-Based Formulation of PRC Problem
As mentioned before, a pedestrian tends to minimize the physical effort expended
over their chosen walking route. Hence, the problem of PRC is to find the route followed
by a pedestrian to minimize the effort . That is the PRC problem can then be stated
formally as: find ( ) and ( ) that:
min{ ( ) ( )} ( ( ), ( )) (3.4a)
subject to geometric constraints:
( , ) = 0 (3.4b)
with the initial and final conditions:
( ) = , ( ) = , = , = (3.4c)
It is worth mentioning that, the geometry constraint ( , ) = 0 represents
environmental constraints such as physical obstacles.
The above optimization problem can be solved by resorting to the calculus of
variations (I. M. Gelfand, 1963), which is a field of mathematical analysis that deals with
maximizing or minimizing definite integrals involving functions and their derivatives.
Resorting to experimental data and literature (Zarrugh, Todd and Ralston, 1974), (Cotes
and Meade 1960), it is reported that the relationship between the metabolic power P and
the walking instant speed takes the general functional form:
= ( ) = ( , ) (3.5)
Now recalling that the power is the time rate of the energy, that is:
= = (3.6)
Accordingly, we can write:
= ( ) (3.7)
43
Upon integrating both sides of the above equation from initial time 0 to final time
f, we can obtain the corresponding consumed metabolic energy consumed while
moving along a route starting from the initial point ( 0, 0) to the destination ( f, f),
namely:
= ( ) = ( , ) (3.8)
Then Eq.(3.4a) reduces to
( ) ( ) ( , ) (3.9)
3.2.1 The Euler-Lagrange Equations
The conditions that the solution of the optimization problem (3.9) should satisfy
differential equations known as Euler-Lagrange equations with constraints (Morse, P. M.
and Feshbach, 1953), which can be stated as:
For x-coordinate,
= , ( ) = , = (3.10)
For y-coordinate,
where is the Lagrange multiplier (Zwillinger D, 2003).
= , ( ) = , = (3.11)
44
Apparently, from Eq. (3.5), P = ( , ) is a function of and not of x and
y. This means that the partial derivatives of P with respect to x and y vanish, i.e.:
, = = 0 (3.12)
Hence, Eqs. (3.10& 3.11) can be simplified to:
= , ( ) = , = (3.13)
and
= , ( ) = , = (3.14)
3.2.2 Constraint -Free Pedestrian Walk
Now we consider a very common case of a quadratic form of power with
constraint-free conditions. The quadratic form of metabolic power as reported in the
literature (Morse, P. M. and Feshbach, 1953) can be expressed as:
= ( ) = + + (3.15a)
with coefficients A, B and C evaluated:
= 1.5 ( + ) (3.15b) = 0.35 ( + ) (3.15c)
= 1.5 + 2( + )( / ) (3.15d)
where denotes the walking speed (m/s), X the external load (kg. m/s2), W the individual
weight (kg. m/s2), G the grade (%), and the terrain and surrounding factor defined as 1
for free walking.
More specifically, = = 0 and hence, Eqs. (3.13&3.14) can be reduced to:
= 0, ( ) = , = (3.16)
and
45
= 0, ( ) = , = (3.17)
Upon integrating over time, the above two equations turn out to be of the form:
= (3.18)
and
= (3.19)
where and are constants that will be determined from the initial conditions.
Figure 3.3 shows the characteristics curve of power P, per unit weight, versus
speed for a special case of walking where the walking surface is flat (G=0), there is no
external load (X=0), and the terrain enables unrestricted walking = 1.
Figure 3.3: A Characteristic curve of power P
46
The expression of the total metabolic energy consumed of Eq. (3.8) can be
written considering Eq. (3.15a) as:
= ( + + ) (3.20)
It is more convenient to express P and E in terms of route variable derivatives
and ,
( , ) = ( + ) + + + (3.21)
Then ( , ) = ( , )
= ( + ) + + + (3.22)
Evaluating the relevant derivatives and using Eq. (3.21), we obtain:
= 2 + + (3.23)
and
= 2 + + (3.24)
Hence,
2 + + = (3.25)
After simplifications, 2 + + 2 = + (3.26)
Similarly, for
47
2 + + = (3.27)
after simplifications,
2 + + 2 = + (3.28)
After manipulating, the above two equations, we obtain:
(2 + + 2 ) = + (3.29)
and
(2 + + 2 ) = + (3.30)
Dividing the above two equations by each other, we obtain:
= = (3.31)
or
= (3.32)
which leads to
= + (3.33)
This represents the straight line equation describing the path followed by a
pedestrian from the initial destination ( 0, 0) to destination ( f, f).Substituting the initial and final conditions of Eqs. (3.16& 3.17) into Eq. (3.34), we
obtain:
( ) = ( ) + (3.34)
and ( ) = ( ) + (3.35)
Figure 3.4: shows the time history of the coordinates ( ) ( ).
48
The pedestrian speed, in this case, can be evaluated using Eqs. (3.34& 3.35),
= + = + (3.36)
It is apparent that the pedestrian speed calculated in the equation above is simply the
travelled distance between the origin and final destination divided by the time taken.
3.3 Evaluation of the Proposed Effort Formulation; Climbing Stairs vs
Riding Escalator
The metabolic energy expenditure of walking on a flat surface, climbing stairs
and riding escalator, as shown in Figure 3.5 will be calculated as follows.
Figure 3.4: Trajectories x(t) andy(t)
49
P = Av2 + B v + C
E= (Av2 + B v + C) * T
B =
C = 1.5W + 2(W + L) (L/W) 2
General assumption
W=80 kg
L= 10 kg
Riding escalators
Assumptions:
Vescalator = 0.7 m/s
Lescalator = 15.6 m
Vpedestrian/escalator =0 (pedestrian does not walk over the escalator)
Figure 3.5: Route choice between the platform and concourse
50
Calculations:
A=B=0 (as velocity of pedestrian=0, pedestrian stand over the escalator not walking)
C= 1.5*80=120
Tescalator= L esc/ V esc= 15.6/0.7=22.28 sec
Pescalator= C= 120 watt
Eescalator=C* T esc= 120* T esc =2674.28 joule
Climbing stairs
Assumption:
Vstairs= 1 m/s (comfort velocity for climbing)
Lstairs= 15.6 m
= 2
G= 57 %
Calculations:
A = 1.5*2 (80 + 10) = 270
B = 0.35*0.57*2 (80 + 10) = 35.91
C = 1.5*80 + 2(80 + 10) (10/80) 2=122.81
Tstairs=Lstairs/Vstairs=15.6/1=15.6
Pstairs = 270(1)2 + 35.91(1) +122.81= 428.72 watt
Estairs =6688.03 Joule
Table 3.1: Route Cost in terms of Length, Time and Effort without considering the congestion
Selection Length, L (m) Time, T (sec) Effort, E (J) Comments
Escalator 15.6 22.28 2674.28 E escalator/E stairs =
39%Stairs 15.6 15.60 6688.03
51
In general, the energy expenditure of passengers of walking up escalator is 39%
of that consumed by a passenger using stairs.
3.4 Evaluation of the Proposed Effort Formulation; Escalator with
Different Levels of Congestion
Below are the calculations of the metabolic energy expenditure of riding the
escalator with three different congestion levels; no congestion, medium congestion and
high congestion, we assigned values of 1,3 and 10 to the terrain and surrounding
parameter ( ) (Richmond and Army, 2015) to represent those three levels of congestion
Case 1: Origin – point B, case of
Consider v=1.34 m/s, and no grade G=0
A = 1.5*1 (80 + 10) = 135
B = 0, G=0
C = 1.5*80 + 2(80 + 10) (10/80) 2=122.81
T O-B=L O-B / V O-B = 3/1.34 = 2.24 sec
P O-B = 135(1.34)2 + 122.81= 365.22 watt
E O-B =818.08 Case 2: Origin – point B,
Consider =3, v=1 m/s, and no grade G=0
A = 1.5*3 (80 + 10) = 405
B = 0, G=0
C = 1.5*80 + 2(80 + 10) (10/80) 2=122.81
T O-B=L O-B / V O-B = 3/1= 3 sec
P O-B = 405(1)2 + 122.81= 527.81 watt
52
E O-B =1583.43 Case 3: Origin – point B,
Consider =10, v=0.7 m/s, and no grade G=0
A = 1.5*10 (80 + 10) = 1350
B = 0, G=0
C = 1.5*80 + 2(80 + 10) (10/80) 2=122.81
T O-B=L O-B / V O-B = 3/0.7= 4.285 sec
P O-B = 1350 (0.7)2 + 122.81= 784.31 watt
E O-B =3360.76 .
The congestion at the base of the escalator varies with each batch and during the
time that the patches approach the escalator. Congestion is only observed at the escalator
for a limited time at peak hours. The severity of congestion is assessed from the different
shown in Table 3.2. Analysis of origin-destination relations
shows that the congestion on an escalator has a significantly different influence on
pedestrian route choice.
Table 3.2: Route O-B with different terrain and velocities in congested infrastructure.
Origin- BRoute
Low Congestion Medium Congestion High Congestion
1 3 10
Velocity, m/s 1.34 1 0.7
Effort, E (J) 818.08 1583.43 3360.76
53
3.5 Conclusions
The energy expenditure of walking may vary between individuals and vary for a
given individual. The energy expenditure depends on several factors that include body
weight, external weight, walking velocity, type of surface and surrounding, and the grade.
Ideally, prediction of energy expenditure should encompass the entire range of walking
speeds from standing. The upper limit for walking speed has been shown to be
approximately 2 m/s. At greater walking speeds, the efficiency of walking becomes lower
than running (McNeill A, 2002). On the other hand, it was reported in the literature that
the lower limits for walking are approximately 0.7 m/s.
The fundamental concept of physical effort expended by a pedestrian over a route
choice is used in this chapter and applied to solve the PRC problem. For predicting a route
choice, the minimum physical effort potentially offers a route choice option that is
different from that of the shortest or quickest routes. It is demonstrated that physical effort
has a cost in the real world that can be incorporated in pedestrian route choice models.
One main contribution of the work presented in this chapter is a new mathematical
formulation for solving the PRC problem utilising the concept of physical effort that
pedestrians expend during their travel between destinations in different cases and
infrastructure. This effort can be represented using metabolic energy expenditure of
walking, which can be viewed as a criterion or a cost function associated with the route.
Furthermore, we have devised a formulation capable of encapsulating this
complex interplay utilising the principle of least effort and congestion occurrence. We
considered two examples to evaluate the proposed effort formulation. In the first example,
we compared the effort of climbing stairs and riding escalators. The second example
estimates effort for three different levels of congestion. Both examples produced realistic
results, and hence, the proposed formulation will be further validated in Chapter 5.
54
Chapter 4
Comparison between Different Criteria for Pedestrian Route Choice
In this chapter, we use the evaluation framework from the previous chapter to find
the effort-optimal path for pedestrians travelling between two locations of interest. We
formally define how constraints such as an escalator and congestion affect the energy
consumed by a pedestrian and integrate the constraints to find the solution that has the
minimal energy consumption. In this work, we show that the path with the minimal energy
consumption is the path that a pedestrian is likely to take.
Existing route choice models, as mentioned in Chapter 2, are mainly based on the
shortest distance, minimum time criteria or a combination of both. As explained in Chapter
3, we adopt in this dissertation the concept of physical effort and propose a new
formulation for it. In this chapter, we conduct a comparison between the three criteria of
distance, time and effort.
4.1 Route Cost in Terms of Distance, Time and Physical Effort
Traditionally, route choice has been assumed to be the result of minimizing
quantities or costs such as travelled distance, the time taken or effort consumed. To
determine what would be an effective route choice criterion, we have undertaken an
evaluation of PRC, as little research has been reported on comparing different costs (Al-
widyan et al. 2017).
55
4.1.1 Route Cost in Terms of Distance
In order to find the shortest path between points A and B, we need to minimise the
functional L with respect to small variations in the function y(x), subject to the constraint
that the endpoints, A and B, remain fixed to see Figure 4.1
The route selection criteria described in this section is based on shortest route (in
terms of distance). Specifically, the length of a route can be expressed as:
= (4.1)
where the integration limits so and sf refers to the initial and final positions, and is an
infinitesimal distance travelled along the route chosen, from the calculus of variations
(Erich Miersemann, 2012), that the shortest distance between two points in a plane is
straight-line. However, suppose that we wish to demonstrate this result from first
principles. Let us consider the length, L, of various curves, y(x), which run between two
fixed points, A and B, in a plane. L takes the form.
= [ + ] / (4.2)
Or
= [ 1 + ( )] / (4.3)
Figure 4.1: Shortest route between points A and B
56
Using Eq. (3.3b), we can write:
= = + (4.4)
Moreover, using the above expression for Eq. (4.2) can be rewritten as:
= = + (4.5)
Significantly, the equation above involves variables of route choice, i.e., ( ), ( ).
4.1.2 Route Cost in Terms of Time
The minimum time criterion is related to the quickest or fastest route, which is
usually measured as the shortest travel time route. The time T taken to travel over a route
can be expressed as:
= (4.6)
Referring to the magnitude of instance velocity as defined in Eq. (3.3b), where
the integration limits to are the initial time, and tf refers to the final time. The above
expression of T can be written as:
= (4.7)
4.1.3 Route Cost in Terms of Physical Effort
Physical effort can be formulated in terms of the amount of energy a human body
needs to expend in order to perform activates or physical tasks, which is also known as
metabolic energy. The former indicates the sum of the chemical processes that occur in
living organisms, resulting in a production of energy. The metabolic energy expenditure
of walking may vary depending on the factors that encompass total weight, walking
speed, type of surface, and grade.
57
Based on experimental data and practical evidence
Goldman, 1976), it has been widely reported that the relationship between the metabolic
power P and the walking instant speed takes the power form:
= ( ) = (4.8)
A special case is the quadratic form discussed in section 3.2.
4.2 A comparison between Criteria
In this section, we investigate the relationship between the three criteria
mentioned in Section 4.2 for the case of a quadratic form of power defined in Eq. (3.15a).
For this purpose, this equation can be expanded as:
= + + (4.9)
Using integration by parts, we can write:
= + + (4.10)
or
= ( + ) + (4.11)
Referring to Eqs (4.5 and 4.6), the above equation turns out to be:
= ( + ) + (4.12)
Now, for a certain case of constant speed V = L / T, we can write:
= ( + ) + (4.13)
58
Substituting V = L / T into the above expression, we obtain:
= + + (4.14)
After expanding:
= + + (4.15)
The above equation relates the effort criterion to the time and length criteria.
Figure 4.2 depicts a surface showing this relationship, and shows a variation of E with
changes in L and T. Clearly, the function of E has a minimum. Moreover, the function
increases quickly starting from X and moving upright or down-left, and slowly moving
up-left or down-right.
Moreover, for the case of constant speed, Eq. (3.20) can be expressed as:
= + + (4.16)
or, equivalently
= + + (4.17)
Figure 4.2: The surface of effort E versus the time T and the length L
59
The aforementioned equation represents the metabolic energy cost per unit of
distance, which is shown in Figure 4.3. For G=0, X=0, = 1, where the walking
surface is flat (G=0), there is no external load (X=0), and the terrain and surrounding
factor defined as 1 for free walking. It can be deduced from the Figure 4.3, that there is a
critical speed value at which the effort per unit distance E/L is a minimum, the expression
for this speed can be shown to have the value
= = = 0Solving for V,
= (4.18)
Referring to Eqs. (3.15a,3.15b,3.15c) the corresponding numerical values of
parameter A and C are evaluated as,
C = 1.5W + 2(W + L) (L/W) 2 = 1.5 W
Substituting the values of C and A into the above equation, we obtain the optimal
speed as 1 m/s, which is almost identical to the value determined in earlier investigations
(Cotes and Meade, 1960).
Figure 4.3: The relation between the velocity V and the effort E
60
In formulating route choice models, many researchers considered that perceived
walking distance would influence a pedestrian choice of facility. It was, in turn, assumed
that individuals would have a model of expected walking distance internally, which they
would then use to mentally estimate walking distance differences between stairs and
escalators in making their choice. In other words, the perception of physical effort will be
weighted differently for each pedestrian irrespectively of whether their underlying route
choice is based on the same factor (shortest distance in this example).
Theoretically, the shortest distance between two points is a straight line, although
the walking distance towards the escalator is larger than the walking distance towards the
stairs, more pedestrian is expected to choose the escalator. The actual walking distance
on the escalator is larger but the effort consumed is less than walking along the stairs, and
relatively more pedestrian will choose the escalator.
4.3 Example 1:
To illustrate the application of the methodology proposed in this research, we
consider a comparison between two routes as shown in Figure 4.4, in which a pedestrian
walk from the origin A to destination B. For the route choice process two options are
available, namely, Route AB: with an uneven walking surface comprising soft sand all the
way, and Route ADCB comprising a footpath with a hard level walking surface beside a
roadway.
61
Figure 4.4: Comparison between two Routes
Figure 4.5 shows a schematic diagram of the two route options. In Figure 4.4 the
pedestrian travels from origin to destination where the pedestrian chooses the route with
the most direct route and shortest length AB, while in Figure 4.5 B, the pedestrian travels
from origin to destination through points D and C.
A. Route Choice 1 B. Route Choice 2
Figure 4.5 Illustration of key direction of route choice possibilities
For route AB, the distance from point A to point B is 100 m, with = 9, V =1.0
m/s, zero grade (G=0), and no extra load (X=0). The time, distance and physical effort
route costs can be computed as,
62
= . = 100 , = = 100 , = 1500 / For Route ADCB, the distance from destination A to through D and C to
destination B is 120 m, with =1, V=1.5 m/s, and zero grade and no extra load, then,
= . = 80 , = + + = 120 , = 585 / Figure 4.6 shows the distance travelled for the two routes, as a function of time,
while Figure 4.7shows the physical effort consumed for the two routes.
Figure 4.6: The Relation between route length and time
63
Figure 4.7: The Relation between effort and time
Referring to Table 4.1, which includes a comparison between the two routes, it is
apparent that even though Route AB is shorter than Route ADCB, the physical effort cost
of Route AB is greater than that of Route ADCB. Significantly, the route with minimum
time is ADCB, with the shortest-distance route is AB, while the minimum-effort is ADCB.
Table 4.1: Route Cost in terms of Time, Distance and Effort
Selection Time, T (sec) Distance, L (m) Effort, E (J/Kg)
Route AB 100 100 1500
Route ADCB 80 120 585
Apparently, the two possible routes have different costs for time, distance and
physical effort. The shortest distance formulation suggests that more pedestrian would
choose route AB. However, if we consider the sand, which is viewed as an obstacle,
between points A and B, it is reasonable that some pedestrians, due to their personal
64
perceptions of the obstacle and the increased effort of the shortest route will choose Route
ADCB.
The minimum walking time formulation (Cheung & Lam 1998), (Daamen &
Hoogendoorn 2004), would not always be applicable in the presence of obstacles. This
effect is likely to vary considerably between pedestrians. The key point is that individual
pedestrians will have an awareness and appreciation of this before the decision point where
the route choice is determined. In other words, the perception of obstacles will be weighted
differently for each irrespectively of whether their underlying route choice is based on the
same factor (shortest distance in this example).
4.4 Example 2:
To illustrate an application of the PLE, the comparison between two routes is
shown in Figure 4.8 and thereby differentiating between the energy expenditure, distance,
and time, of walking through each route. (Route 1: Straight line with ‘mud’ in the middle,
Route 2: Piecewise with angles of 30 degrees along the x-axis. Where ‘mud’ represents
some instance, which causes increase effort; this could be mud, stairs, heat, congestion,
noise, etc.)
For Route 1, the distance from the origin to destination (OD) equals 100 m, which
includes three stages. Stage1 between points AA is 30m long with ( = 1 ), (v = 1.5
m/s). Stage2 between points A A is 40m long ‘mud’ with ( = 9 ), (v = 1 m/s). Stage3
between points A B is 30m long with ( = 1 ), (v = 1.5 m/s). Pedestrian considered to
have similar weight and carrying the same load with velocity 1.5 m/s and terrains = 1
throughout their way. As a result, for route 2, the distance between O and D is 115.4 m.
As shown in Figure 4.8. And Table 4.2 even though Route 2 is shorter than Route
1, the effort associated with Route 1 is greater than the one for Route 2.
65
Figure 4.8: Comparison between Two Routes
Figure 4.9: Comparison between walk through mud path (more resistance) and least resistance path at the right side in real life.
To calculate the metabolic energy expenditure of walking in the two Routes,
Route 1 which include three stages with different terrain and velocity on each, and
Route 2: Piecewise with angle 30 degrees along the x-axis (ACB).
P = Av2 + B v + C
C = 1.5*W + 2*(W + L) * (L/W) 2
Where;
66
A= 1.5*1(1+1) = 3
B = zero, Flat Grade
C=1.5(1) + 2(1+1) (1/1)2 = 5.5
Route A-A’
= , == = (3 + 5.5)
= 3 + . ( 30) = 8.16 30 = 245Route A’-A’’
= = [1.5(9)(1 + 1) + 1.5(1) + 2(1 + 1(1/1) ] = (27 + 5.5)
= 27(1) + 5.51 ( 70 30) = 1300 Route A’’- B
= , == = (3 + 5.5)
= 3 + . ( 100 70) = 8.16 30 = 245
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The total energy expenditure in Path 1
E = Route AA’ + Route A’A’’ + Route A’’B
E = 245 + 1300 + 245 = 1790 Route 2
Length for cord = = 57.73 = = (3 + 5.5)
= 3 + . ( 2 57.73) = 8.16 30 = 942.2 As shown in Table 4.2 even though Route 1 is shorter than Route 2, the effort
associated with Route 1 is greater than the one for Route 2 and the time is slightly more
as well.
Table 4.2: Shows an Overview of Route Usage
Selection Time, T (sec) Distance, L (m) Effort, E (J/Kg)
Route 1 76.93 115.4 942.2
Route 2 80 100 1790
As an assumption, the ‘mud’ on Route 1 leads to congestion mainly because of a
decrease in the subject’s walking velocity and increase in time delay and effort as shown
in Figure 4.8.
Even though in the two examples above, it happens that the road with least effort
matches with the road of minimum time, this cannot be generalized, as in certain cases
the least effort route could take more time than the one that requires more effort (e.g.
stairs vs long ramp).
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4.5 ConclusionsShortest distance, minimum time and least effort criteria are formulated and
assessed in this chapter, to give insight and gain a better understanding of pedestrian route
choice behaviour.
The research shows that the three criteria are correlated and provide different
perspectives on route choice behaviour and different depths of understanding. This
research has also used increase insight into the relation of time, distance, and physical
effort for walking via each route.
A comparison is conducted between the three main evaluation criteria using two
simulated examples. An explanation is included for the rationale behind the proposed
minimum effort criterion in real life scenarios.
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Chapter 5
Experimental Results of a Bottleneck Investigation at the Brisbane Central Train Station
In this chapter, we validate the effort-based model with various environmental
constraints by demonstrating a series of case studies. We first introduce the techniques
used to collect the dataset from Brisbane Central Rail Train Station, where the case
studies are evaluated over. We then demonstrate the case where we evaluate efforts of
taking escalator against stairs with the formal model and assumptions we made. We also
present the case where we study the bottleneck scenario in which congestions exist at the
entries. In this case study, we are particularly interested in the entry of escalator and stairs.
In this chapter, we demonstrate that our model is a more accurate representation of
pedestrian preferences over different criteria. We validate our result by comparing
existing time- and distance-based models against the Brisbane dataset.
5.1 Data Collection Techniques
In our experiment, we collected a real dataset from Brisbane train station and
performed various tests to validate the model that developed in Chapter 3, effort based
formulation for pedestrian route choice behaviour by metabolic energy and congestion.
Such model congestion states that passengers are most likely prefer to choose escalators
rather than stairs, as the former is associated with least effort. Data were collected to
monitor the route choice behaviour of a passenger from (9:05 am- 9:45 am) on a weekday.
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The data collection approach applied in this research used an Asus Xtion camera,
which is a 3D Sensor that was mounted at the column of the platforms at a height of 2.30
m observing an area of approximately 3 m by 6 m at an angle of 15o. A wide lens was
used, enabling the camera to view the entire walking area. The experiments are recorded
using our Sensing Hardware Platform (SHP), which has been demonstrated to be capable
of robust person detection and tracking in situ in public train stations (Kirchner et al.
2014). The SHP was used to produce a real-data dataset of individual passengers’
movements and to develop more detailed insights into pedestrian behaviour in order to
keep all information.
Experiments were conducted in Brisbane Central Train Station during peak hours
to investigate the route choice behaviour of a pedestrian on the vertical level. The data
collection techniques used in this research with respect to route choice behaviour are
described in more detail in the following:
Manual counting by human
Manual counting by a human was used to collect data on egress time. The flow
of pedestrians was measured by counting the numbers of pedestrian’s number at
a given section in a certain time interval throughout a station.
Video Analysis,
Video Analysis is the most useful data collection technique that has been widely
used for pedestrian detection and tracking; using video camera data gathered by
video recordings. The recorder unit of the video data is to be mounted right above
the walking area, which is difficult to implement in the many stations (Xu, Liu
and Fujimura, 2005, Virgona, Kirchner and Alempijevic, 2015). Further
requirements call for constant light conditions, continuous supervision, and a
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fixed location of the camera on the recorder, then converting the digital images
into data to perform analyses. This sensing unit was located at the entrance and
the exits of the pertinent pedestrian facilities to record the walking behaviour of
the pedestrian from the concourse to platform and vice versa.
5.2 Case Study 1: Stairs or Escalator
In this case study, we validate our effort-based model presented in Section 3.2 by
comparing it with the traditional models assuming either shortest walking time or
distance. The case study below focuses on the different types of walking infrastructure
and congestion on passenger route choice. In this section, the real congestion data is used
to assess the influence of congestion on pedestrian route choice behaviour. We apply the
concept and methodology developed in this research to investigate pedestrian route
choice between two alternative facilities: Escalator and Stairs, as shown in Figure 5.1,
Figure 5.2 and Figure 5.3.
Figure 5.1: Queensland Rail field layout for Brisbane Central Station Feb-2015, (Box 4)
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Figure 5.2: Escalator and Stairs, in Brisbane Rail Station
Figure 5.3: Our SHP located at Brisbane train station
For pedestrian behaviour on the vertical level, the pedestrian will choose their
desired route according to the shortest walking time or shortest walking distance, or a
combination of both. For the process of pedestrian walking behaviour in the train station,
the movement of pedestrians includes route choice in both the vertical and horizontal
level, with the latter including mainly the choice between stairs and escalator. For the
vertical level, the pedestrians not only choose the shortest walking time and shortest
walking distance but also consider the least effort consumed in climbing the stairs.
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The congestion at the base of the escalator varied with each batch and during the
time that the patch passed through the escalator. Congestion is only observed at the
escalator for a limited time at peak hours. The severity of congestion is assessed from the
waiting times and the number of passengers on the escalator derived from our SHP data.
Analysis of origin-destination relations shows that the congestion on an escalator has a
significantly different influence on pedestrian route choice.
The frequency of stairs and escalator users appeared to vary with the density of
passenger at the base of the escalator. To facilitate a consistent method of measuring the
congestion at the base of the escalator, a region measuring approximately (4m * 3m) in
the stairs and the escalator was defined by our SHP.
Figure 5.4: Number of pedestrians over time on the escalator at Queensland Rail field for Brisbane Central Station Feb-2015
The number of passengers in the region of the train station platform was counted
to determine the congestion on escalator within the region.
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Figure 5.5: Percentage of passengers walking up escalator/stairs without congestion
On the contrary, three views of the region show three different congestion states.
To highlight each passenger within the catchment area a blue circle has been placed on
each occupant's head. This region was then considered congested when the number of
passenger in the area, who intended travelling up the stairs or escalator, equalled (0-2)
passengers upon low escalator congestion, (3-6) passenger upon escalator medium
congestion and (7-8) passengers upon escalator high congested. High congestion was
selected as a critical crowd passenger’s density as it represents the situation in which
normal walking speeds are reduced due to queue in the escalator. As shown in Figure 5.6,
a significant difference in the state of congestion is evidence by comparing the high
congestion state shown in Figure 5.6a) with the low congestion state, as shown in Figure
5.6c).
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A. High Congestion
B. Medium Congestion
C. Low Congestion
Figure 5.6: Route Choice Behavior Passengers’ based on congestion state
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A sample of 328 passengers was recorded ascending to the upper level either to
choose between the alternative escalator or stairs when train arrivals, 46 escalator users
were recorded, 13 stairs users were recorded from a total 59 passengers during low
congestion state, 101 escalator users were recorded, 32 stairs users were recorded from a
total 133 passengers during medium congestion state. However, 85 stairs users were
recorded, 51 escalator users were recorded from a total 136 passengers during high
congestion state.
During the low congestion state, approximately 78% of the passenger that arrived
preferred to use escalator and 22% of the passenger use stairs based on the PLE approach
seek for least effort, the escalator was the most preferred device. However, approximately
62% of the passengers that arrived preferred to use stairs and 38% of the passenger use
escalator during the high congestion state they do to avoid congestion and other
considerations.
With high congestion, the alternative route stairs will provide a travel time gain.
It is furthermore shown that approximately 65% of total pedestrians choose the stairs
route during all congestion periods, as shown in Figure 5.7.
Figure 5.7 shows the number of pedestrians in three different congestion levels.
The upper side represents the number and the percentage of the pedestrians using the
stairs and the lower is those for the escalator. The data shows that the usage of each
infrastructure with respect to the congestion state is not linear; the usage of stairs stays
constant until the congestion gets high. This follows our intuition on the pedestrian effort.
The severity of congestion is assessed from the different terrain and surroundings such as
, , , and is
shown in Table 3.2. Significantly, high congestion levels represent the situation in which
normal walking speeds are reduced due to queuing to approach the escalator.
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Figure 5.7: Congestion occurrence prediction with numbers and percentages of passengers’ who travelling over stairs and escalator
Apparently, when the congestion state is low passengers certainly choose the
escalator. When the congestion state is medium, the passengers likely choose 76%
escalator and 24% stairs, and for the high congestion state, passengers likely choose stairs
to avoid congestion as shown in Figure 5.7. The reduction in pedestrian speed caused by
congestion is considered. Furthermore, it is reasonable that the desire of the pedestrian to
move towards it is preferred destination decreases, as gets closer to the escalator
infrastructure at the congestion state. Pedestrians are inclined to change their route to
avoid the congestion (Hoogendoorn & Bovy 2004). Counting of the passengers indicated
that relative usage of stairs increases when the queue in front of the escalator increases
(Chueng and Lam, 1998). In fact, the research work of this dissertation predicts the
percentages of escalator and stairs usage. Moreover, the work presented here
demonstrated that perceive congestion on a path alternative has a cost in the real world
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(using real data from a field study) and that passenger path choice models can exploit this
to describe behaviour. The results obtained using the formulation proposed in this
research are found to be consistent with the findings from a real-world field study in
Brisbane Central Rail Train Station.
Table 5.1 A comparison of effort with a different state of congestion.
length, L (m) Time, T (sec) Effort, E (J) Effort Percentage, %
EscalatorLow Congestion
3+15.6=18.6 3/1.34 +22.28= 24.52 2674.28+818.08= 3492.36 32%
3492.36/ (3492.36+7233.48) = 32%
EscalatorMedium Congestion
18.6 3/1 + 22.28= 25.28 2674.28+1583.43 =4257.71 37%
4257.71/ (4257.71+7233.48) = 37%
EscalatorHigh Congestion
18.6 3/0.7 +22.28= 26.57 2674.28+3360.76 =6035.04 45.8%
6035.04/ (6035.04+7233.48) = 45%
Stairs 3+15.6=18.6 3/1.34 +11.19= 13.43 6688.03 +545.45 =7233.48
Table 5.1 compares our framework against the time- and length-based models. In
order to evaluate the estimated effort for each of the three congestion cases, we used the
following formula:
PE = EE/(EE + SE) 100 % (5.1)
Where PE is Percentage of effort, EE is estimated the effort of using the escalator, and
SE has estimated the effort of using stairs. Now the above equation can be rewritten as
PE = (EE/SE)/(1 + (EE/SE)) 100 % (5.2)
The above formula would be useful in identifying the choice between escalators and
stairs.
If the effort of both stairs and escalator is equal (EE=SE), then the outcome of the
formula will be 50%. If the effort of the escalator is less than that of the stairs, then the
percentage will be less than 50%, while a higher effort of the escalator will produce a
percentage that is greater than 50%.
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The observation from Figure 5.7 shows that there exists a sudden jump in
pedestrian preference as congestion increases to high. Our effort-based model in Table
5.1 is validated against the observation that the effort percentage jumps from 32% and
37% to 45%. On the other hand, the distance-based model shows the constant preference
and the time-based model shows a linear preference with respect to congestion level. The
comparison clearly illustrates that our model is a good representation of how pedestrians
choose their path with respect to the congestion level.
5.3 Case Study 2: Escalator Entry Bottleneck
In this case study, we use our model in Section 3.2 to analyse the passenger
behaviour in the presence of transition bottlenecks, such as an escalator. We use the
Brisbane dataset to evaluate passenger route in terms of choosing either escalator and
stairs subject to different conditions.
Escalators are essential for passenger’s movements through multi-level rail station
concourse environments. Despite the access benefits that escalators provide, they can
make travel time longer and pose some challenges when bottlenecks appear at entry.
Studying the passenger behaviour of bottlenecks at escalator entrances is essential for
planning, designing and control of engineering transportation systems. In this case study,
we investigate passenger route choice behaviour while approaching an escalator-stair
infrastructure set at Brisbane Central train station.
We demonstrate the pedestrian behaviour in the congested environments based on
the principle of least effort. In fact, here we present a model evaluated to the passenger
route selection behaviour on the escalator entry from real data. The proposed model
considerers the escalator entry capacity and queue growth on the base of the escalator.
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5.3.1 Bottleneck and Queuing
In designing a transport facility, it is important to predict passenger selection
behaviour, since it is one of the key factors affecting the passenger flows between the
entrance and exits points (platforms, train gates, etc.). Typically, these stations are
designed with the intention of limiting passenger’s route choices where information
systems are usually present to direct egress. Some simulation tools have been developed
to predict passenger flows in walking facilities, SimPed (Daamen and S. Hoogendoorn,
2003), NOMAD (Hoogendoorn and Bovy, 2004), and Legion (Still 2000). On the other
hand, very little research has been devoted to the escalator entry bottleneck.
In the modern world, the facility of using escalators at train station reduces the
passenger walking time, particularly when the area is congested. There is a bottleneck on
the escalator entry with a fixed capacity or service rate, and if the arrival rate of a
pedestrian at the escalator entry exceeds the capacity, a queue develops. Congestion that
happens in the entry of an escalator is termed escalator entry bottleneck (Fixed
Bottleneck) which corresponds to passengers jam and gridlock (Kauffmann & Kikuchi
2013, Voskamp 2012).
Bottlenecks impose a wide range of problems for passengers especially at
escalator entry in train stations, like delay in travel time, rescheduling train timings, and
unhappy experiences for passengers mainly because of pushing and shoving (Palma and
Lindsey, 2001). Permanent bottlenecks will occur at escalator entry, for short time
periods. The capacity of the escalator is generally supposed to depend on the speed of the
bottleneck movement (Laval and Daganzo, 2006). Some empirical studies have been
carried out on bottlenecks and focused on the behaviour of passengers in a narrow
bottleneck experiment (Shiwakoti1 et al. 2015, Cepolina & Tyler 2005, Fosgerau & de
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Palma 2012, Davis & Dutta 2002, Kinsey et al. 2014, Arnott et al. 1990). However, none
of these empirical studies provides any data about the escalator entry bottleneck
phenomena.
Such research efforts are inherently limited in that they focus on passenger
selection behaviour in case of bottlenecks. Meanwhile (Voskamp, 2012) argued that fixed
bottlenecks could be occurring at escalator entry while moving bottlenecks might be
found in the overtaking process on an escalator. Moreover, the core of this research is to
create a model of passenger behaviour on escalator entry bottleneck.
5.3.2 Bottleneck Capacity
Capacity is certainly important in the design of the area around the escalator and
has a significant impact on the escalator performance. Lower passenger densities are
desirable in uncongested environments so that passengers may manoeuvre and pass each
other in order to maintain their desired speed (Kauffmann and Kikuchi, 2013).
Conversely, in congested environments, it is important to provide adequate queuing space
under crush loading conditions like train arrivals or emergency evacuations so that
passenger safety is assured. Queues are developed when the arrival rate of passengers the
escalator entry exceeds its capacity (Kauffmann and Kikuchi, 2013). For that, we need to
improve our knowledge of escalator entry bottleneck influencing passenger selection
behaviour.
To evaluate and improve approaches in that walking infrastructures in the train
station are used sufficiently, knowledge is required regarding bottleneck and capacity.
Bottleneck capacity is specified by parameters such as a width of the bottleneck, wall
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surface, and interaction behaviour of passengers passing the bottleneck (Hoogendoorn
and Daamen, 2005).
Most available research focuses on the relation between the bottlenecks and its
capacity. This is important in any passenger environment to understand and monitor for
passenger traffic management (Seyfried et al., 2009), where there is a change in size of
escalator which might give rise to a change in capacity, and involve congestion with the
influence on passenger route choice, for instance in train stations and emergency exits
(Braid 1989, Fosgerau & de Palma 2012, Yang & Hai-Jun 1997, Still 2000, Hoogendoorn
& Daamen 2005).
5.3.3 Model Formulation escalator entry bottleneck
Generally, the passenger must first access the escalator, and to do that the
passengers must walk into an escalator entry bottleneck. The rigid fenders that line the
sides of escalators constrict the passengers flow into a narrow stream no more than one
metre wide. The most common escalator step width is 1 metre (Hoogendoorn and
Daamen, 2005). In our approach, the capacity of an escalator entry is first determined
based on an assumed maximum step capacity, typically two passengers per step.
Consider a simplified infrastructure as the one shown in Figure 5.8, which shows
an escalator entry bottleneck. The bottleneck, whose capacity is finite, is subject to
congestion. The crowd starts developing when the arrival rate of passengers at the
escalator entry exceeds its capacity. Explicit analytical solutions can help us understand
the queuing characteristics of the bottlenecks (Al-widyan et al., 2016).
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Figure 5.8: Train station layout
Let the number of passengers in the queue be denoted by q(t) and the rate of
passengers existing from bottleneck denoted by n(t) which can be expressed,
( ) = ( ), ( ) = 0 ( ) < , ( ) > 0 ( ) >Where m(t) is passenger rate departing from the train at a time, t, C is escalator
capacity (maximum number of passenger rate that can pass the entrance of the escalator
at a time t). This scenario is illustrated in Figure 5.8.
We demonstrate three cases with different constraints. When applying the
escalator entry bottleneck model to real data that describe the pedestrian flow at the
Brisbane train station we can realise the following three cases:
1) Case A: q (t) = 0, and m (t) < C
This case represents no congestion; if the passenger travels from platforms to the station
hall at a time, he/she will pass the escalator entry bottleneck easily as shown in Figure
5.9.
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a) The flow commences (Real-time scenario) a) Overview of the experiment
Figure 5.9: Case A, no congestion
2) Case B: q (t) = 0, and m (t) = C
In this case, the number of passengers travelling over an escalator equal escalator
capacity. As shown in Figure 5.10 two lanes are formed: pedestrians tend to walk
diagonally behind each other, thereby reducing the headways and thus maximising the
use of the infrastructure supply.
a) The flow increases towards the maximum b) Overview of the experiment
(Real-time scenario)
Figure 5.10: Case B, the number of passengers travelling over an escalator equal
escalator capacity
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3) Case C: m (t) > C
This case describes the authority’s reaction when high- level congestion occurs, if the
numbers of passengers, travelling from platforms to station hall, are more than escalator
capacity a queue commences as shown in Figure 5.11.
Referring to Figures 5.9, 5.10 and 5.11, is apparent that queues form when a
bottleneck is over congested. Queuing is an organised pattern occurring, for instance, in
front of an escalator entry. Passengers do not always keep a large distance between each
other in the queue. In contrast to queue formation, queues are typically organised in the
form of passengers accumulation (Fruin, 1971). When passengers are queuing, their
desire to move grows. As a result, passengers stand closer to each other over time that
can be observed by an increase in density, and a decrease in queue length (Helbing D., P.
Molnár, 2001).
a) The point of maximum accumulation b) Overview of the experiment
for pedestrians, the capacity drop occurs
Figure 5.11: Case C, high- level congestion occurs
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5.3.4 Experimental Results
Experimental evaluation was conducted at the central Brisbane train station and
we performed various tests to validate the model developed in the previous section based
on the Escalator entry bottleneck and congestion occurrence. Our Sensing Hardware
Platform (SHP), was again used for data collection as shown in the right image of Figure
5.12, which has demonstrated capability of robust person detection and tracking in situ in
public train stations and used to produce a real-data or individual passengers movements
(Kirchner et al. 2014, Virgona et al. 2015, Collart et al. 2015).
Figure 5.12: the sensing (SHP) located at Brisbane train station
During the peak hour period, the platforms at Brisbane Central Train Station are
densely populated. When the trains arrive, the formation of queues at escalator entry is
common. In total, 328 passengers were recorded from (9:05 am- 9:46 am). To facilitate a
consistent method of measuring the bottlenecks at the base of the escalator, a region
observing approximately (3 m by 6 m and angle 15o) in the base of the escalator was
defined by our SHP, with which depth images for the 49-minute video. The number of
passengers in the region of the station platform was counted manually to determine the
escalator entry bottleneck within the region.
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Figure 5.13 shows passenger rate versus time when the queue occurs. It is
apparent that the passenger rate exceeds the capacity in case C. We conclude that the
escalator has a capacity C = 6. That is, the maximum number of passenger rate that can
pass the entrance of the escalator at a time t is 6.
Figure 5.13: Bottlenecks in a peak hour situation at a Brisbane central rail station
5.4 Conclusions
In this chapter, this research demonstrates that perceive congestion on path
alternative has a cost in a real world (using real data from a field study) and that passenger
path choice models can exploit this to describe behaviour. We compared our effort-based
model against traditional assumptions with time and distance and validated that our model
performs better than the existing approaches by comparing it to the dataset. We have
shown that pedestrians choose to take stairs over the elevator only while highly congested.
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The results obtained using the formulation proposed in this research are found to be
consistent with the findings from a real-world field study in Brisbane train station.
In experiment 1, data collection for pedestrian route choice alternatives in Brisbane
station is discussed. These data have been collected in public train stations by recording
their chosen route. This research shows that pedestrians change their route choice with
perceived congestion, and anticipate different route choice selection behaviour during
congestion and without congestion. Data suggest that part of the population has a habit to
avoid congestion routes even when no congestion is present. It is expected that station
travellers, in general, will adapt their route choice behaviour to daily congestion
situations. The analysis shows that the number of passengers avoiding escalators
increases when congestion occurs.
In experiment 2, pedestrian behaviour in the escalator entry bottleneck was studied.
Analysis of video images showed that during near-capacity Case (B) and over-capacity
Case (C) flow, the bottleneck is used differently than free flow Case (A). While in case
(A), passengers will walk in the centre of the bottleneck, thereby maximising the distance
between themselves and the escalator fence. Like the findings of Experiment 1, that
escalator usage decrease for increasing waiting time. This data shows that pedestrians in
this area change their routes to avoid waiting, and they do not consider travel time again.
The route choice model indicates that the relation between escalator entry bottleneck
usage within the region can be determined when the escalator has a capacity C = 6. We
conclude that the escalator has a capacity C = 6. That is, the maximum number of
passenger rate that can pass the entrance of the escalator at a time t is 6.
It is apparent that at a bottleneck, many observations indicate avoidance of escalator
entry bottleneck even for minimum waiting times due to habit, some of the pedestrians
are used to avoiding the bottleneck, or they have a higher preference for an alternative
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route. As illustrated in section 5.3.3, the results of case C, high- level congestion, show
that the route choice is greatly affected by the congestion occurrence; this shows that
route choice is affected by the escalator entry bottleneck. As illustrated in section 5.3, the
escalator entry bottleneck on route selection has a cost in the real world (using real data
from a field study), and that passenger route selection models can exploit this to describe
behaviour.
Also, we have not used any public or synthetic datasets in the research. Public
datasets were available for the route choice behaviour at the time of research, but these
datasets were not able to provide the extensive real-time data to carry out the research
work on the public transportation system, and for this reason, the data from the Brisbane
station is the best choice.
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Chapter 6
Conclusions and Future Work
In this dissertation, we improved the method to evaluate pedestrian effort in
traversing from one location to another in terms of required metabolic energy. We
proposed to formulate models with various pragmatic constraints such as bottleneck
capacity and criterion choices based on mathematical formulations and realistic
assumptions. We also have validated our models against the Brisbane Central Rail Train
Station Datasets and showed that our model has higher efficacy than the existing time and
distance-based approaches. We also show interesting properties in pedestrian preference
and justify why it occurs. The benefits of this work go to researchers, practitioners,
engineers, and the public transportation infrastructure designers who work on monitoring
and predicting traffic conditions and redesign of facilities and services of stations.
6.1 Summary
It is important to predict pedestrian route choice in public transport facilities.
However, pedestrian route choice exhibits non-linear phenomena involving various
factors such as walking distance, walking time, pleasantness, crowdedness, familiarity,
passenger characteristic and numerous dynamic and or static environment constraints.
Further, in order to plan an efficient and comfortable pedestrian behaviour, a thorough
understanding of these phenomena is a requisite. In the end, the research presented in this
dissertation brings a step in that direction to provide a reliable, accurate, and efficient
model of pedestrian route choice behaviour on the principle of least effort, through
congested rail station environments.
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6.2 Main Findings
In this research work, it is contended that the entire behaviour of an individual is
subject to effort minimization. Hence, a route minimizes the total energy expended while
moving from current position to destination. The problem of route choice is formulated
as a constrained non-linear optimization problem whose objective function is the effort
consumed over the route.
The research shows three criteria: time, distance and physical effort. They are
mutually related. In fact, the preceding criterion provides different perspectives on route
choice behaviour and different levels of understanding. This study augments the domain
knowledge by providing insights into the relation between time, distance and physical
effort for walking via each route.
Congestion is an important concept in transport analysis because its presence can
change the behaviour of people’s movement and travel choices. The work shows that
pedestrians change their routes when congestion occurs or is likely to be present. As a
result, it is generally expected that station travellers will adapt their route choice
behaviour to daily congestion situations.
The shortest path assignment of pedestrians to the station infrastructure appears very
well suited to detect crowded areas. Infrastructure parts used by many pedestrians are
potential bottlenecks in the train station, which should be kept unrestricted to fulfil the
pedestrian’s desire for short routes in distance. Since a general model is sought, it is
recommended to consider the fact that the dataset consists of two different samples with
corresponding different scale factors.
In the case of escalators and stairs, as examples, the particular behaviour of many
pedestrians going towards and using an escalator can be captured using the Principle of
Least Effort. Besides, how pedestrians interact with the decision to use the escalator or
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stairs can be captured as well. Apparently, resorting to the PLE with no congestion, the
escalator route choice is associated with zero effort, as the passenger moves with zero
speed. This leads to the fact that the escalator route choice is preferable over the stair
route choice. However, this is not valid in the presence of congestion.
At Brisbane central train station, congestion at escalators causes pedestrians to
choose stairs. What the added comfort of an escalator compares at stairs is compensated.
This influences the compromise between capacity and cost-effectiveness for the design
of egress points, which also relates to physical implementation and capacity. A large set
of route choice observations were performed in the train station from which the impact
of specific factors, such as availability of level infrastructure included escalators and
stairs, were estimated for various pedestrian categories. From the observations of Section
5.3, our route choice model was established with high predictive performance. The
analysis indicated that the number of passengers avoiding escalators increases in the
presence of congestion at the escalator entry bottleneck.
From a scientific point of view, performance evaluation using experiments is most
relevant. Especially, the escalator entry bottleneck experiment gives a new look at
pedestrian behaviour concerning queue formation in front of the escalator. The
implications of these findings will shape further model development. Specifically, this
re-conceptualization of the fundamental basis of the model to allow for co-variants
contingent on passenger perceptions has increased the scope of the general model through
drawing previous outlier cases under the explanatory boundaries of the model. In simple
terms, this re-conceptualization builds the foundations to generate knowledge to enable
improved planning and design of public transport facilities.
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6.3 Future Work
This dissertation focused on many new insights relating to the problem of
pedestrian route choice, particularly with respect to behaviour in train stations including
stairs and escalators. However, further research work in a number of aspects and
directions is needed. This future research should tackle a number of areas.
Although the experiments conducted in this research concerned pedestrian route
choice behaviour on level indoor infrastructure (stairs and escalator), additional
experiments are necessary on different compositions: various bottleneck widths, different
types of infrastructure such as stairs, escalator, ramp, gates, and queue formation.
For future work, this present work can be extended further by considering
pedestrian categories depending on walking behaviour and classifying people into groups
such as business, tourist and other casual pedestrians.
The developed model can be used to obtain design guidelines concerning pedestrian
facilities. Actually, such guidelines can help designers to develop plans that can
efficiently handle pedestrian movement, which helps to prevent bottlenecks and stressful
situations. Designers need a theoretical model on which they simply make successive
design decisions to plan route choices based on the principle of least effort in complicated
public transport facilities. This will facilitate the process of design, hand the designer
guidelines valid for his specific design, and help the designer with making decisions and
taking choices. Crowded stations contain more environment constraint such as obstacles
and infrastructure (static and dynamic) than escalator or stairs. It is recommended to
extend this research work by developing a model that takes into account the moving and
fixed obstacles to serve the design process of public transport facilities.
94
Although this research has given many new insights into pedestrian behaviour,
particularly route choice behaviour in public stations facilities, more experiments under
field data observations are needed on level-of-service and comfort while designing the
infrastructure for pedestrians. Pedestrian comfort must be considered, depending on least
effort of occurring capacity. Such comfort is characterized by the level-of-service concept
that is an index of walking comfort in relation to the available free space. In fact, comfort
includes factors such as a condition of the walking surface, terrain and surroundings,
grade, and egress point capacity.
This work follows a deterministic approach, which assumes that the perceived
utility of a route is deterministic and that pedestrians will only choose the route that has
minimum average cost. On the other hand, probabilistic choice models assume that the
perceived utility of a route is stochastic, and express the probability that pedestrians will
choose each of the available alternatives. An extension of the work presented in this
dissertation to the stochastic case can be done as future work.
The work reported in this dissertation has several benefits to the practitioners of the
relevant field. The salient benefits include a theoretical framework of route choice
behaviour which is essential in developing a powerful model. The model developed in
this dissertation can predict the route selected by a pedestrian to reach a final destination.
However, this model cannot predict the number of pedestrians that will likely choose a
specific route; this problem can be the focus of future research work. Another aspect of
pedestrian behaviour showing demand for research is choice behaviour.
95
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