ma_hartl thesis.pdf
TRANSCRIPT
-
7/25/2019 MA_Hartl thesis.pdf
1/115
Master Thesis Nr. 1
Route choice in macroscopic andmicroscopic assignment models
for public transport
Author: Maximilian Hartl, BSc.
Supervisors: Prof. Dr.-Ing. Markus Friedrich
Dipl.-Ing. Matthias Schmaus
October 2013
Universitt Stuttgart
Institut fr Straen- und Verkehrswesen
Lehrstuhl fr Verkehrsplanung und Verkehrsleittechnik
Hartl
-
7/25/2019 MA_Hartl thesis.pdf
2/115
Abstract
VuV 2013 2
Abstract
A task of traffic engineers is to investigate the impact of traffic demand on past,
present, and future transport networks while considering social, ecological, and
economic issues. The challenge in transport planning is to find the right balancebetween all aspects. To solve this optimization problem, methods like transit
assignment models have been developed to support the traffic engineer to analyze the
current deficiencies and design better public transport networks. Depending on the
purpose of planning, the requirements differ among the transit assignment models
according to the type of public transport system modeled, supply and demand
representation, level of details, input and output values, reliability and effort. Each
model has strengths and weaknesses, and suggests specific assumptions about the
information provided to the travelers. Consequently, the results of the models vary.
The aim of this thesis is to compare route choice in the macroscopic schedule-basedassignment in VISUM and microscopic simulation-based assignment in BusMezzo, and
thus giving transport planners a good understanding of the model characteristics by
explaining the underlying modeling principles, comparing route choice behavior, and
evaluating the assignment results.
The model comparison done in this thesis brings light to
how the effect of overcrowded vehicles is represented in both models,
how passengers are distributed in the network due to capacity restrictions and
how different degrees of information are affect assignment results.
The challenge of comparing two transit assignment models, which are structured quite
differently, is to use an appropriate network. The network example needs to be as
simple as possible but still covering all relevant phenomena. Before comparing the
models, it is necessary to define the initial conditions: what is actually comparable and
which level of similarities are achievable? The main focus lies not on simplifying the
models as much as possible in order to reproduce the same results. Rather, it is more
important to ensure that the same starting condition is used to evaluate the output data
and point out the difference of the models. Transport supply of the schedule-basedassignment in VISUM is modeled deterministically based on the assumption that all
passengers have the knowledge of a reliable timetable. In BusMezzo, however,
transport supply is not deterministic, but based on a stochastic simulation-based
model. To make the models in some way comparable BusMezzo is forced to have a
deterministic transport supply. This is done by assuming that all agents have real-time
information of the entire network. This accommodates for the knowledge of the reliable
timetable used in the schedule-based transit assignment model in VISUM.
To analyze the differences of the two models, first the deterministic state with the same
degree of information is compared. Then, different sets of scenarios and subsets are
-
7/25/2019 MA_Hartl thesis.pdf
3/115
Abstract
VuV 2013 3
defined to investigate the influence of varying the information degree provided to
agents as well as the effects of capacity restriction and the feeling of discomfort from
crowding for the assignment results.
To capture the effect of overcrowded vehicles BusMezzo uses an absolute limitation of
capacity. In contrast, the schedule-based transit assignment model in VIUSM describes
the phenomenon of overcrowded vehicles by a crowding function. It describes the
feeling of discomfort from crowding and adds additional impedance to the connection
mainly depending on the ratio of volume to capacity multiplied by the travel time of the
vehicle journey item. As a result, this implementation is not able to capture the
limitation of capacity appropriately since travelers are generally always able to board a
vehicle. This is based on the macroscopic structure of travel demand and is a
characteristic of the schedule-based transit assignment model. Therefore, it is
important to adapt the congestion function in a way that the level of unattractiveness
rises to an adequate level and travelers avoid this connection. The option to model thebehavior of public transit participants under congestion conditions is not properly
considered at the current state of implementation.
A major difference between the two models is the way of distributing the demand on
the network. The schedule-based transit assignment model first looks for connections
in the network and subsequently filters all reasonable connections. It assigns
impedance, depending on the impedance function, to the connections and calculates
the distribution of the demand according to the probabilistic distribution model as a
single shot decision. BusMezzo does not estimate the impedance of connections.Instead it filters all reasonable paths as foundation of the dynamically adaptive decision
process. Once the path set is calculated, each traveler faces a sequence of decisions
while traveling through the network. The selected connections are not an input for the
choice model, but instead they are the result of the dynamic sequence of decisions.
Along the way, travelers make several decisions, for example connections boarding
and alighting decisions, to adapt their behavior to the dynamic network conditions. At
the first glance, this feature is a major strength compared to the static schedule-based
transit assignment model and allows implementations of real-time information and
holding strategies to improve the network performance by regulating the departure
time. However, in special cases of high-frequented lines, BusMezzo overestimates the
distribution of travelers. Obviously, a high-frequented line approaches more often than
a less frequented line and travelers need to face a decision more often. Each
alternative holds a certain probability. The traveler chooses an actual alternative by
picking a randomly generated number and sets it in correlation to the probability of the
alternative. Since all provided alternatives hold a certain probability, there is a chance
that travelers choose this less attractive option. If this decision needs to be faced
several times in a row, the amount of travelers increases, taking a less attractive line in
favor of a high-frequented line. This shortcoming needs to be compensated by a
logical, dynamically adaptive filtering rule.
-
7/25/2019 MA_Hartl thesis.pdf
4/115
Abstract
VuV 2013 4
Furthermore, increasing the demand, decreasing the vehicle capacity or reducing the
frequency in order to enforce capacity constraints in BusMezzo significantly raises the
average total travel time because of denied boarding. The schedule-based transit
assignment model covers crowding effects by a using crowding function, but the effect
is marginal on the passengers travel time, because the schedule-based transitassignment model optimizes the total impedance value to a stochastic equilibrium.
The comparison between the BusMezzo and the schedule-based transit assignment
model clearly shows the strengths and shortcomings of both model classes.
Furthermore, it contributes to the understanding of the basic fundamentals of each
model structure and highlights the right of existence. The appropriate application of the
models strongly depends on the scope of work. The decision which model fits best to
the assignment needs to be considered by the traffic planner and his/her experience.
The comparison also shows that more scientific work needs to be done to compromise
the shortcoming (e.g. crowding function and the limitation of congestion, overestimationto high-frequented lines, and travel time calculations) to an adequate level of
acceptance to approximate the real behaviorof travelers.
-
7/25/2019 MA_Hartl thesis.pdf
5/115
Zusammenfassung
VuV 2013 5
Zusammenfassung
Die Aufgabe eines Verkehrsingenieurs ist den Einfluss von vergangenen,
gegenwrtigen und zuknftigen Ereignissen auf das Verhalten von
Verkehrsteilnehmern zu untersuchen. Die Herausforderung fr die zielorientierteLsungsfindung liegt in der Bercksichtigung von sozialen, konomischen und
kologischen Gesichtspunkten. Um die Lsungsfindung zu erleichtern, sind Methoden
wie Verkehrsumlegungsmodelle entwickelt worden. Abhngig vom Planungszweck
unterscheiden sich die Anforderungen an das Modell erheblich in Bezug auf den Typ,
die Darstellung von Angebot und Nachfrage, Detailierungsgrad, Eingangs- und
Ausgangsgren, Zuverlssigkeit und Performance. Jedes Modell besitzt Strken und
Schwchen und trifft unterschiedliche Annahmen ber die Informiertheit, die dem
Reisenden zu Verfgung gestellt wird. In Folge dessen unterscheiden sich die
Ergebnisse.
In der Masterarbeit wird die Routenwahl des mikroskopischen, simulationsbasierten
Verkehrsmodell BusMezzo mit der makroskopischen, fahrplanfeinen Umlegung,
implementiert in der Software VISUM, verglichen. Das Ziel der Arbeit ist dem
Verkehrsplaner ein Verstndnis darber zu geben wie sich die zwei Modelle im
direkten Vergleich Verhalten, wo ihre Schwchen und Strken liegen und wie die
Defizite kompensiert werden knnten.
Der Modelvergleich der Arbeit behandelt vordergrndig
wie der Effekt von berfllten Verkehrsmittel in beiden Modellen dargestellt wird,
wie Reisende im Netz unter Beachtung von Kapazittsbeschrnkungen verteilt
werden und
wie die Informiertheit von Reisenden die Umlegungsergebnisse beeinflussen.
Eine Herausforderung beim Vergleich von zwei unterschiedlich strukturierten Modellen
liegt in der Verwendung eines adquaten Beispielnetzes. Das Netz muss so einfach
wie mglich sein, dennoch aber alle untersuchungsrelevanten Phnomene abdecken.
Bevor die Modelle verglichen werden knnen, ist es notwendig die Ausgangssituation
zu definieren, was verglichen werden kann und welche Gemeinsamkeiten sich dieModelle teilen. Der Anspruch liegt nicht darin, die Modelle soweit zu vereinfachen bis
sie die gleichen Ergebnisse reproduzieren. Vielmehr geht es darum, die gleichen
Bedingungen zu schaffen, um die Modelle vergleichen zu knnen.
Die Angebotsseite der fahrplanfeinen Umlegung ist deterministisch modelliert unter der
Annahme, dass alle Reisende mit zuverlssiger Fahrplaninformation ihre
Verbindungswahl treffen. Das steht im Gegensatz zum simulationsbasierten,
stochastischen Modell BusMezzo. Um die Modelle vergleichbar zu machen, mssen in
BusMezzo auf der Angebotsseite die zuflligen Einflsse eliminiert werden. Wenn sich
BusMezzo deterministisch verhlt, mit gleichzeitiger netzweiter Echtzeitinformation fr
-
7/25/2019 MA_Hartl thesis.pdf
6/115
Zusammenfassung
VuV 2013 6
alle Reisenden, fhrt das zu zuverlssiger Fahrplankenntnis und erfllt die Ansprche
an die Vergleichbarkeit.
Der Vergleich der Modelle beginnt auf der deterministischen Ebene mit der gleichen
Bereitstellung von Information. Anschlieend werden unterschiedliche Sets und
Szenarios entwickelt, um u.a. den Einfluss von Kapazittseinschrnkungen und dem
Einfluss von Informiertheit zu untersuchen.
Kapazittsengpsse in Form von berfllten Fahrzeugen werden in BusMezzo durch
eine absolute Beschrnkung der Platzanzahl erreicht. Im Gegensatz dazu steht der
Ansatz der fahrplanfeinen Umlegung. Es beschreibt das Gefhl des Unbehagens durch
berfllung mittels einer Kapazittsbeschrnkungsfunktion. Dabei verringert sich die
Attraktivitt der Verbindung je voller das Verkehrsmittel ist. Die Attraktivitt, auch
Widerstand genannt, hngt unter anderem vom Auslastungsgrad multipliziert mit der
Dauer des Fahrplanfahrtelements ab. Diese Art der Implementierung ist nicht fhigKapazittsbeschrnkungen mit dem richtigen Ma abzubilden, da Reisende
grundstzlich immer in der Lage sind einzusteigen. Das liegt in der Abbildung der
Nachfrage der fahrplanfeinen Umlegung. Deswegen ist es wichtig die Funktion der
Kapazittsbeschrnkung anzupassen, damit berfllte Verbindungen nicht weiter
genutzt werden. Diese Eigenschaft ist zum derzeitigen Entwicklungsstand nicht
adquat umgesetzt.
Ein wesentlicher Unterschied zwischen den Modellen besteht in der Verteilung der
Nachfrage auf das Netz. Die fahrplanfeine Umlegung sucht erst nach mglichen
Verbindungen und filtert anschlieend die Verbindungen heraus, die am
wahrscheinlichsten unter realen Bedingungen gewhlt werden. Der Menge an
gefilterten Verbindungen wird ein Widerstand mittels einer Widerstandsfunktion
zugeordnet. Ausgehend vom Widerstand der Verbindung wird die Nachfrage mittels
eines wahrscheinlichkeitstheoretischen Verteilungsmodell als Einzelentscheidung auf
das Netz modelliert. BusMezzo berechnet keine Verbindungen, sondern filtert alle
sinnvollen Wege als Input fr den situationsangepassten Entscheidungsprozess. Jeder
Reisende trifft entlang seines Weges eine Vielzahl von Entscheidungen. Die am Ende
entstandene Verbindung ist nicht das Ergebnis einer Verbindungswahl, sondern vieler
Einzelentscheidung, angepasst an die Situation im Netz. Auf den ersten Blick ist dasein wesentlicher Vorteil gegenber der statischen fahrplanfeinen Umlegung in VISUM.
Es erlaubt u.a. die Bereitstellung von Echtzeitinformation und die dynamische
Fahrzeugkoordinierung. In Fllen bei denen eine Linie mit einem geringem Takt einer
Linie mit hoher Taktfolge gegenbergestellt wird, berschtzt BusMezzo die Anzahl der
Reisenden zu Gunsten der Linie mit hoher Taktfolge. Im Modell whlt ein Reisender
seine (Teil-)Verbindung indem er eine Zufallszahl zieht und diese in Beziehung zur
Wahrscheinlichkeit der Alternativen setzt. Da alle verfgbaren Verbindungen eine
Wahrscheinlichkeit besitzen, besteht immer die Chance, dass Reisende die weniger
attraktive Verbindung whlen. Wenn diese Entscheidungen oft hintereinander getroffenwerden muss, erhht sich die Anzahl derjenigen, die sich fr die unattraktive,
-
7/25/2019 MA_Hartl thesis.pdf
7/115
Zusammenfassung
VuV 2013 7
hochfrequentierte Linie entscheiden. Diese Schwche sollte mit einer sinnvollen an die
Situation angepassten Filterungsregel kompensiert werden.
Wird die Nachfrage erhht, die Fahrzeugkapazitt verringert oder die Frequenz der
Linie reduziert, entstehen Kapazittsengpsse. Diese Engpsse wirken sich in
BusMezzo direkt auf die Reisezeit aus, da Reisende nicht in der Lage sind in das
gewnschte Fahrzeug einzusteigen und somit auf das nchste Fahrzeug warten oder
ihre Verbindungswahl berdenken mssen. Die fahrplanfeine Umlegung deckt
berfllungseffekte mit einer Kapazittsbeschrnkungsfunktion ab. Die Auswirkungen
auf die Reisezeit von Passagieren sind jedoch marginal, da das Umlegungsverfahren
den Widerstand in Netz in einem iterativen Prozess zu einem stochastischen
Gleichgewicht optimiert.
Der Vergleich zwischen BusMezzo und der fahrplanfeinen Umlegung zeigt die Vor- und
Nachteile beider Modelle in Bezug auf das verwendete Beispielnetz. Zudem trgt derVergleich und die Erklrung der grundlegenden implementierten Theorien zum
Verstndnis des jeweiligen Modells und ihrer Daseinsberechtigung bei. Die geeignete
Anwendung des jeweiligen Modells hngt stark vom jeweiligen Einsatzzweck ab und
muss jeweils vom Verkehrsplaner auf Grund seiner Erfahrung entschieden werden.
Der Vergleich zeigt zudem, dass mehr wissenschaftliche Arbeit ntig ist, um die
Schwachstellen der Modelle (z.B. Kapazittsbeschrnkungsfunktion zur Einschrnkung
der berfllten Verbindungen, berschtzung von hochfrequentierten Linien und
Reisezeit Berechnung) auf ein adquates Ma zu reduzieren, um das Verhalten von
Verkehrsteilnehmern bestmglich abzubilden.
-
7/25/2019 MA_Hartl thesis.pdf
8/115
Selbstndigkeitserklrung
VuV 2013 8
Selbstndigkeitserklrung
Hiermit erklre ich, dass ich die vorliegende Masterarbeit eigenstndig verfasst habe
und keine anderen Hilfestellungen oder Quellen als die angegebenen in Anspruch
genommen habe.
Insbesondere habe ich keinen bezahlten Dienst mit der Anfertigung der gesamten
Arbeit oder Teilen der Arbeit beauftragt.
Stuttgart, den 15.10.2013
Maximilian Hartl
-
7/25/2019 MA_Hartl thesis.pdf
9/115
Glossary
VuV 2013 9
Glossary
ADC Automated Data Collection
APC Automated Passenger Counts
ATTT Average Total Travel Time describes the average time atraveler spends in the network.
AVL Automated Vehicle Location
CONNECTION describes the spatial and time depending choice between an
OD-pair
D Destination
FB Frequency-Based
GTC Generation Time Capacity
HDWY HeadwayINTEGER is a number with no fractional part Z={0-2,-1,0,1,2,}
IVT In-Vehicle Time
LINK is defined between two nodes
LOAD is the amount of travelers on a link/trip/connection
M Model (BusMezzo or VISUM)
MNL Multinomial Logit Model
NI Network Indicator
NrTransfer Number of Transfers.NODE starting or ending point of a link
O Origin
OD-PAIR Relation between origin and destination
PrT Private Transport
PuT Public Transport
SB Schedule-Based
SCENARIO Scenarios are a subset of a set and describes the actual model
executionSET A Set is a group of scenario with the same general conditions
STOP is the location where transit users might start, transfer or
terminate their trip.
TAM Transit Assignment Model
TRAVELER General expression with no model relation
TRIP refers to a single vehicle which serves one run of the schedule
TRIP SEGMENT is defined between to stops
VoT Value-of-TimeWalkT Walking Time
-
7/25/2019 MA_Hartl thesis.pdf
10/115
Glossary
VuV 2013 10
BusMezzo Related Expressions
AGENT Represents a single traveler in the network
BM BusMezzo
RTI Real-Time InformationWaitT(BM) Waiting Time is defined as time an agent needs to transfer
between vehicles or the time between the generation process
and the departure time of the chosen vehicle at the origin stop
VISUM Related Expressions
PASSENGER Represents the amount of travelers in the network in terms of
flows
PJT Perceived Journey TimeSB-TAM Schedule-Based Transit Assignment Model
V VISUM
WaitT(V) Waiting Time is defined as time a passenger needs to transfer
between vehicles at a transfer stop
-
7/25/2019 MA_Hartl thesis.pdf
11/115
Contents
VuV 2013 11
Contents
1 Introduction 13
1.1 Motivation 13
1.2 Research Goals 14
1.3
Outline of Work 14
2 Survey 16
2.1 Structure of the Survey 16
2.2
General Information 19
2.3 Estimation Process 20
3
Traffic Modeling Fundamentals 22
3.1 Traffic Model Principles 22
3.2 Private Traffic Assignment Models 25
3.3
Public Transit Assignment Models 26
3.4 Level of Information 28
3.5 Capacity Constraints 29
3.6
Stochastic or Deterministic User Equilibrium 30
4 Simulation-Based Transit Assignment Model 33
4.1 Mezzo 33
4.2
BusMezzo 34
4.2.1 Object Framework 34
4.2.2 Simulation Flow 35
4.2.3
Implemented Models 37
4.2.4 Dynamic Path Choice Model 40
4.2.5 Real-Time Information 49
5 Schedule-Based Transit Assignment Model 51
5.1 Connection Search 51
5.2 Pre-Selection 52
5.3
Impedance and perceived journey time of a connection 53
5.4 Connection Choice 53
-
7/25/2019 MA_Hartl thesis.pdf
12/115
Contents
VuV 2013 12
5.5 Crowding Functions 54
6 Model Comparison 58
6.1
Classification 59
6.2 Comparable Level and Information Degree 61
6.3 Simplifications to make the models comparable 62
6.4
Travel Time Correlation 65
6.5 Example Network 65
6.6 Set and Scenario Overview 70
6.7
SET A: Unlimited and Limited Vehicle Capacity with Low Demand 74
6.8 SET B: Unlimited and Limited Vehicle Capacity with High Demand 85
6.8.1
SET B Demand Variation 89
6.9 SET D: Frequency and Vehicle Capacity Variation 91
6.10 SET C: Degree of Information 95
7
Conclusion 98
8 References 101
9 List of Tables 104
10 List of Figures 105
Appendix 107
-
7/25/2019 MA_Hartl thesis.pdf
13/115
Introduction
VuV 2013 13
1 Introduction
1.1 Motivation
A task of traffic engineers is to investigate the impact of traffic demand on past,present, and future transport networks while considering social, ecological and
economic issues. The challenge in transport planning is to find the right balance
between all aspects. To solve this optimization problem, methods like transit
assignment models have been developed to support the traffic engineer to analyze the
current deficiencies and design better public transport (PuT) networks. Since the prize
of manpower constantly increase and the computing capacity steadily increases, in
terms of calculation time, transit assignment models play a more and more important
role for estimating traffic impacts. Many implemented theories in transit assignment
models are derived by observing the natural behavior of travelers. The aim of transport
models is to describe the complexity of the real world with the best possible
approximation by balancing between the degree of simplification, input quantity and the
quality of the out coming results. Thus, empirical investigations form the foundation for
most implemented theories in transit assignment models. Great efforts have been
made within the past decades to investigate the characteristic travel behavior in private
and public transport respectively the interaction of those two. Depending on the
purpose of planning, the requirements differ among the transit assignment models
according to the type of transport system modeled, supply and demand representation,
level of details, input and output values, reliability and effort. Each model has strengths
and weaknesses, and suggests specific assumptions about the information provided to
the travelers. Consequently, the results of the models vary.
Traffic assignment models form the core of any travel demand model. They model the
route choice of travelers and thus determine traffic flows on links and on public
transport line routes. Additionally, assignment models provide skim matrices describing
the service quality of a network between origin (O) and destination (D) pairs (OD-pairs).
Private and public transport networks have specific characteristics which need to be
considered in the assignment. This led to the development of a variety of models. The
various public transport assignment models replicate the transport supply, traveldemand, and travel behavior using different levels of modeling detail in representing
supply and demand. They also suggest specific assumptions about the information
provided to the travelers. Consequently, the results of the models differ. The planners
task is to apprehend the model which is most suitable to address to the existing
problem and delivers the most confidential results compared to passenger counts, for
example. Therefore, it is necessary to make the models comprehensible for transport
traffic planners and provide summarized tutorials as well as detailed model evaluations.
But any kind of transport model can always be used to assist the planner. It never
replaces the knowledge of the expert and in the end, the engineer is in charge to take
responsibility for the measurements chosen to improve the current short-comings.
-
7/25/2019 MA_Hartl thesis.pdf
14/115
Introduction
VuV 2013 14
1.2 Research Goals
The objective of the thesis is to facilitate the planners comprehension of the model
characteristics by comparing, explaining, and evaluating the route choice of the
microscopic simulation-based transit assignment model BusMezzo (BM) and themacroscopic schedule-based transit assignment model (SB-TAM) implemented in the
software framework of VISUM.
1.3 Outline of Work
This work starts by presenting a survey in chapter2 Survey on the estimation of the
value-of-time (VoT) for a transfer between two transit lines, as well as the willingness of
passengers to accept longer travel times when traveling in less crowded vehicles
depending on the ratio of volume to capacity. The survey is used as introductory part to
specify some of the fundamental relations between the real world and the simplified
implementations in transit assignment models.
To evaluate the models BusMezzo and the schedule-based transit assignment model
in VISUM, first the fundamentals of modern traffic simulation are outlined in chapter3
Traffic Modeling Fundamentals.Therefore, the different model types according to the
level of aggregation (Micro-, Meso, Macroscopic) and time relation (static vs. dynamic)
are classified followed by a short description of the modeling principles for private and
public assignment models. Furthermore, the impact of information and capacity
restrictions are described. Chapter3 closes with the definition of the deterministic andstochastic user equilibrium.
Chapter4 Simulation-Based Transit Assignment Model explains the principal model
structure of BusMezzo. It concentrates on the subjects of simulation flow, implemented
models, and dynamic path choice models. The latter describes in detail the choice-set
generation process followed by the path choice decision process as well as the
evaluation of alternative paths and the actual path decision. The chapter closes with a
description of real-time information (RTI) in BusMezzo.
Chapter5 presents the principle model structure of the Schedule-Based TransitAssignment Model.It begins with the description of the connection search, followed by
the filtering process of all reasonable connections and the calculation of the
connections impedance. Furthermore, the connection choice and the distribution of
travelers are explained. The chapter closes with an analysis of the impact of the
additionally provided capacity restriction function.
Chapter6 Model Comparison forms the core of the work. It describes the model
classification, travel behavior aspects considered in the model, the comparable level of
the two models, the information degree provided in each model and necessary
simplifications. Additionally, it describes the travel time correlation between VISUM and
-
7/25/2019 MA_Hartl thesis.pdf
15/115
Introduction
VuV 2013 15
BusMezzo which contributes to the description of the example network. Subsequently,
an overview of all comparable parameter sets and scenarios is provided. The
comparison first outlines the model differences in the path choice model, number of
transfers (NrTransfer), and load distribution on public transport lines. Secondly, the
model behavior by increasing the demand, reducing the vehicle capacity, as well as thefrequency is analyzed. The chapter ends with the comparison of different information
levels in BusMezzo.
Chapter7 Conclusionsummarizes the accomplishments and major findings. The thesis
concludes with an evaluation of the results, outlines the strength and weaknesses of
the compared models and formulates recommendations for the application of
BusMezzo and/or the schedule-based transit assignment model in VISUM.
To facilitate the comprehension of the thesis, the term traveler is used as general
expression for somebody who travels in the network. If the characteristics of a traveleris related to VISUM, the expressionpassenger, and respectively to BusMezzo the term
agentis used.
-
7/25/2019 MA_Hartl thesis.pdf
16/115
Survey
VuV 2013 16
2 Survey
The originally idea of the survey was to estimate the coefficients of the utility function,
used in the schedule-based transit assignment model and BusMezzo, in the analysis in
chapter6.Unfortunately, it was not possible, within the limited time of the thesis, toanalyze the survey before implementing the network and running the assignments.
Therefore, the survey is used as introductory part to specify some of the fundamental
relations between the real world and the simplified implementations in transit
assignment models.
Many implemented theories in transit assignment models are derived by observing the
natural behavior of travelers. The observation is transferred into a mathematical
approach to simulate and, especially, to forecast travelers behavior for planning
purposes. One of the major parameters, besides travel time, which influences the route
choice in public transport, is the transfer rate. Since transit assignment models are notable to reflect all influencing parameters in a one-to-one correlation, parameters are
transferred into impedance. The impedance is mainly represented through the unit
time. This means that all influencing parameters with or without a correlation to time
are transferred to a value-of-time. This is also true for the number of transfers. Since
transferring has no direct relation to time, surveys try to estimate the value-of-time
which expresses to what amount travelers would accept to travel with a more time
consuming connection instead of transferring once. This kind of survey is called stated
preference survey (see (Hicks & Turner, 1999) for details). The method of stated
preference tries to derive the value-of-time by providing a choice of several discreteoptions to the respondents. The aim of the survey is to define the coefficient of the
parameter transfer rate for public transport within a travel time shorter than one hour.
Another focus of the survey is to allocate the importance of overcrowded vehicles. It
follows the same principles but analyses the dependency of the value-of-time
depending on the ratio between volume and capacity.
This chapter first presents the structure of the survey. Secondly, the general
information (Gender, Age etc.) of the respondents is analyzed. Finally, the estimation
process is explained and the results are presented.
2.1 Structure of the Survey
The survey is designed in the framework of the web-platform SurveyMonkey and was
conducted in German. The link to participate in this survey was open to public access
for about ten weeks and started in July 2013. The link was available on the homepage
of the Department for Transport Planning and Traffic Engineering of the Institute for
Road and Transport Science, University of Stuttgart and was also passed to the
authors personal mailing list. In total 243, people responded to the survey. About 90%
-
7/25/2019 MA_Hartl thesis.pdf
17/115
Survey
VuV 2013 17
of the participants answered all questions. The survey itself was structured into three
main parts, as seen inTable 1.
Table 1 Survey Structure
Part Type of QueryResponse
Rate
a General information (Table 19) 98 %
b Estimating the value-of-time for one transfer (Table 20) 92 %
c Estimating the value-of-time for overcrowded vehicles (Table 21) 87 %
It was interesting to observe that with the progress of the survey, the response rate
decreased. This is derivable by the motivation of the respondents to finish the survey
along the process of answering the monotonous questions. A complete list of the
translated queries and the corresponding answers are given in AppendixA.
Since it was unforeseeable who would actually participate in the survey, the choice
situations of the stated preference experiment are constructed in a way that everybody
is able to answer them without any additional knowledge. This is done with the best of
authors knowledge to avoid that people cancel the survey before completing all choice
situations but, even more important, that people understand and answer the question
correctly. To make it easy for the survey participants to grasp the context of the
decision situation, the survey is equipped with sketches, pictures and explanatory text
passages given in surveys screenshots inFigure 1.Most of the time, transferring is aregular part of a connection (except direct connections) and therefore most people are
familiar with the personal correlated meaning of it. More difficult to capture is the
parameter congestion and what it means to travel in a crowded vehicle. Especially, the
abstract degree of volume to capacity ratio, explained in chapter2.3 is hard to imagine.
Therefore, pictures are provided to illustrated different degrees of crowded respectively
overcrowded public transport systems
Since the number of questions in a survey is limited to a for the participant acceptable
number, the range of travel time is within one hour. It represents the regular travel time
for inner city OD-pairs. The travel time values of both connections are chosen such thatthe statistical experimental design is most likely to captures all representative travel
times and correlations. To exclude the propagation of the same question order, the
questions in part b and c are given to each respondent randomly. The provided answer
to choose both connections is considered in the analysis as half an answer for each
connection. This is derived by the question type. To force the participants to give an
answer, most questions are carried out as a single select answer. But the possibility to
choose both connections as a third choice is also provided. The assumption: If a
participant would accept both connections but needs to decide which one he/she
chooses, the distribution is equally. That is the reason why the answer for bothconnections can be spitted into half an answer for connections.
-
7/25/2019 MA_Hartl thesis.pdf
18/115
Survey
VuV 2013 18
Figure 1 Screenshots Survey
-
7/25/2019 MA_Hartl thesis.pdf
19/115
Survey
VuV 2013 19
2.2 General Information
Due to the fact that most of the respondents are from the authors family environment
or related to the environment of the University of Stuttgart, the responding group is
characterized as young educated people with an affinity to use public transport as astandard transport mode, but with equally distributed income. Therefore, the amount of
respondents cannot be seen as a representative cross-section of society. The
distribution between female and male is almost equally represented. This is deducible
by analyzing Figure 2 and Figure 3.However, the respondent group is very familiar
with the properties of public transport, hence they are able to rate the queries about the
connection choices properly.
Figure 2 Gender (left), Age (middle), Income (right)
Figure 3 Education Degree (left), Percentage of Main Means of Transportations(middle), Public Transport Modes for Regular Location Chances (right)
-
7/25/2019 MA_Hartl thesis.pdf
20/115
Survey
VuV 2013 20
2.3 Estimation Process
To estimate the value-of-time for the coefficient of the transferring parameter or
discomfort due to crowding, the method of Maximum-Likelihood is used. Maximum-
Likelihood describes a parametric estimation method. The coefficient is simplyestimated to the value which fits with the highest probability to the available data.
According to the surveys structure, the respondent have to weigh a time attractive
against a comfortable connection (non-transfer or less congestion). The impedance of
the connection is expressed by the impedance function for each estimation process
respectively. The impedance is evaluated by the multinomial Logit model (MNL) into a
probability. The likelihood of a connection is weighted by the sum of respondents to
calculate the value-of-time according to the following formula:
() [
]
Where:
Query Impedance of connection for query The amount of respondents chosen connection Value-of-Time for One Transfer
The value-of-time for one transfer is calculated with the given impedance function to
7 min. This corresponds to the range of 5-10 minutes of other surveys and
assumptions in software products or standardized assessments (ITP, VWI, 2006),
(Wardman, 2001). The used impedance function is given below:
Value-of-Time for Overcrowded Vehicles
The meaning of overcrowded vehicles is more difficult to define since the willingness of
spending more time in public transport vehicles compared to the travel time in
congested vehicles depends on the travel time and the volume to capacity ratio.
Compared with the estimation process of transferring, different types of variables are
considered. In both cases, the travel time varies up to one hour among the
connections. Yet while the transfer is a binary decision, in contrary the congestion rate
varies between a half, three-fourths and almost completely full transit vehicle. The
travel time stays the same for each set of the three named volume to capacity ratio
degrees. The respondent needs to balance between the volume to capacity ratio and
the travel time. To estimate the coefficient, the same choice model from the estimation
process from the preview chapter is used. The parameter becomes more important the
-
7/25/2019 MA_Hartl thesis.pdf
21/115
Survey
VuV 2013 21
higher the congestion rate becomes. Therefore, the following impedance function is
used.
The coefficient is calculated to about 13.5 min for an almost completely fullvehicle over all queries. This implementation assumes a linear relationship for the
volume to capacity ratio up to one hour travel time regardless of the in-vehicle time
(IVT). A more appropriate way to define congestion is to take into account the travel
time (PTV VISUM 12.5 Fundamentals, 2012). By estimating the value-of-time for the
same travel time correlation (blue dots) with different degrees of overcrowding,Figure
4 shows a linear relation (trend line). This is comprehensible by the subjective
perception. The longer the travel time and the higher the crowding level, the higher the
discomfort of the connection. Ergo, the connection becomes less attractive andtravelers shift to connections with more travel time and less travelers on board. The
linear correlation is in line with the presented results of (Pownall, Prior, & Segal, 2008)
at the 21st European Transport Conference 2008. The linear crowding function to
capture the effect of congestion is considered in the transport planning software VISUM
and will be discussed in chapter5.
Figure 4 Value-of-Time Congestion
-
7/25/2019 MA_Hartl thesis.pdf
22/115
Traffic Modeling Fundamentals
VuV 2013 22
3 Traffic Modeling Fundamentals
This chapter first presents a classification of the different model types according to the
level of aggregation (Micro-, Meso, Macroscopic) and time relation (static vs. dynamic)
followed by a short description of the modeling principles for private and public transitassignment models. In addition, the impact of information and capacity restrictions are
described. The chapter closes with the definition of the deterministic and stochastic
user equilibrium as a preparatory step to classify the type of equilibrium used in the
model comparison.
3.1 Traffic Model Principles
The typical approach in transport demand models to represent travelers decision
processes is captured with the classical four step algorithm. The algorithm covers the
decision process with the following four sub models (Boyce, 2001):
Trip or traffic generation models determine the
amount of inhabitants activities within a defined time
period. Thereby, focusing on activities, which lead to
a change of location.
Trip distribution or traffic destination choice models
identify the place where the activity takes place.
Modal split or transport mode models describe thetype of transport system which is used for changing
location.
Assignment or route choice models determine the
used path through the network with or without
capacity constraints.
Because route choice affects network elements or skim categories (e.g. travel time),
the traffic demand generally depends on the assignment result. Therefore, a feedback
loop is normally implemented between the sub models.
The transit assignment model emulates the correlation between supply and demand
and mainly calculates three output values (Friedrich, 2012):
Traffic flows: Estimate the route/connection loads for
given OD-pairs.
Loads on single network elements: Calculates the loads for single elements
of the network-like links, nodes, turning
movements, trips or stops.
Skim categories: Determine the skim values e.g. travel
time, travel costs and transits.
-
7/25/2019 MA_Hartl thesis.pdf
23/115
Traffic Modeling Fundamentals
VuV 2013 23
Static Transit Assignment Models
A transit assignment model is called static if the model does not consider a timeline.
Travelers with a fixed origin and destination are distributed onto networks routes
without considering the departure time. This means that demand is assumed to beconstant within the transit assignment period. Therefore, it is not possible for a static
model to provide information about the exact location of a traveler at a specify point in
time (Friedrich, 2012).
Dynamic Transit Assignment Models
A transit assignment model is called dynamic if the model does consider a timeline.
Travelers are distributed onto networks connections with a given departure time at the
origin. A requirement to fulfill the dynamic assumptions is to provide information of the
temporal distribution of a travelers movement along the route. The movement alongthe route is described with a flow model to determine a travelers location at a specific
point in time (Friedrich, 2012).
Depending on the modeled decision, specific names are used for transport models.
Transport Demand Model: Imitates the behavior of an activity decision
process, destination choice, modal split,
departure time choice and route choice for
passenger traffic.
Traffic Flow Model: Simulates the velocity choice, lane choice and
choice of vehiclesheadway in road networks.
Most transit assignment models are classified into three major steps as listed below. To
fulfill stable convergence conditions, some of the steps need an iterative procedure.
Search process: Estimates a set of alternative routes. The routes
are subjected to logical constraints to filter all
reasonable routes which might become
attractive to travelers within the assignment.
Choice process: Models travelers behavior for the route choice
and assigns a suitable proportion of the demand
to the route set.
(Assignment equilibrium vs. decision probability)
Traffic flow models: Simulates the movements of travelers along
their route.
To simulate the movements of travelers along their route, traffic flow models use
different levels of aggregation. They are classified into classes: microscopic,
mesoscopic and macroscopic, according to the level of detail and aggregation.
-
7/25/2019 MA_Hartl thesis.pdf
24/115
Traffic Modeling Fundamentals
VuV 2013 24
Macroscopic Models
According to (Papageorgious, 1997) the macroscopic transit assignment model
describes the transition to the continuum theory. Probably the most famous
macroscopic transit model was developed by Lighthill-Whitham and has its origin in thescientific research field of hydromechanics.
Microscopic Models
Another extreme, according to the level of detail, is the microscopic traffic model.
Vehicles are represented individually and the behavior of each vehicle depends on the
interaction with other vehicles. Additionally, vehicles subject to braking and
acceleration processes, as well as to the characteristics of the transport network (e.g.
light-signal system, right of way rules, lane assignment). Furthermore, the human factor
is considered by the models cognitive and reactive capability. Since some of thecomponents are subjected to stochastic processes the assignment needs to be
repeated until the results present an adequate mean situation of the network.
Mesoscopic Models
Mesoscopic models are a combination of macroscopic and microscopic modeling
approaches. That means that skim categories of the network are used but vehicles are
simulated individually, however, their second-by-second movement is not modeled.
Figure 5 Aggregation Level according to (PTV AG, 2012)
The characteristics of private (PrT) and public transport (PuT) differ significantly.
Therefore, it is necessary to specify individual assignment models separately in order
to simulate the model characteristics properly. Note that the separation of the models is
-
7/25/2019 MA_Hartl thesis.pdf
25/115
Traffic Modeling Fundamentals
VuV 2013 25
required, but the interaction (e.g. bus lines are usually on regular streets and flow with
the surrounding traffic) should not be neglected. The classification and explanation in
chapter3.2 and3.3 are taken from (Friedrich, 2012)
3.2 Private Traffic Assignment Models
A private transport (PrT) model can be described in the major steps. Firstly, a route
search is performed which finds the choice-set of all alternative routes a traveler
considers on his way from his origin to his destination. Secondly, the route choice is
selected, in which the traveler chooses one of the alternative routes in the choice-set
according to the routes utility. And lastly, the traffic flow through the network, in which
vehicles are processed along their chosen routes and interact with each other.
Route Search in Private Transport
Route search methods, as they are provided in navigation systems or on the internet
(e. g. journey planners such as (Google Maps)) are based on shortest-path algorithms.
Only the shortest path according to the travel time is calculated. These mono-criterial
methods consider only one search criterion in the objective function. But the route
choice is influenced by many other factors, e.g. cost, road type, and road charge. To
extend the number of criteria, the variables are transferred with the help of value-of-
time to an abstract value of impedance. Since travelers evaluate the variables
differently, it is advisable to work with bi-criterial methods to obtain all reasonable
routes (Wardman, 2001).
Route Choice in Private Transport
Since the route choice of each traveler reduces the capacity of the chosen path, hence
the travel time increases and the route becomes less attractive to remaining travelers.
For this reason decision models working with probabilities (e.g. Logit, Kirchhoff
(Ortzar & Willumsen, 2011)) are less suitable to simulate the distribution of private
traffic in the network. Instead a load-dependent route choice model is required to
describe the interaction between demand and route choice. These equilibrium models
are designed to the principles of (Wardrop, 1952). The deterministic user equilibrium(DUE) can be extended to a stochastic user equilibrium (SUE) where the traveler
optimizes the perceived travel time rather than the real travel time.
Traffic Flow Model in Private Transport
One of the simplest traffic assignment models is the load-dependent model. The travel
time is calculated for each link individually depending on the utility and volume-delay
function developed by (Bureau of Puplic Roads, 1964).
-
7/25/2019 MA_Hartl thesis.pdf
26/115
Traffic Modeling Fundamentals
VuV 2013 26
Capacity-Depending
Model
Macroscopic Flow
Model
Microscopic Flow
Model
Figure 6 Types of traffic flow models for private transport according to
(Wiedemann, 1974) and (Kemper, 2006)
In macroscopic models, the traffic flow is considered as continuous flow like a fluid
through a pipe. The velocity is derived from the traffic density . The density isdefined as the number of vehicles within a path interval of the length withoutexplicitly modeling lanes or vehicles. The correlation between velocity and density is
presented in the fundamental chart.
The most detailed representation of traffic flow is given in a microscopic traffic
assignment model. The complexity reaches from simple models like the cellular
automate (Nagel & Schreckenberg, 1992) to complex psycho-physical vehicle-following
models (Wiedemann, 1974).
3.3 Public Transit Assignment Models
One of the major differences between private and public transport is the time
dependency. Public transport participants are not able to decide freely when to depart
at their origin, because they depend on the schedule times of the transport system, e.g.
i+1i-1
Link i Link i+1
Link i Link i+1
Individual Vehiclesunified
-
7/25/2019 MA_Hartl thesis.pdf
27/115
Traffic Modeling Fundamentals
VuV 2013 27
bus or train. Therefore, the decision process is extended from a spatial route to a time
dependent connection.
Connection Search in Public Transport
The connection search in public transit assignments is mainly divided into the
categories frequency-based (FB-TAM) and schedule-based transit assignment (SB-
TAM) models:
The frequency-based connection search does not use the actual departure time of
the line nor the exact coordination between lines. It estimates the transfer waiting
time depending on the lines headway (HDWY) and the assumption about the
accessible information. The aspect about the information degree will be discussed in
chapter3.4.The calculated paths do not represent connections. Instead, they are
routes, since no time axis is considered. Merely travel time and headways are thefoundation for the connection search (PTV VISUM 12.5 Fundamentals, 2012). This
search method is mainly used for planning purposes where the coordination of the
timetable is negligible or the line density (e.g. inner city) is so high that travelers do
not coordinate their arrival time. The frequency-based transit assignment model
provides four different levels of information (PTV VISUM 12.5 Fundamentals, 2012):
1. No information and exponentially distributed headway,
2. No information and constant headways,
3. Information about elapsed waiting time,4. Information about the next departure time of the lines from the stop
A search method is called schedule-based if all arrival and departure times of a
public transport line are taken into account. The method assumes that travelers are
provided with exact timetable knowledge and they coordinate their arrival time to the
departure time of the first line (PTV VISUM 12.5 Fundamentals, 2012). The
schedule-based transit assignment is presented in detail in chapter5.
In simulation-based transit assignment models, each individual traveler is provided
with a static pre-defined path set which forms the foundation of the decisionprocess. Along the travelers path the decision process is dynamically applied to the
changing network environment. In terms of the dynamic path choice model, the
output of a travelers path choice is referred to as an adaptive path choice
depending on the travelers progress in the network. Since the decision progress is
a sequence of single decisions, the implemented dynamic path choice model is
dissimilar to static assignment models. Travelers in static assignment models
consider a path choice as a single decision for the whole path. The simulation-based
assignment model implemented in the framework of BusMezzo is presented in
chapter4.
-
7/25/2019 MA_Hartl thesis.pdf
28/115
Traffic Modeling Fundamentals
VuV 2013 28
Connection Choice in Public Transport
Similar to private transport, the travel time and costs play a major role in the decision
process. Additionally, the transfer frequency and the temporal utility influence the
connection choice. The temporal utility describes the difference between the actual andthe desired departure time (PTV VISUM 12.5 Fundamentals, 2012). The demand is
distributed with a probabilistic choice model (e.g. Logit, Kirchhoff (Ortzar & Willumsen,
2011)). This method is also called random utility model since the evaluation process is
based on a utility of each alternative which is split into an objective deterministic and
subjective stochastic proportion. The traveler chooses the option among a set of
alternatives where he/she maximizes his/her utility.
Traffic Flow Model in Public Transport
Another substantial characteristic of public transport is that travelers do not drivethemselves. Instead, they board a public transport system as a passenger. Therefore, it
is necessary to distinguish between travelers and public transit vehicles.
Public transit vehicles are assigned to the network according to the lines timetable.
If all vehicles of a line coordinate their travel time strictly to a timetable, it is called a
microscopic flow model. In contrast, in a microscopic model each vehicle is
simulated individually and considers eventual occurring unreliability, e.g. travel time
fluctuations caused by the current traffic conditions. Since the location to a specific
time point is known, microscopic flow models are able to simulate the interaction
between private and public transport systems.
Public transport participants are introduced to the system as travelers who start their
trip at their origin stop, board the desired vehicle and move through the network on
board their chosen vehicle. The congestion process is captured in macroscopic
models with a feeling of discomfort due to crowding. This means that travelers are in
principle always able to board a vehicle, but the connection might become less
attractive according to a reduced utility because of crowding. Since each traveler is
modeled individually in microscopic models, the vehicle capacity is a strict limitation
of travelers boarding the vehicle. If the vehicle capacity is exceeded, travelers are
denied boarding the vehicle and they need to wait for the next approaching vehicle
or re-evaluate the alternative connections. Since travelers move in vehicles through
the network, this does not affect the travel time of the vehicle besides the extended
boarding and alighting process. The effect of congestion will be discussed in
chapter3.5 in detail.
3.4 Level of Information
Depending on the specific model and the aggregation, different levels of timetable
information are provided to public transport travelers. Therefore, it is necessary todistinguish between two types of information:
-
7/25/2019 MA_Hartl thesis.pdf
29/115
Traffic Modeling Fundamentals
VuV 2013 29
Information level in static assignment models referring to the frequency-based
transit assignment model estimate the information degree of passengers and the
reliability of the public transport system, for example, the waiting time is estimated
as exponentially distributed or half the headway of a line. Additionally, the elapsed
waiting time at a stop or the next departure time of a line from a stop might be usedto calculate the choice-set. The information degree decides indirectly on the
attractiveness of paths and the number of selectable alternative paths. The
assumption of the line reliability is converted into the information provided to
travelers. The decision process is represented as a single decision according the
decision model. The schedule-based transit assignment model assumes full
information and considers the actual departure and arrival time of a line. Hence, the
search process considers paths and the temporal distribution of a line. The process
delivers reasonable alternative connections. Once the choice-set is calculated,
travelers chose their connection as a single decision according to the decision
model. If capacity constraints are considered, the decision process is carried out
iteratively depending on the discomfort factor but the choice-set remains the same.
Simulation-based transit assignment models do not estimate connections. Instead,
they estimate all reasonable paths as a foundation for the dynamically adaptive
decision process. Once the path set is calculated, each traveler faces a sequence of
decisions. The selected path is not an input for the choice model, instead it is the
result of the dynamic sequence of decisions. Since unreliability is simulated, the
timetable is used as coordination for public transport systems to adapt the actual
travel time to the predetermined timetable. This improves the network performance
by regulating the departure time also known as holding strategies. Therefore,
information has a different meaning. It represents the difference between expected
departure/arrival time according to the timetable and the actually departure/arrival
time according the existing situation. This can be referred to as real-time information
(RTI). The degree of real-time information given to travelers influences the amount
(no RTI vs. stop RTI) of information and the place (stop RTI vs. Network RTI) where
information is given to public transport travelers. This will be discussed in detail in
chapter4.2.5.
3.5 Capacity Constraints
Traditional assignment models assume that travel time and costs are the main
attributes influencing travelers decisions. Empirical studies prove that passengers, in
reality, consider several qualitative aspects, which impair or improve the experience of
travelling (Tirachini, Hensher, & Rose, 2013). In the case of public transport, this
includes the number of travelers sharing one bus or train. The relevance of these
qualities becomes more important in developing and developed economies, since the
income of the population increases over time (Tirachini, Hensher, & Rose, 2013).
Consequently, public transport travelers are more likely to attach more value to theservice quality and comfort features (Tirachini, Hensher, & Rose, 2013). The disregard
-
7/25/2019 MA_Hartl thesis.pdf
30/115
Traffic Modeling Fundamentals
VuV 2013 30
for capacity limitations is an unsatisfactorily simplification which does not reflect the
reality in highly loaded public transport systems (PTV VISUM 12.5 Fundamentals,
2012). Capacity limitations can affect travelersdecision process in different ways:
Absolute vehicle capacity: A single vehicle is only able to carry as
many passengers as capacity is allows.
(e.g. BusMezzo)
Discomfort in the vehicle: Travelers feel discomfort due to crowding
in a densely loaded vehicle. The effect can
increase if all seats are occupied. (e.g.
SB-TAM)
Discomfort outside the vehicle: Transferring at a highly frequented transfer
stop is perceived uncomfortable. Aside
from the discomfort, delays may occurbecause of queuing processes.
3.6 Stochastic or Deterministic User Equilibrium
The terms stochastic and deterministic will be widely used in chapter6 to define the
comparable level of the two models, as well as for the determination of the input, output
and data characteristics. To obtain a fundamental comprehension of these
expressions, the following example will be used to clarify the underlying principles.
The example network shown in Figure 7 is simply structured. The demand of 1000vehicles requests to travel between the origin and destination. The network provides
two alternatives; one with short travel time but less capacity and the other one with
longer travel time but more capacity. Depending on the equilibriumsobjective function
the demand will be distributed differently to route 1 and 2. Therefore, the deterministic
(DUE) and stochastic user equilibrium (SUE) as well as the system optimum (SO) will
be highlighted and described.
Equilibrium methods are widely spread in every-day planning to estimate the
distribution of traffic flows in transport networks. To optimize the objective function it isnecessary to distinguish between two deterministic approaches, also known as
Wardrops principles (Wardrop, 1952).
Deterministic User Equilibrium (DUE)
DUE provides full information to travelers and every traveler acts totally rational. The
utility is evaluated by the presented volume-delay function. To optimize the target
function, Wardrops first principle is used: Under equilibrium conditions traffic arranges
itself in congested networks such that all routes between any origin-destination pair
have equal and minimum costs while all unused routes have greater or equal costs.(Wardrop, 1952). In other words, it is not worth changing routes because all other
-
7/25/2019 MA_Hartl thesis.pdf
31/115
Traffic Modeling Fundamentals
VuV 2013 31
routes hold higher or equal impedance and everybody chooses the best route. In the
example networks chart, the two blue solid lines present the impedance (travel time)
for route 1 and 2 according to the actual volume. The equilibrium state is reached if the
condition
is fulfilled.
The approach is based on the principle of the individual trying to maximize the personal
utility. For practical use however, the assumption that travelers are provided with full
information is questionable, because not each traveler can be continuously served with
information or acts without personal preferences (Boden & Treiber, 2009). These
weaknesses are compensated in the stochastic user equilibrium with variables to
estimate spontaneity and individuality and lack of information.
Stochastic User Equilibrium (SUE)
The stochastic user equilibrium assumes that travelers in principle choose the bestavailable route, but evaluate the alternative routes differently due to incomplete
information. In addition, the stochastic assignment for private transport, similar to public
transport, uses a distribution model (e.g. Logit, Kirchhoff (Ortzar & Willumsen, 2011))
to assign demand to alternative routes. In contrast to the deterministic user equilibrium,
the stochastic assignment distributes demand even to suboptimal routes due to the
used distribution model. This approach is closer to reality than the strict application of
Wardrops first principle (PTV VISUM 12.5 Fundamentals, 2012).
In the chart, the red line represents the stochastic impedance for route 1. The input for
the stochastic impedance calculation is the volume from the distribution model .The volume of the distribution model is calculated with the current travel time and a Logit model. The Logit model evaluates the difference of impedance between the
two alternatives. The stochastic equilibrium has reached stable conditions if .The willingness of travelers to accept routes which are more time consuming is
considered in regards to the corresponding parameter of the distribution model. DUE
and SUE correlate with the value of the parameter. The higher the value, the stricter
travelers evaluate the difference in impedance between the two routes and SUE comescloser to a deterministic user equilibrium.
System Optimum (SO)
The system optimum pursues the approach of Wardrops second principle. The aim is
not to equalize all route impedances (DUE) but to minimize the total amount of
impedance in the network. This contributes to the fact that no traveler is able to benefit
without causing damage to other participants. The dashed green line is the weighed
sum of travel time and volume for route 1 and 2. The optimum network condition, in
terms of minimizing impedance (travel time), is fulfilled if the dashed line reaches theminimum .
-
7/25/2019 MA_Hartl thesis.pdf
32/115
Traffic Modeling Fundamentals
VuV 2013 32
Demand CR-Function according to BPR:
,
Route 1: Route 2:
Figure 7 Deterministic vs. Stochastic User Equilibrium
O D
Route 1t0,1= 8Cap1= 500
Dij= 1000
Route 2t0,2= 16Cap2= 800
-
7/25/2019 MA_Hartl thesis.pdf
33/115
Simulation-Based Transit Assignment Model
VuV 2013 33
4 Simulation-Based Transit Assignment Model
The complexity of public transport systems increases with the interaction of various
modes, services, information and communication technologies, and transit operation
strategies. This increases the need of dynamic transit analysis evaluation tools whichrepresent timetables, operation strategies, real-time information, passenger adaptive
choices, and traffic dynamics. In order to simulate the interaction on a detailed scale,
the private transport simulation model Mezzo was developed by (Burghout W. , 2004),
and forms the framework for the private transport model BusMezzo. The developed
microscopic transit model BusMezzo by (Oded & Tomer, 2008) is an extension and
fully integrated in the framework of the mesoscopic traffic simulation model Mezzo. It
allows taking a dynamic perspective while comparing various scenarios of complex
interaction of system components (Centre for Traffic Research, 2013).
This chapter presents the principal model structure of Mezzo followed by theframework of BusMezzo. The chapter concentrates on the explanation of BusMezzo
and responds to additional objects, simulation flow, implemented models, and the
dynamic path choice models. The latter describes in detail the choice-set generation
process followed by the path choice decision process, as well as the evaluation of
alternative paths and the actual path decision. The chapter closes with a description of
real-time information. The explanations and sketches in chapter4 are taken from
(Burghout W. , 2004) and (Cats O. , 2011).
4.1 Mezzo
Most of the existing transit models are time-based assignment models. The core of the
simulation is the progress from one to the next time step while each equally scaled time
step calculates the changes and updates the network status. In contrast, Mezzo is an
event-based traffic simulation tool which progresses from one to the next event. The
model specifies which changes are classified as events and orders them into an event
list. Events are called as they appear in the event stack (Oded & Tomer, 2008).
Vehicles are simulated individually, but lanes are not explicitly presented. The link
structure is divided into a running and a queuing part. The running part is not affected
by the downstream capacity limit and describes the earliest link exit time. The travel
time on the link depends on the ratio between loads and link capacity. The queuing part
imitates the delay process if capacity is exceeded and characterizes the process of
vehicles queuing in a single lane waiting to exit the link. Queue servers determine the
capacity limitation on turning movements. Turning movements are modeled
stochastically to regulate delays. Vehicles are randomly generated following a negative
exponential distribution by time-dependent OD-pair flow matrices according to a pre-
specified vehicle mix. The route choice follows a multinomial Logit model and might be
influenced by the information degree provided to the vehicle.
-
7/25/2019 MA_Hartl thesis.pdf
34/115
Simulation-Based Transit Assignment Model
VuV 2013 34
4.2 BusMezzo
By extending the model Mezzo to simulate the interaction between private and public
transport, the modularized object-orientated framework helps to implement the dynamic
transit operation and assignment model BusMezzo.
4.2.1 Object Framework
Additional classes like bus types, bus vehicles, bus lines, bus routes, bus trips and bus
stops are implemented and define the characteristics of the objects shown inFigure 8.
The subclass vehicle type inherits its characteristics from the object bus type and on
the other hand the object bus vehicle is described by the bus type, bus route, and bus
trip. Each bus trip is assigned to a bus line and a bus route. The bus route is specified
with an ID and an ordered sequence of links. Bus lines initialize the subclass of the
object actions, which defines general procedures in the simulation, determine the
scheduled trips, and the list of stops. The deposited timetable is used as a reference
point for each bus trip to adjust the actual travel time to the timetable with the help of
holding strategies to absorb delays. Stops are allocated to links with the characteristic
assumptions about the spatial position, dwell time, and waiting time of individual
travelers represented by an agent. Each time a bus arrives, the dwell time function
calculates the time the bus needs to spend in the station until all agents are alighted
and have boarded the vehicle, and summarizes the waiting time of agents which are
forced to wait because of denied boarding.
Figure 8 Object-oriented framework for the public transport model BusMezzo
according to (Oded & Tomer, 2008).
-
7/25/2019 MA_Hartl thesis.pdf
35/115
Simulation-Based Transit Assignment Model
VuV 2013 35
4.2.2 Simulation Flow
At the beginning of the simulation all objects are initialized. By initializing the objects,
some of them register an event and save them in the event stack. Most of the events
result in a new sequence of results. Aside from the introduced objects, it is necessaryto implement several new event types to properly represent the transit simulation
model BusMezzo. A general overview of the simulation flow is given in Figure 9.
When the simulation starts, BusMezzo reads the bus line list and generates individual
trips with the corresponding objects bus lines, bus routes and bus types, and registers
the events in the event stack. If the vehicle has not been introduced to the system yet
(first trip on its trip chain), it generates a bus vehicle object and assigns it to the
required bus type. After that, the vehicle enters the first link on the line route. Once a
bus enters a link as sequence of its trip, it checks whether there is a stop and if the bus
services it. If no stop is located on the link, BusMezzo calculates the link travel timedepending on the current traffic conditions. In this case, there is no difference between
vehicles in Mezzo and busses in BusMezzo, because both objects are running on the
same network and are treated as agents with different attributes (e.g. seat capacity,
length). If a stop is on the link, BusMezzo calculates the travel time to the stop, and
books an event for entering the stop. When the bus enters the stop the dwell time is
calculated and the model checks if the bus is subjected to any control strategies (e.g.
coordination of the departure time to a predefined timetable).
The implementation of holding control strategies in the main loop requires additionalsteps to execute the control logic and to determine the appropriate action. For
example, if a bus enters a stop, and holding strategies are activated, the control
strategy checks for how long the bus needs to be held in the station to minimize
accumulated delays according to the timetable and the actual temporal position of the
bus.
The outputs of the queries determine if the process books an event for the stop exit
time. Exiting a stop is similar to entering a link, the model checks if there are any
further stops downstream on the link, calculates the travel time for the link section
based on the traffic conditions and the loop starts over. By reaching the end of its routeBusMezzo checks if any additional trips are assigned to the vehicle. If yes, then the trip
process is activated and progressed through the system (trip chaining). If this is the last
trip of the line, the vehicle terminates.
On the output level, the simulation lists the collected data on stop level for each
individual traveler or bus. The main outputs of BusMezzo are line ID, trip ID, vehicle ID,
stop ID, traveler ID, early and late arrivals, dwell times, boarding and alighting
passengers, occupancy, denied boardings, selected paths, and travel times between
stops. On a larger scale of aggregation, e.g. at trip level, line or OD-stop level, itpresents a summarized list of the chosen paths or line loads.
-
7/25/2019 MA_Hartl thesis.pdf
36/115
Simulation-Based Transit Assignment Model
VuV 2013 36
Figure 9 Flowchart of the transit simulation process according to (Oded & Tomer,
2008)
-
7/25/2019 MA_Hartl thesis.pdf
37/115
Simulation-Based Transit Assignment Model
VuV 2013 37
Number of Replications
BusMezzo, according to its definition, is a stochastic simulation-based transit
assignment model. Therefore, it is necessary to run several simulations in order to find
a meaningful average and to evaluate each execution. Each run of a simulation is asingle shot of the current situation, also called within-day learning. That means that
there is no interdisciplinary exchange between the simulations. In fact, no learning
process takes place as it is performed in a day-to-day learning process. At the current
state, this feature is under development by (Gkioulou, 2013). This would also enable
access to simulate travelers behavior by shifting from overcrowded to less crowded
vehicles depending on travelers practical experience.
To receive statistically verified results, several simulations are needed. To quantify the
number of simulations, the following formula can be used (Dowling, Skabardonis, &
Vassili, 2004).
Where:
number of required simulations mean value on the base of initial simulations
standard deviation on the base of
initial simulations
indicates the student distribution table level of significance allowable error term to estimateAs measurement for the service quality in the analysis of chapter6,the average travel
time is used. To estimate the expected number of required simulations, ten were
calculated and used as a mean base with an allowable error of five percent and a
significance level of . Each result set represents at least the average of tenreplications even if the required calculated number of simulations is below ten. Due to
the simple structure of the example network and the elimination of the stochasticinfluence (see analysis of chapter6), ten simulations are adequate. If the exact number
of simulations is not mentioned, the results are calculated as an average of ten
calculations.
4.2.3 Implemented Models
BusMezzo requires a detailed representation of its basic attributes to describe the main
elements such as travelers arrival and alighting process, dwell time, travel time, and
trip chaining.
-
7/25/2019 MA_Hartl thesis.pdf
38/115
Simulation-Based Transit Assignment Model
VuV 2013 38
Travelers arrival and alighting process
Depending on the line frequency, passengers arrive randomly or coordinate their
departure time to the arrival at the stop to minimize the start waiting time. The line
characteristic strongly depends on the spatial situation where the line runs. Often, thefrequency in urban areas is higher than in rural areas. Therefore, one can say that
people in cities with a dense transit infrastructure network normally do not coordinate
the arrival time to the stop. This is in contrast to rural areas where the start waiting time
could grow largely by missing a connection. In between these characteristic areas or
even within a city, there is a large variety of these assumptions. Investigations in the
1980s e.g. by (Abkowitz & Tozzi, 1987) showed that the threshold between
coordination and random arrival to board a line is estimated to the dimension of ten
minutes headway.
BusMezzo is continuously developed to simulate the impact of Stockholms busnetwork and to analyze the network structure. The frequency in the capital of Sweden
is relatively high in the inner city and decreases the further the lines go outside to
sparsely populated areas. Although there are discrepancies in the literature, most
research indicates a Poison distribution to describe the right skewed arrival process
(Fu & Yang, 2002), (Dessouky M. , Hall, Zhang, & Singh, 2003) and a Binomial
distribution for travelers alighting process (Morgen, 2002), (Liu & Wirasinghe, 2001).
This assumption is also adopted in BusMezzo.
Dwell Time
The implemented travel time calculation consists of two parts. One is the riding time
between stops, which depends on the vehicle density and the dwell time. The dwell
time describes the process at the stop from the start of opening the doors, travelers
boarding and alighting until the transit vehicle closes the door and leaves the stop to
enter the link again. The dwell time function implemented in BusMezzo is based on the
Transit Capacity and Quality of Service Manual (Kittelson & Associates, KFH Group,
Parsons Brinkkerhoff Quade & Douglass, & Hunter-Zawarski, 2003). This approach
distinguishes between boarding and alighting separately for each door. The door with
the longest service time is crucial for the dwell time. If the bus stop is placed in-lane oruses a bus bay, the delay time is captured by the used function because more time is
needed to re-join the traffic flow. The dwell time function is given by:
-
7/25/2019 MA_Hartl thesis.pdf
39/115
Simulation-Based Transit Assignment Model
VuV 2013 39
Where:
is the dwell time for line at stopon trip is the required service time for the front respectively rear door. Itdepends on the total number of travelers boarding and alightingand the crowding level on the bus indicates if the bus top is in-lane or a bus bay describes the physical space at the bus stop (e.g. 20 meters) are parameters to specify the dwell time function describes the error term for unpredictable events
To support the implemented holding strategies, the departure time is given by the
following formula for line
at stop
on trip
:
Where:
Departure Time Actual Arrival Time Dwell Time Departure Time as results of the holding strategyTravel Time
The driving time between stops is the major part of a transit trip. Levinson (Levinson,
1983) estimated in his research that 9 to 26 percent of the total travel time is
contributed to dwell time and 12 to 26 percent of the time is spend in traffic delays. The
variables affecting the riding time in urban busses are subjected to deceleration and
acceleration processes due to the high density of stops every few hundred meters.
Depending on the independency of the public transport system (bus on links floating
with PrT vs. trains on independent rail tracks) the travel time reliability increases while
the service variability decreases. According to several researchers, the travel time ofbusses and the arrival process tends to follow a right skewed distribution (Strathman,
et al., 1999), (Dessouky M. , Hall, Nowroozi, & Maurikas, 1999). BusMezzo keeps the
flexibility according to the estimated distribution and provides several functions like
normal, lognormal, Gumbel and gamma distribution to describe the travel time
variability with its characteristic runs.
Trip chaining
Besides the published timetables which show the service frequency to public transport
users, an additional schedule exists. It is known as a driving roster and is used by the
-
7/25/2019 MA_Hartl thesis.pdf
40/115
Simulation-Based Transit Assignment Model
VuV 2013 40
operating company to manage the fleet and driver coordination. Each transit vehicle
and driver needs to fulfill a certain workload within a working period. From the time a
transit vehicle leaves the depot until it returns for servicing, it makes several trips.
Therefore, it is required to simulate trip chains. Mezzo usually generates and eliminates
vehicles between OD-pairs. But transit vehicles have different characteristics thanprivate vehicles. That is why busses should only be eliminated when they reach the
destination of their last trip. If busses would not be affected by unreliability and were
always on time, trip chains would be unnecessary. Since traffic is subjected to
stochastic processes, the feature of trip chains is needed to simulate the propagation of
delays and layover times adequately. Layover times have the goal to buffer delay to
avoid delay propagations along the route. Layover times may be spread along the line,
at the end of the line or a combination of the two (TCRP, 2003). Alternatively, these
recovery times are necessary for servicing (e.g. refuel) and breaks for drivers. Thus,
there is always some recovery time needed. The actual departure time of a trip from
the origin bus stop (dispatching time) is calculated as the maximum between the
schedule departure time and the arrival time of the bus from the previous trip at the
origin stop of the following trip plus a minimum recovery time plus a lognormal
distributed error term describing the stochastic departure delays. The actual
dispatching time is given by:
Where:
Actual Departure Time for trip by bus Schedule Departure Time for trip by bus describes the arrival time of bus from the previous trip minimum recovery time presents the stochastic error term of the recovery time.The following chapter describes the demand side of the model, specifies the generation
procedure of travelers and the dynamic path choice model.
4.2.4 Dynamic Path Choice Model
The transit path choice model approach in BusMezzo is a two stage choice process
shown in Figure 10. The first stage is determined by the base of the deterministic
network configuration (timetable and walking distances), the static path set for each
given OD-pair and uses it as input for the dynamic path choice model. Each generated
agent takes successive decisions along its path which is triggered by events. Each
alternative is evaluated by agents preferences and expectations. The expectations
depend on prior knowledge and the accessibility to real-time information. Agents
choice execution relies on capacity restriction.
-
7/25/2019 MA_Hartl thesis.pdf
41/115
Simulation-Based Transit Assignment Model
VuV 2013 41
The separation allows determining a general set of paths as a pre-assignment step and
hence this step needs to be executed only once. It optimizes the performance in terms
of computing time, but it is no essential requirement for the principle work flow of the
model. Therefore, this step could be implemented either statically or dynamically.
Figure 10 Two-Stage Modeling Approach according to (Cats O. , 2011)
4.2.4.1 Choice-Set-Generation
The spatial choice-set generation is the basis for the dynamic path choice model. In
terms of route choice, the path choice is not trivial and aims to find all reasonable paths
for given OD-pairs. Because the path set is used as input for the path choice, the
model needs to also find paths for OD-pairs with no demand since they might become
attractive alternatives under some circumstances during the dynamic assignment. The
elimination process of paths is an optimization problem between dismissing irrelevant
paths and keeping the majority of the travelers used paths. By referring to the
elimination criterion of the schedule-based assignment model in chapter5,both models
face the same problem in this step of the assignment but the number of paths in
VISUM will be the same or even more likely smaller compared to BusMezzo. The
filtering rules in BusMezzo are looser than in VISUM, because agents are facing the
decision of alternative connections dynamically. Note that the path set in VISUM is a
subset of BusMezzos path set. The principles in this assignment step are the same for
both models. Figure 11 shows a general overview of the choice-set generationprocess. The dashed line in the figure marks the steps until the models assume the
same approaches. After this, different settings regarding the strictness of the filtering
process can be applied.
-
7/25/2019 MA_Hartl thesis.pdf
42/115
Simulation-Based Transit Assignment Model
VuV 2013 42
Figure 11 Flowchart of the Choice-Set-Generation Model according to (Cats O. ,2011)
Path Generator