ma_hartl thesis.pdf

7/25/2019 MA_Hartl thesis.pdf

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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


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Abstract

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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


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Abstract

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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.


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Abstract

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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.


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Zusammenfassung

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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


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Zusammenfassung

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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,


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Zusammenfassung

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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.


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Selbstndigkeitserklrung

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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


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Glossary

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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


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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


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Contents

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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


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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


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Introduction

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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.


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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


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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.


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Survey

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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%


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Survey

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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.


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Figure 1 Screenshots Survey


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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)


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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


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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


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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.


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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.


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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


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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).


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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


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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.


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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:


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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


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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


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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 .


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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


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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.


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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).


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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.


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Figure 9 Flowchart of the transit simulation process according to (Oded & Tomer,

2008)


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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.


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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:


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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


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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.


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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.


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Figure 11 Flowchart of the Choice-Set-Generation Model according to (Cats O. ,2011)

Path Generator

ma_hartl thesis.pdf

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