Table of Contents
Preface vii
List of Figures xiii
List of Tables xv
Notation xvii
I Optimal toll design problem specification 1
1 Introduction 3
1.1 Pricing as a policy instrument in transport planning . . . . . . . . . . . . 3
1.2 Research context of the thesis . . . . . . . . . . . . ………… 5
1.3 Planning context of a toll system design tool . . . . . . . . . . . . . . . . 7
1.4 A multi-actor perspective on the road pricing policy problem . . . . . . . 9
1.5 Research issues of the thesis ………….. . . . . . . . . . . 13
1.6 Scientific and practical contributions of the thesis . . . . . . . . . . . . . 14
1.7 Set-up of the thesis . . . . . . …………. . . . . . . . . . . 15
2 The road pricing design problem: elaboration of key concepts 19
2.1 Introduction . . . . . . . . . . . ………….. . . . . . . . . 19
2.2 Policy objectives/purposes of road pricing . . . . . . . . . . . . . . . . . 20
2.3 Conditions and constraints . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.4 Tolling regimes . . . . . . . ………….. . . . . . . . . . . 23
2.5 Operationalization of possible tolling regimes . . . . . . . . . . . . . . . 25
2.5.1 An overview of some possible tolling regimes . . . . . . . . . . . 25
2.5.2 Mathematical formulations of different tolling regimes . . . . . . 28
2.6 Problem types for road pricing studies . . . . . . . . . . . . . . . . . . . 30
2.7 Summary of literature on road pricing . . . . . . . . . . . . . . . . . . . 33
2.7.1 The first-best pricing problems . . . . . . . . . . . . . . . . . . . 33
2.7.2 The second-best pricing problems . . . . . . . . . . . . . . . . . 34
2.7.3 Dynamic road pricing problem . . . . . . . . . . . . . . . . . . . 34
2.8 Research approach in this thesis . . . . . . . . . . . . . . . . . . . . . . 37
2.9 Summary and Conclusions . . …………. . . . . . . . . . . 39
ix
x TRAIL Thesis series
II Micro-foundations of road pricing – a game theory approach 43
3 Conceptual analysis of the road pricing problem – a game theory approach 45
3.1 Introduction . . . . . . . . . . . ………….. . . . . . . . . 45
3.2 Basic concepts of game theory . . . . . . . . . . . . . . . . . . . . . . . 47
3.2.1 Basic notions of a game …………. . . . . . . . . . . 47
3.2.2 Basic notions of different game types . . . . . . . . . . . . . . . 48
3.2.3 Basic notions of different game concepts . . . . . . . . . . . . . . 48
3.2.4 Classification of games – an overview . . . . . . . . . . . . . . . 50
3.3 Literature review of game theory applied to transportation problems . . . 50
3.3.1 Transportation problems and game theory . . . . . . . . . . . . . 50
3.3.2 Heterogeneous users . . . . . . . . . . . . . . . . . . . . . . . . 53
3.4 Game theory concepts applied to the optimal toll design problem with
heterogeneous users . . . . . . …………. . . . . . . . . . . 53
3.5 Problem definition of the optimal toll design problem as a non-cooperative
game and assumptions . . . . . ………….. . . . . . . . . 56
3.6 Model formulation of the optimal toll design game . . . . . . . . . . . . 57
3.6.1 Inner level game: Network equilibrium problem . . . . . . . . . . 59
3.6.2 Outer level game: toll design problem . . . . . . . . . . . . . . . 60
3.7 Different objectives of the road authority in the optimal toll design problem 60
3.8 Different game concepts applied to the optimal toll design problem . . . . 61
3.8.1 Monopoly game (’social planner’ game) . . . . . . . . . . . . . . 62
3.8.2 Stackelberg game . . . . ………….. . . . . . . . . 62
3.8.3 Cournot game . . . . . . ………….. . . . . . . . . 64
3.9 Summary and Conclusions . . …………. . . . . . . . . . . 66
4 Solving the optimal toll design game using game theory – a few experiments 69
4.1 Introduction . . . . . . . . . . . ………….. . . . . . . . . 69
4.2 A few experiments including different policy objectives . . . . . . . . . . 70
4.3 Case Study 1: Policy objective of the road authority: Maximizing total
travel utility . . . . . . . . . . . ………….. . . . . . . . . 73
4.3.1 Monopoly (social planner) game . . . . . . . . . . . . . . . . . . 74
4.3.2 Stackelberg game solution . . . . . . . . . . . . . . . . . . . . . 75
4.3.3 Cournot game . . . . . . ………….. . . . . . . . . 79
4.3.4 Comparison of games for the policy objective of maximizing the
total time utility . . . . . ………….. . . . . . . . . 80
4.4 Case Study 2: Policy objective of the road authority: Maximizing total
toll revenues . . . . . . . . . . . ………….. . . . . . . . . 81
4.5 Case Study 3: Policy objective of the road authority: Maximizing social
surplus . . . . . . . . . . . . . . . . . ……….. . . . . . . . . 82
4.6 Comparison among different policy objectives with regard to Stackelberg
game . . . . . . . . . . . ……………. . . . . . . . . . . 84
4.7 Case Study 4: Optimal toll design game with heterogeneous users . . . . 85
4.8 Summary and Conclusions . . …………. . . . . . . . . . . 87
CONTENTS xi
III Macro-foundations of road pricing- bi-level modeling framework 89
5 Mathematical formulation of the dynamic optimal toll design (DOTD) problem 91
5.1 Introduction . . . . . . . . . . . ………….. . . . . . . . . 91
5.2 DOTD problem as a bi-level network design problem . . . . . . . . . . . 92
5.3 Framework of the DOTD problem formulation . . . . . . . . . . . . . . . 94
5.3.1 MPEC problem – general formulation . . . . . . . . . . . . . . . 95
5.3.2 MPEC formulation of the DOTD problem . . . . . . . . . . . . . 96
5.4 Toll constraints . . . . . . . ………….. . . . . . . . . . . 97
5.5 Policy objective functions ……………. . . . . . . . . . . 98
5.6 Summary and Conclusions . . …………. . . . . . . . . . . 100
6 Mathematical formulation of the travelers’ behavior of the DOTD problem 101
6.1 Introduction . . . . . . . . . . . ………….. . . . . . . . . 101
6.2 DTA problem formulations ………….. . . . . . . . . . . 102
6.3 Framework of the DTA model for road pricing . . . . . . . . . . . . . . . 103
6.4 Travel behavior model for road pricing . . . . . . . . . . . . . . . . . . . 106
6.4.1 Specification of the generalized travel cost function to capture
road pricing . . . . . . . . . . ……….. . . . . . . . . 106
6.4.2 Dynamic stochastic user equilibrium conditions . . . . . . . . . . 108
6.4.3 Route and departure time choice models . . . . . . . . . . . . . . 108
6.4.4 VI problem formulation of the DTA for road pricing . . . . . . . 109
6.5 DNL component of the proposed DTA model . . . . . . . . . . . . . . . 110
6.6 Summary and Conclusions . . …………. . . . . . . . . . . 112
IV Computational experiments 113
7 Computational experiments on ‘small-networks’ 115
7.1 Introduction . . . . . . . . . . . ………….. . . . . . . . . 115
7.2 Toll patterns adopted in the experiments . . . . . . . . . . . . . . . . . . 116
7.3 Experimental set-up of the DOTD problem . . . . . . . . . . . . . . . . . 117
7.4 Case studies on a corridor network (E1 − E4) . . . . . . . . . . . . . . . 120
7.4.1 Description of a corridor network (the supply part of the DOTD
problem) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
7.4.2 Travel demand input . . ………….. . . . . . . . . 122
7.4.3 Experiments on corridor network with groups of travelers with
different VOT only (E1, E2) . . . . . . . . . . . . . . . . . . . . 123
7.4.4 Additional case studies (E3 and E4) with groups of travelers with
different parameters for VOT and VOSD . . . . . . . . . . . . . . 132
7.4.5 Discussion of corridor experiments (E1 – E4) . . . . . . . . . . . 136
7.5 Case studies with dual route network (E5-E10) . . . . . . . . . . . . . . 137
xii TRAIL Thesis series
7.5.1 Network description . …………. . . . . . . . . . . 137
7.5.2 Link travel time functions . . . . . . . . . . . . . . . . . . . . . . 138
7.5.3 Zero-toll case . . . . . . ………….. . . . . . . . . 139
7.5.4 Toll pattern . . . . . . . ………….. . . . . . . . . 139
7.5.5 Results with tolls . . . …………. . . . . . . . . . . 139
7.5.6 Discussion of experiments E5 − E10 . . . . . . . . . . . . . . . 145
7.6 CASE Study 3: Case studies with a multiple OD-pair network (E11, E12) 145
7.6.1 Network description . …………. . . . . . . . . . . 146
7.6.2 Link travel time functions . . . . . . . . . . . . . . . . . . . . . . 146
7.6.3 Travel demand description and input parameters . . . . . . . . . . 148
7.6.4 Zero toll case . . . . . . ………….. . . . . . . . . 148
7.6.5 Toll pattern . . . . . . . ………….. . . . . . . . . 149
7.6.6 Results with tolls on links 2 and 5 . . . . . . . . . . . . . . . . . 150
7.6.7 Discussion of results ………….. . . . . . . . . . . 153
7.7 Summary and conclusions from experiments . . . . . . . . . . . . . . . . 154
8 Conclusions and Further Research 157
8.1 Scope of conducted research ………….. . . . . . . . . . . 157
8.2 Summary of conducted research . . . . . . . . . . . . . . . . . . . . . . 159
8.3 Findings and Conclusions . . ………….. . . . . . . . . . . 160
8.4 Recommendations . . . . . . ………….. . . . . . . . . . . 162
Bibliography 165
Summary 177
Sadrzaj 181
About the author 185
TRAIL Thesis Series 187
Abstract
The subject of this thesis is the application of dynamic road pricing in dynamic networks.Both forms of dynamics represent the outstanding elements of this dissertation. Its objective is the formulation and testing of a design methodology for an optimized tolling system for road networks.
Download Paper