CONTENTS
Preface V
1 Introduction1
1.1 Motivation and approach
Network representation 2
Modes of travel 3
Network equilibrium 3
Generalised costs 5
Demand curves 6
Link cost functions 6
Supply curves 10
Intermodal equilibrium 12
User benefit and surplus 14
Time dependency 1§
Structure of the book 15
2 Transportation Networks 17
Introduction 17
Network terminology 19
Transportation network types 21
Flow and cost variables 22
Incidence matrices 24
Conservation relationships 25
Shortest path algorithms 29
Path enumeration and column generation 29
Link choice probabilities 33
Utility maximisation and expected minimum cost 34
Network capacity 34
Space-time networks 37
Network equilibrium 40
Concluding remarks 40
3 Optimality
Introduction 41
Kinds of variable 41
Matrix operations 42
Objective functions 45
Constraints 47
Optimality conditions 49
Dual variables 51
Lagrangian equation 54
Sensitivities 56
Method of successive averages 59
Iterative balancing 59
Summary 61
Notation 65
4 Cost Functions 67
Introduction 67
Traffic representation 67
Link costs 68
Junction costs 72
Priority junctions 78
Signal controlled junctions 78
Discussion 82
5 Deterministic User Equilibrium Assignment 83
Introduction 83
Existence and uniqueness ' 86
Solution algorithms 89
Sensitivity 95
Most likely path flows 100
Elastic demand 102
Time-dependent networks 108
Discussion 111
6 Stochastic User Equilibrium Assignment 113
Introduction 113
Existence and uniqueness 115
A general equivalent optimisation problem 118
Logit assignment 120
Probit assignment 133
Sensitivity 134
Elastic demand 138
Space-time networks 140
Discussion 148
7 Trip Table Estimation 149
Introduction 149
Maximum entropy 150
An generalised least squares 155
Bi-level programming 156
Linear path flow estimation 160
Log-linear path flow estimation 164
Time-dependent methods 170
Conclusions 176
8 Network Reliability 179
Introduction 179
Connectivity 179
Structure function 180
Structure function and reliability value 183
Exact methods 185
Heuristic methods 186
Travel time reliability 191
Future challenges 192
9 Network Design 193
Introduction 193
Objective function 195
Bi-Level programming 196
Sensitivities 197
Numerical example 199
Conclusions 204
10 Conclusions 205
Network equilibrium 205
Traffic assignment 206
Path flow estimation 207
Network reliability 208
Network design 208
References 209
Index 215