Acronyms p. xiii
Glossary of Notation p. xv
Preface p. xix
1 Introduction p. 1
1.1 Background p. 1
1.2 Theoretical Developments p. 1
1.2.1 The first-best pricing problem p. 2
1.2.2 The second-best pricing problems p. 3
1.2.3 Value of time and road pricing p. 4
1.2.4 Equity issues and revenue redistribution in road pricing p. 5
1.2.5 The road pricing and capacity choice problem p. 6
1.2.6 Mathematical programming approach to road pricing p. 8
1.2.7 Dynamic road pricing problem p. 9
1.3 Outline of the Book p. 10
2 Fundamentals of User-Equilibrium Problems p. 13
2.1 Introduction p. 13
2.2 Formulations of the Standard User-Equilibrium (UE) Problems p. 15
2.2.1 The UE model with fixed demand p. 15
2.2.2 Solution method for the fixed demand UE problem p. 17
2.2.3 The UE model with elastic demand p. 19
2.2.4 Solution method for the elastic demand UE problem p. 20
2.3 Traffic Assignment with Link Capacity Constraints p. 22
2.3.1 Model formulation p. 22
2.3.2 Solution algorithm p. 24
2.4 Traffic Assignment with Non-Separable Link Travel Time Functions p. 27
2.4.1 Asymmetric link flow interactions p. 27
2.4.2 Symmetric link flow interactions p. 30
2.4.3 Flow interactions between multiple types of vehicles p. 31
2.4.4 Positive definiteness of link cost functions with flow interactions p. 31
2.4.5 Practical asymmetric link cost functions p. 32
2.4.6 Diagonalization solution algorithm p. 34
2.5 Traffic Assignment of Multi-Class Users with Different Values of Time p. 34
2.5.1 Model formulation p. 35
2.5.2 Equivalence of the time-based and cost-based multi-class traffic equilibrium p. 36
2.6 Traffic Assignment with Non-Additive Path Costs p. 38
2.6.1 Model formulation p. 38
2.6.2 Solution algorithm p. 39
2.6.3 An analytical example p. 40
2.7 Traffic Assignment with Stochastic Route Choice p. 41
2.7.1 Utility function and discrete route choice model p. 41
2.7.2 Model formulation with fixed demand p. 42
2.7.3 Model formulation with elastic demand p. 43
2.8 System Optimum Traffic Assignment p. 43
2.9 Sources and Notes p. 45
3 The First-Best Road Pricing Problems p. 47
3.1 Introduction p. 47
3.2 Marginal-Cost Pricing under Standard User-Equilibrium p. 48
3.2.1 Graphical interpretation p. 48
3.2.2 Fixed demand case p. 50
3.2.3 Elastic demand case p. 52
3.3 Marginal-Cost Pricing with Link Capacity Constraints p. 54
3.3.1 Pricing model with capacity constraints p. 54
3.3.2 Speed-flow relationship for congestion pricing p. 56
3.4 Marginal-Cost Pricing with a Total Environmental Quality Constraint p. 60
3.5 Marginal-Cost Pricing with Link Flow Interactions and Multiple Vehicle Types p. 62
3.5.1 The case with link flow interactions p. 62
3.5.2 The case with multiple vehicle types p. 63
3.6 Marginal-Cost Pricing and Uniqueness of Social Optimum p. 64
3.6.1 Uniqueness of OD demands p. 64
3.6.2 Uniqueness of link flows with separable link cost functions p. 65
3.6.3 Uniqueness of link flows with non-separable link cost functions p. 66
3.6.4 Analytical examples p. 71
3.7 Marginal-Cost Pricing under Stochastic User Equilibrium p. 74
3.7.1 Economic benefit measure and maximization p. 74
3.7.2 Equivalence to the minimization of expected perceived travel cost p. 76
3.7.3 An analytical example p. 77
3.8 Summary p. 79
3.9 Sources and Notes p. 79
4 The Second-Best Road Pricing Problems: A Sensitivity Analysis Based Approach p. 81
4.1 Introduction p. 81
4.2 Formulation as a Mathematical Program with Equilibrium Constraints p. 82
4.3 Sensitivity Analysis of Traffic Equilibria with Pricing p. 84
4.3.1 Sensitivity analysis of the restricted network equilibrium problem p. 84
4.3.2 Relations to other gradient-based sensitivity analysis methods p. 91
4.3.3 Dissection of sensitivity analysis with analytical examples p. 93
4.3.4 A sensitivity analysis based algorithm p. 108
4.4 Applications of the Sensitivity Analysis Method p. 109
4.5 Traffic Restraint and Road Pricing Problem p. 113
4.5.1 A conceptual framework p. 113
4.5.2 Direct solution with the queuing network equilibrium model p. 114
4.5.3 Non-uniqueness of link tolls for environmental capacity constraint p. 116
4.5.4 Selection of optimal tolls by bi-level programming p. 117
4.6 Summary p. 120
4.7 Sources and Notes p. 121
5 The Second-Best Road Pricing Problems: A Gap Function Based Approach p. 123
5.1 Introduction p. 123
5.2 Marginal Function Based Approach p. 124
5.2.1 Gap function for the VI based traffic equilibrium models p. 124
5.2.2 Gap function for the optimization based traffic equilibrium models p. 127
5.2.3 Reformulation as continuously differentiable optimization problems p. 129
5.2.4 A scheme of the augmented Lagrangian algorithm p. 130
5.3 Applications of the Gap Function Approach p. 131
5.4 Entry-Exit Based Toll Design Problems p. 139
5.4.1 A UE model with entry-exit specific tolls p. 140
5.4.2 Solving the UE model with entry-exit specific tolls by network decomposition p. 144
5.4.3 Alternative tolling schemes p. 146
5.4.4 BLPP formulation and gap function approach p. 148
5.4.5 Solution by the augmented Lagrangian algorithm p. 150
5.4.6 Numerical example and discussion of results p. 153
5.5 Summary p. 159
5.6 Sources and Notes p. 160
6 Discriminatory and Anonymous Road Pricing p. 161
6.1 Introduction p. 161
6.2 Toll Properties for the Single Class UE and SO Problems p. 163
6.2.1 Characterization of link tolls for SO p. 163
6.2.2 A simple example for the valid link toll set to decentralize SO p. 166
6.3 Time-Based and Cost-Based Multi-Class UE and SO Problems p. 168
6.3.1 System optimum in time units and pricing for equilibrium p. 169
6.3.2 System optimum in cost units and pricing for equilibrium p. 174
6.3.3 Analytical examples p. 176
6.4 Multiple Equilibrium Behaviors and SO Problems p. 181
6.4.1 UE-CN multiple behavior equilibrium and system optimum p. 182
6.4.2 Anonymous link tolls to decentralize a system optimum p. 186
6.4.3 An analytical example p. 189
6.5 Multi-UE-Class and Multi-CN-Class Behavior Equilibrium and SO Problem p. 192
6.5.1 Multi-criteria and multiple behavior equilibrium and system optimum p. 193
6.5.2 Anonymous link tolls to decentralize a system optimum p. 195
6.5.3 An analytical example p. 197
6.6 Summary p. 200
6.7 Sources and Notes p. 201
7 Social and Spatial Equities and Revenue Redistribution p. 203
7.1 Introduction p. 203
7.2 The Social and Spatial Inequity: An Example p. 204
7.3 Redistribution of Congestion Pricing Revenue p. 210
7.3.1 Existence of a Pareto refunding scheme p. 210
7.3.2 Design of Pareto refunding schemes p. 218
7.3.3 Remarks on the Pareto refunding schemes p. 224
7.4 Network Toll Design Models with Equity Constraints p. 225
7.4.1 Traffic equilibrium and social welfare with pricing p. 225
7.4.2 Specification of equity constraints p. 226
7.4.3 Network toll design with equity constraints p. 228
7.5 Alternative Solution Approaches p. 230
7.5.1 Solution for bi-level model p. 230
7.5.2 Solution for tri-level model p. 232
7.6 A Numerical Example p. 232
7.7 Summary p. 237
7.8 Sources and Notes p. 238
8 Pricing, Capacity Choice and Financing p. 239
8.1 Introduction p. 239
8.2 User Equilibrium and Performance Evaluation for Private Toll Roads p. 240
8.2.1 Multi-class UE model with elastic demand p. 240
8.2.2 Alternative performance measures p. 241
8.3 Profitability, Social Welfare Gain and Optimal Price-Capacity Adjustments p. 243
8.3.1 Experiment setting p. 243
8.3.2 Characterization and analysis of numerical results p. 245
8.4 Profitability and Welfare Gain of Private Toll Roads with Heterogeneous Users p. 247
8.4.1 Experiment setting p. 248
8.4.2 Characterization and analysis of numerical results p. 251
8.5 Self-Financial in General Networks p. 255
8.5.1 Self-financing rules with a single type of vehicles p. 255
8.5.2 Self-financing rules with multiple types of vehicles p. 263
8.6 Competition and Equilibria of Private Toll Roads p. 267
8.6.1 Monopolistic competition p. 267
8.6.2 Alternative formulation p. 268
8.6.3 Solution methods p. 270
8.6.4 Two analytical examples p. 272
8.6.5 Graphical characterization of toll competition p. 274
8.7 Summary p. 281
8.8 Sources and Notes p. 282
9 Simultaneous Determination of Optimal Toll Levels and Locations p. 283
9.1 Introduction p. 283
9.2 The Link-Based Pricing: Methodology p. 284
9.2.1 Genetic algorithm for determination of optimal tolling links p. 284
9.2.2 Selection of minimal number and locations of tolling links p. 287
9.3 The Link-Based Pricing: Example p. 287
9.4 The Cordon-Based Pricing: Methodology p. 290
9.4.1 Mathematical properties of toll cordons p. 291
9.4.2 Types of cordon p. 294
9.4.3 Determination of tolling cordons p. 296
9.5 The Cordon-Based Pricing: Example p. 301
9.5.1 Determination of location of a single-layered tolling cordon p. 303
9.5.2 Determination of location of double-layered tolling cordons p. 303
9.5.3 Impact of the cordon-based pricing on trip length distribution p. 304
9.5.4 Sensitivity analysis of demand elasticity p. 306
9.6 Summary p. 306
9.7 Sources and Notes p. 307
10 Sequential Pricing Experiments with Limited Information p. 309
10.1 Introduction p. 309
10.2 Implementation of the First-Best Pricing Scheme p. 310
10.2.1 An iterative toll adjustment procedure for a single road p. 310
10.2.2 An iterative toll adjustment procedure for a general network p. 313
10.2.3 Proof of convergence p. 316
10.2.4 A numerical example p. 320
10.3 Implementation of the Second-Best Pricing Scheme p. 325
10.3.1 A sequential implementation procedure p. 325
10.3.2 Sequential linear approximation p. 328
10.3.3 Two numerical examples p. 329
10.4 Implementation of the Traffic Restraint and Road Pricing Scheme p. 335
10.4.1 The primal and dual formulation p. 335
10.4.2 Trial-and-error implementation procedure p. 337
10.4.3 A numerical example p. 339
10.5 Summary p. 341
10.6 Sources and Notes p. 343
11 Bounding the Efficiency Gain or Loss of Road Pricing p. 345
11.1 Introduction p. 345
11.2 Maximum Efficiency Gain of First-Best Pricing Schemes p. 346
11.2.1 Efficiency gain with fixed demand p. 346
11.2.2 Efficiency gain for cost functions with limited congestion effects p. 352
11.2.3 Efficiency gain with elastic demand p. 354
11.3 Inefficiency of Stochastic User Equilibria p. 358
11.3.1 Determination of the cost inefficiency bound p. 358
11.3.2 Interpretation of the cost inefficiency bound p. 362
11.4 Inefficiency of Cournot-Nash Equilibria p. 363
11.4.1 CN equilibrium with a finite number of players p. 363
11.4.2 Upper-bound of the inefficiency of CN equilibria p. 365
11.4.3 Upper-bound of special cases and a numerical example p. 367
11.5 Maximum Efficiency Loss of Second-Best Pricing Schemes p. 369
11.5.1 Measure of efficiency loss p. 369
11.5.2 Bound for traffic equilibria with fixed demands p. 370
11.5.3 Bound with polynomial cost functions p. 375
11.5.4 Bound for traffic equilibria with elastic demands p. 378
11.5.5 Alternative approach for bounding efficiency loss p. 383
11.5.6 Determination of the inefficiency bound for actual pricing schemes p. 384
11.6 Summary p. 387
11.7 Sources and Notes p. 387
12 Dynamic Road Pricing: Single and Parallel Bottleneck Models p. 389
12.1 Introduction p. 389
12.2 Single Bottleneck Models p. 389
12.2.1 The case with homogeneous commuters p. 390
12.2.2 The case with heterogeneous commuters p. 395
12.3 Parallel Bottleneck Models p. 400
12.3.1 Dynamic tolls on all routes p. 400
12.3.2 Dynamic tolls on partial routes p. 402
12.4 Bottleneck Pricing and Modal Split p. 403
12.4.1 Competition between mass transit and highway p. 404
12.4.2 Pricing and logit-based mode choice with elastic demand p. 414
12.5 Summary p. 420
12.6 Sources and Notes p. 421
13 Dynamic Road Pricing: General Network Models p. 423
13.1 Introduction p. 423
13.2 Problem Description p. 424
13.3 Space-Time Expanded Network p. 426
13.3.1 Basic assumptions p. 426
13.3.2 Static temporal expanded network p. 427
13.3.3 Traffic on the STEN p. 429
13.3.4 Link exit capacity and travel cost on the STEN p. 430
13.4 System Optimum, Externality and Congestion Toll p. 431
13.4.1 Model formulation p. 431
13.4.2 Optimality conditions p. 432
13.4.3 Externality and congestion toll p. 434
13.5 Numerical Examples p. 435
13.5.1 A single bottleneck network p. 435
13.5.2 A general bottleneck network p. 438
13.6 Summary p. 441
13.7 Sources and Notes p. 441
References p. 443
Subject Index p. 461