Modelling Transport

Dr. Juan de Dios Ortúzar is Emeritus Professor in the School of Engineering at Pontificia Universidad Católica de Chile and also Key Researcher at Instituto Sistemas Complejos de Ingeniería (ISCI) and the BRT+ Centre of Excellence. He specializes in discrete choice modelling and survey design with particular focus on transport demand modelling and the valuation of transport externalities. Dr. Luis G. Willumsen is an internationally recognised authority in transport and traffic modelling and has over 35 years of experience in this area. He previously lectured at Leeds University and University College London, and was also a Director of Steer before leaving in 2009 to set up his own independent practice. He is also Managing Partner of Nommon Solutions and Technologies, a company processing big data to provide location and mobility intelligence.

Preface xviii

About the Companion Website xxii

1 Introduction 1

1.1 Background 1

1.2 Models and Their Role 2

1.3 Characteristics of Transport Problems 3

1.3.1 Characteristics of Transport Demand 3

1.3.2 Characteristics of Transport Supply 4

1.3.3 A View of Transport Problems 6

1.3.4 A Simple Model 7

1.3.5 Classic and New Modes of Transport 9

1.4 Modelling and Decision-Making 9

1.5 Issues in Transport Modelling 12

1.5.1 General Modelling Issues 12

1.5.1.1 The Roles of Theory and Data 12

1.5.1.2 Model Assumptions 13

1.5.1.3 Model Specification 14

1.5.1.4 Model Calibration, Validation, and Use 15

1.5.1.5 Modelling, Forecasting, and Judgement 16

1.5.2 Aggregate and Disaggregate Modelling 17

1.5.3 Homo Sapiens and Homo Economicus 18

1.5.4 Cross-Section and Time Series 20

1.5.5 Revealed and Stated Preferences 21

1.6 The Structure of the Classic Transport Model 22

1.6.1 The Classic 4/5 Stage Model 22

1.6.2 Granularity 24

1.6.3 Macro, Meso, and Micro Models 27

1.7 Transport Planning and Uncertainty 27

1.8 Theoretical Basis Versus Expedience 31

1.9 Becoming a Better Modeller 33

Exercises 33

2 Data 35

2.1 Basic Sampling Theory 36

2.1.1 Statistical Considerations 36

2.1.1.1 Basic Definitions 36

2.1.1.2 Sample Size to Estimate Population Parameters 38

2.1.1.3 Obtaining the Sample 40

2.1.2 Practical Considerations in Sampling 43

2.1.2.1 The Implementation Problem 43

2.1.2.2 Finding the Size of Each Subpopulation 43

2.2 Errors in Modelling and Forecasting 44

2.2.1 Different Types of Error 45

2.2.1.1 Measurement Errors 45

2.2.1.2 Sampling Errors 46

2.2.1.3 Computational Errors 46

2.2.1.4 Specification Errors 46

2.2.1.5 Transfer Errors 47

2.2.1.6 Aggregation Errors 47

2.2.2 The Model Complexity/Data Accuracy Trade-off 48

2.2.3 Forecasting Errors 51

2.3 Basic Data-collection Methods 53

2.3.1 Practical Considerations 53

2.3.1.1 Length of the Study 53

2.3.1.2 Study Horizon 53

2.3.1.3 Limits of the Study Area 54

2.3.1.4 Study Resources 54

2.3.2 Types of Surveys 54

2.3.2.1 Survey Scope 55

2.3.2.2 Home Interview Travel Surveys 57

2.3.2.3 Other Important Types of Surveys 66

2.3.3 Data Correction, Expansion, and Validation 68

2.3.3.1 Data Correction 69

2.3.3.2 Imputation Methods 71

2.3.3.3 Sample Expansion 72

2.3.3.4 Validation of Results 72

2.3.4 Longitudinal Data Collection 73

2.3.4.1 Basic Definitions 73

2.3.4.2 Representative Sampling 74

2.3.4.3 Sources of Error in Panel Data 75

2.3.4.4 Relative Costs of Longitudinal Surveys 76

2.3.5 Travel Time Surveys 76

2.3.6 Digital Data Sources 77

2.4 Stated Preference Surveys 79

2.4.1 Introduction 79

2.4.1.1 Contingent Valuation and Conjoint Analysis 79

2.4.1.2 Stated Choice Methods 81

2.4.2 The Survey Process 83

2.4.2.1 Clarifying Study Objectives and Defining Objects of Interest 84

2.4.2.2 Defining Experimental Assumptions 86

2.4.2.3 Generating the Experimental Design 92

2.4.2.4 Conduct Post Design Generation Testing 97

2.4.2.5 Conduct Questionnaire 98

2.4.2.6 Nothing is Important 99

2.4.2.7 Realism and Complexity 100

2.4.2.8 Use of Computers in SP Surveys 101

2.4.2.9 Quality Issues in Stated Preference Surveys 102

2.4.3 Case Study Example 103

2.4.4 Limitations of Stated Preference Methods 115

Exercises 115

3 Zones and Networks 119

3.1 Zoning Design 120

3.2 Road Network Representation 122

3.2.1 Traffic Flow 123

3.2.2 Network Details 123

3.3 Link Properties and Functions 125

3.3.1 Link Properties 125

3.3.2 Network Costs 126

3.3.3 Definitions and Notation 127

3.3.4 Speed-Flow and Cost-Flow Curves 127

3.3.5 Public Transport Networks 131

Exercises 132

4 Trip Generation Modelling 133

4.1 Introduction 134

4.1.1 Some Basic Definitions 134

4.1.2 Characterisation of Journeys 135

4.1.2.1 By Purpose 135

4.1.2.2 By Time of Day 135

4.1.2.3 By Person Type 136

4.1.3 Factors Affecting Trip Generation 136

4.1.3.1 Personal Trip Productions 137

4.1.3.2 Personal Trip Attractions 137

4.1.3.3 Freight Trip Productions and Attractions 137

4.1.4 Growth-Factor Modelling 138

4.2 Regression Analysis 139

4.2.1 The Linear Regression Model 139

4.2.2 Zonal-Based Multiple Regression 148

4.2.3 Household-Based Regression 149

4.2.4 The Problem of Non-Linearity 151

4.2.5 Obtaining Zonal Totals 152

4.2.6 Matching Generations and Attractions 153

4.3 Cross-Classification or Category Analysis 153

4.3.1 The Classical Model 153

4.3.1.1 Introduction 153

4.3.1.2 Variable Definition and Model Specification 154

4.3.1.3 Model Application at Aggregate Level 155

4.3.2 Improvements to the Basic Model 156

4.3.2.1 Equivalence Between Category Analysis and Linear Regression 156

4.3.2.2 Regression Analysis for Household Strata 158

4.4 Other Trip Generation Formulations 159

4.4.1 Alternative Model Formulations 159

4.4.1.1 The Negative Binomial (NB) Approach 159

4.4.1.2 The Ordinal Probit Model 160

4.4.1.3 Comparing the Performance of Count Data and Linear Regression Models 160

4.5 Trip Generation and Accessibility 161

4.6 The Frequency Choice Logit Model 162

4.7 Tour Generation 164

4.8 Forecasting Variables in Trip Generation Analysis 165

4.9 Stability and Updating of Trip Generation Parameters 167

4.9.1 Temporal Stability 167

4.9.2 Geographic Stability 168

4.9.3 Bayesian Updating of Trip Generation Parameters 168

Exercises 171

5 Trip Distribution Modelling 173

5.1 Definitions and Notation 174

5.2 Growth-Factor Methods 176

5.2.1 Uniform Growth Factor 176

5.2.2 Singly Constrained Growth-Factor Methods 177

5.2.3 Doubly Constrained Growth Factors 178

5.2.4 Advantages and Limitations of Growth-Factor Methods 180

5.3 Synthetic or Gravity Models 180

5.3.1 The Gravity Distribution Model 180

5.3.2 Singly and Doubly Constrained Models 182

5.4 The Entropy-Maximising Approach 183

5.4.1 Entropy and Model Generation 183

5.4.2 Generation of the Gravity Model 185

5.4.3 Properties of the Gravity Model 187

5.4.4 Production–Attraction Format 189

5.4.5 Segmentation 190

5.5 Calibration of Gravity Models 190

5.5.1 Calibration and Validation 190

5.5.2 Calibration Techniques 191

5.6 The Tri-Proportional Approach 192

5.6.1 Bi-Proportional Fitting 192

5.6.2 A Tri-Proportional Problem 194

5.6.3 Partial Matrix Techniques 195

5.7 Other Synthetic Models 197

5.7.1 Generalisations of the Gravity Model 197

5.7.2 Intervening Opportunities Model 198

5.7.3 Disaggregate Approaches 200

5.8 Practical Considerations 200

5.8.1 Sparse Matrices 200

5.8.2 Treatment of External Zones 201

5.8.3 Special Generators 201

5.8.4 Intra-Zonal Trips 201

5.8.5 Journey Purposes 202

5.8.6 K Factors 202

5.8.7 Adjusting Trip Matrices 203

5.8.8 Errors in Modelling 203

5.8.9 The Stability of Trip Matrices 204

5.8.10 Sense Checks 206

Exercises 206

6 Modal Split and Direct Demand Models 209

6.1 Introduction 209

6.2 Factors Influencing the Choice of Mode 209

6.3 Trip-End Modal-Split Models 211

6.4 Trip Interchange Modal-Split Models 211

6.5 Synthetic Models 213

6.5.1 Distribution and Modal-Split Models 213

6.5.2 Distribution and Modal-Split Structures 215

6.5.3 Multimodal-Split Models 216

6.5.4 Calibration of Binary Logit Models 219

6.5.5 Calibration of Hierarchical Modal-Split Models 220

6.6 Direct Demand Models 222

6.6.1 Introduction 222

6.6.2 Direct Demand Models 222

6.6.3 An Improvement on Direct Demand Modelling 224

6.7 Sense Checks 225

Exercises 227

7 Discrete Choice Models 231

7.1 General Considerations 231

7.2 Theoretical Framework 234

7.3 The Multinomial Logit (MNL) Model 236

7.3.1 Specification Searches 238

7.3.2 Universal Choice Set Specification 239

7.3.3 Some Properties of the MNL 240

7.4 The Nested Logit Model (NL) 241

7.4.1 Correlation and Model Structure 241

7.4.2 Fundamentals of Nested Logit Modelling 242

7.4.2.1 The Model of Williams and of Daly–Zachary 243

7.4.2.2 The Formulation of McFadden: The GEV Family 244

7.4.3 The NL in Practice 246

7.4.3.1 Limitations of the NL 247

7.4.4 Controversies About Some Properties of the NL Model 247

7.4.4.1 Specifications Which Address the Non-Identifiability Problem 247

7.4.4.2 On the Limits of the Structural Parameters 249

7.4.4.3 Two Further Issues 251

7.5 The Multinomial Probit Model 253

7.5.1 The Binary Probit Model 253

7.5.2 Multinomial Probit and Taste Variations 254

7.5.3 Comparing Independent Probit and Logit Models 255

7.6 The Mixed Logit Model 255

7.6.1 Model Formulation 255

7.6.2 Model Specifications 256

7.6.2.1 Basic Formulations 256

7.6.2.2 More Advanced Formulations 258

7.6.3 Identification Problems 259

7.6.3.1 Theoretical Identification 260

7.6.3.2 Empirical Identification 260

7.7 Other Choice Models and Paradigms 261

7.7.1 Other Choice Models 261

7.7.2 Choice by Elimination and Satisfaction 262

7.7.2.1 Compensatory Rule 263

7.7.2.2 Non-Compensatory Rules 263

7.7.3 Habit and Hysteresis 264

7.7.4 Modelling with Panel Data 265

7.7.4.1 Panel Data Models 266

7.7.4.2 Efficiency and Repeated Observations 267

7.7.4.3 Dealing with Temporal Effects 269

7.7.5 Hybrid Choice Models Incorporating Latent Variables 271

7.7.5.1 Modelling with Latent Variables 272

7.7.5.2 Hybrid Discrete Choice Model 272

7.7.6 Attribute Non-Attendance and Other Heuristics 273

Exercises 276

8 Specification and Estimation of Discrete Choice Models 279

8.1 Introduction 279

8.2 Choice-Set Determination 280

8.2.1 Choice-Set Size 280

8.2.2 Choice-Set Formation 281

8.3 Specification and Functional Form 282

8.3.1 Functional Form and Transformations 282

8.3.1.1 Basic Box–Cox Transformation 283

8.3.1.2 Box–Tukey Transformation 283

8.3.2 Theoretical Considerations and Functional Form 283

8.3.3 Intrinsic Non-Linearities: Destination Choice 284

8.4 Statistical Estimation 285

8.4.1 Estimation of Models from Random Samples 285

8.4.1.1 The t-test for Significance of any Component θ∗k of θ∗ 288

8.4.1.2 The Likelihood Ratio Test 291

8.4.1.3 The Overall Test of Fit 292

8.4.1.4 The ρ2 Index 293

8.4.1.5 The Percentage Right or First Preference Recovery (FPR) Measure 294

8.4.1.6 Working with Validation Samples 295

8.4.2 Estimation of Models from Choice-based Samples 299

8.4.3 Estimation of Hybrid Choice Models with Latent Variables 300

8.4.4 Comparison of Non-Nested Models 304

8.4.5 Correcting for Endogeneity in Discrete Choice Models 305

8.4.6 Accounting for Stochastic Variables in Choice Models 307

8.4.6.1 Econometric Analysis 309

8.4.6.2 Stochastic Variables Model 310

8.4.6.3 Random Coefficients Model 311

8.5 Estimating the Multinomial Probit Model 311

8.5.1 Numerical Integration 313

8.5.2 Simulated Maximum Likelihood 314

8.5.2.1 The Basic Approach 314

8.5.2.2 Advanced Techniques 315

8.6 Estimating the Mixed Logit Model 317

8.6.1 Classical Estimation 317

8.6.1.1 Estimation of Population Parameters 317

8.6.1.2 Estimating Individual Parameters 318

8.6.2 Bayesian Estimation 319

8.6.3 Choice of a Mixing Distribution 323

8.6.3.1 Alternative Mixing Distributions 324

8.6.3.2 Discrete Mixtures and Latent Class Modelling 325

8.6.3.3 Empirical Identifiability of Latent Class Models 327

8.6.4 Binary Choice Case 327

8.6.5 Random and Quasi Random Numbers 330

8.6.6 Estimation of Panel Data Models 332

8.7 Modelling with Stated-Preference Data 334

8.7.1 Identifying Functional Form 334

8.7.2 Stated Preference Data and Discrete Choice Modelling 336

8.7.2.1 Naive Methods 337

8.7.2.2 Discrete Choice Modelling with Rating Data 339

8.7.2.3 Discrete Choice Modelling with Rank Data 339

8.7.2.4 Modelling with Stated Choice Data 341

8.7.2.5 Model Estimation with Generalised Choice Data 342

8.7.2.6 Modelling with Indifference Alternatives 345

8.7.2.7 Interactions in SC Modelling 351

8.7.2.8 The Problem of Repeated Observations 354

8.7.3 Model Estimation with Mixed SC and RP Data 355

8.7.3.1 Estimation without Considering Correlation among Repeated Observations 355

8.7.3.2 Joint Estimation Considering Correlation between Repeated Observations 358

8.7.3.3 Forecasting with Joint RP–SC Models 359

Exercises 362

9 Model Aggregation and Transferability 365

9.1 Introduction 365

9.2 Aggregation Bias and Forecasting 366

9.3 Confidence Intervals for Predictions 367

9.3.1 Linear Approximation 368

9.3.2 Non-Linear Programming 369

9.4 Aggregation Methods 370

9.5 Model Updating or Transference 373

9.5.1 Introduction 373

9.5.2 Methods to Evaluate Model Transferability 373

9.5.2.1 Test of Model Parameter for Equality 374

9.5.2.2 Disaggregate Transferability Measures 374

9.5.3 Updating with Disaggregate Data 375

9.5.3.1 Updating the Constants 376

9.5.3.2 Updating of Constants and Scale 376

9.5.4 Updating with Aggregate Data 377

Exercises 378

10 Static Assignment 381

10.1 Basic Concepts 381

10.1.1 Introduction 381

10.1.2 Traffic and Queues 383

10.1.3 Factors Influencing Route Choice 385

10.2 Static Traffic Assignment Methods 386

10.2.1 Introduction 386

10.2.2 Modelling Route Choice 387

10.2.3 Tree Building 388

10.3 All-or-Nothing Assignment 390

10.4 Stochastic Methods 392

10.4.1 Simulation-Based Methods 392

10.4.2 Proportional Stochastic Methods 393

10.4.3 Emerging Approaches 395

10.5 Congested Assignment 398

10.5.1 Wardrop’s Equilibrium 398

10.5.2 Hard and Soft Speed-Change Methods 400

10.5.3 Incremental Assignment 401

10.5.4 Method of Successive Averages 402

10.5.5 Braess’s Paradox 403

10.6 Public-Transport Assignment 405

10.6.1 Introduction 405

10.6.2 Issues in Public-Transport Assignment 405

10.6.2.1 Supply 405

10.6.2.2 Passengers 407

10.6.2.3 Monetary Costs 407

10.6.2.4 The Definition of Generalised Costs 407

10.6.2.5 The Common Lines Problem 408

10.6.2.6 Frequency or Schedule-Based Route Choice 408

10.6.3 Modelling Public-Transport Route Choice 408

10.6.4 Assignment of Public Transport Trips 412

10.6.5 Discrete Route Choice Modelling 413

10.7 Limitations of the Classic Methods 415

10.7.1 The Assumption of Perfect Information about Costs in all Parts of the Network 415

10.7.2 The Assumption that all Movements can be Represented by a Trip Matrix 415

10.7.3 Limitations in the Node-link Model of the Road Network 415

10.7.4 Errors in Defining Average Perceived Costs 416

10.7.5 Not all Trip Makers Perceive Costs in the Same Way 416

10.7.6 Day-to-Day Variations in Demand 417

10.7.7 Imperfect Estimation of Travel Time Changes with Link Flow Changes 417

10.7.8 The Dynamic Nature of Traffic 418

10.7.9 Input Errors 418

10.8 Practical Considerations 418

Exercises 422

11 Dynamic Assignment 425

11.1 Introduction 425

11.2 Travel Time Reliability 425

11.3 Junction Interaction Methods 426

11.4 The Dynamic Nature of Traffic 427

11.4.1 Delays over Time and Space 427

11.4.2 Average and Experienced Travel Times 431

11.5 Dynamic Traffic Assignment (DTA) 432

11.5.1 General Requirements 432

11.5.2 Discretising Time in DTA 433

11.5.3 Micro- and Meso-Simulation 433

11.5.4 Equilibrium and Simulation 435

Exercises 438

12 Equilibrium 439

12.1 Introduction 439

12.2 Equilibrium 439

12.2.1 A Mathematical Programming Approach 440

12.2.2 Social Equilibrium 444

12.2.3 Solution Methods 445

12.2.3.1 The Frank–Wolfe Algorithm 446

12.2.3.2 Route-Based Assignment 447

12.2.3.3 Origin-Based Assignment 448

12.2.4 Stochastic Equilibrium Assignment 450

12.2.5 Congested Public Transport Assignment 451

12.3 Transport System Equilibrium 452

12.3.1 Equilibrium and Feedback 452

12.3.2 Formulation of the Combined Model System 455

12.3.3 Solving General Combined Models 458

12.3.4 Monitoring Convergence 459

Exercises 460

13 Departure Time Choice 463

13.1 Introduction 463

13.2 Macro and Micro Departure Time Choice 463

13.3 Underlying Principles of Micro Departure TIME Choice 464

13.4 Simple Supply/Demand Equilibrium Models 466

13.5 Time of Travel Choice and Equilibrium Assignment 467

13.6 Modelling Disaggregate Time of Day Choice 469

13.7 Joint Mode/Time of Day Choice 474

13.7.1 Data Collection 474

13.7.1.1 Alternatives and Their Attributes 475

13.7.1.2 Stated Preference Data 475

13.7.2 Model Estimation 476

13.7.2.1 Analysis of Results 478

13.7.2.2 Model Valuations 479

13.8 Conclusion 479

14 Complementary Techniques 481

14.1 Introduction 481

14.2 Sketch Planning Methods 482

14.3 Incremental Demand Models 483

14.3.1 Incremental Elasticity Analysis 484

14.3.2 Incremental or Pivot-Point Modelling 485

14.4 Model Estimation From Traffic Counts 488

14.4.1 Introduction 488

14.4.2 Route Choice and Matrix Estimation 489

14.4.3 Transport Model Estimation from Traffic Counts 489

14.4.4 Matrix Adjustments Using Traffic Counts 492

14.4.5 Traffic Counts and Matrix Estimation 497

14.4.5.1 Independence 497

14.4.5.2 Inconsistency 498

14.4.6 Limitations of ME 2 499

14.4.7 Improved Matrix Estimation Models 501

14.4.8 Treatment of Non-Proportional Assignment 502

14.4.9 Quality of Matrix Estimation Results 503

14.4.10 Estimation of Trip Matrix and Mode Choice 504

14.4.10.1 Simple Unimodal Case 504

14.4.10.2 Updating with Aggregate Modal Shares 505

14.4.10.3 Updating with Traffic Counts 505

14.4.10.4 Updating with Combined Information 505

14.5 Gaming Simulation 506

Exercises 508

15 Freight Demand Models 511

15.1 A Subject of Increasing Importance 511

15.2 Factors Affecting Goods Movements 512

15.3 Pricing Freight Services 513

15.4 Data Collection for Freight Studies 514

15.5 Aggregate Freight Modelling 515

15.5.1 Freight Generations and Attractions 516

15.5.2 Distribution Models 516

15.5.3 Mode Choice 518

15.5.4 Assignment 518

15.5.5 Equilibrium 519

15.5.6 Freight and Service Trips 520

15.6 Disaggregate Approaches 521

15.7 Conclusions 522

16 Activity-Based Models 523

16.1 Introduction 523

16.2 Activities, Tours, and Trips 524

16.3 Tours, Individuals, and Representative Individuals 527

16.4 Agent-Based Modelling 528

16.5 Activity-Based Modelling 529

16.5.1 Introduction 529

16.5.2 Population Synthesis 530

16.5.3 Monte Carlo and Probabilistic Processes 533

16.5.4 Structuring, Activities, and Tours 533

16.5.5 Solving ABM 535

16.5.6 Integration with Assignment 536

16.6 Refining Activity or Tour-Based Models 537

16.6.1 Choice of Usual Place of Work and Education 537

16.6.2 Car Ownership 537

16.6.3 In and Out of Home Activities 538

16.6.4 Person Day-Patterns Linked Across Household Members 538

16.6.5 Activities Allocated Explicitly Among Members of the Household 538

16.6.6 Number of Zones Used 538

16.6.7 Time Periods and Time Constraints 538

16.6.8 Network Equilibrium 539

16.7 Challenges of Activity-Based Models 539

16.8 Extending Random Utility Approaches 540

17 Model Design 541

17.1 Introduction 541

17.2 Accuracy and Precision 542

17.3 Model Specification 543

17.3.1 Model Objectives 543

17.3.2 Identify Possible Interventions 544

17.3.3 Identify Relevant Behavioural Responses 544

17.3.4 Technical Specification and Data Requirements 545

17.3.5 Quality Assurance 546

17.4 Model Calibration and Validation 547

17.5 Model Review 548

17.6 Plan Making 548

17.7 Dealing with Uncertainty 550

18 Key Parameters, Planning Variables, and Value Functions 553

18.1 Forecasting Planning Variables 553

18.1.1 Introduction 553

18.1.2 Use of Official Forecasts 554

18.1.3 Forecasting Population and Employment 555

18.1.3.1 Trend Extrapolation 555

18.1.3.2 Cohort Survival 555

18.1.3.3 Transitional Probabilities 556

18.1.3.4 Economic Base 556

18.1.3.5 Input–Output Analysis 556

18.1.4 The Spatial Location of Population and Employment 557

18.2 Land-Use Transport Interaction Modelling 557

18.2.1 The Lowry Model 559

18.2.2 The Bid-Choice Model 560

18.2.2.1 Elasticities in Bid-Auction Location Choice Models 560

18.2.2.2 Consumer Surplus 561

18.2.3 Systems Dynamics Approach 561

18.2.4 Urban Simulation 563

18.3 Car-Ownership Forecasting 564

18.3.1 Background 564

18.3.2 Time-Series Extrapolations 565

18.3.3 Econometric Methods 568

18.3.3.1 The Method of Quarmby and Bates (1970) 568

18.3.3.2 The Regional Highway Transport Model (RHTM) Method 570

18.3.3.3 Models of Car Ownership and Use 570

18.3.3.4 Models of Motorcycle Ownership 571

18.3.4 International Comparisons 571

18.4 The Value of Travel Time 573

18.4.1 Introduction 573

18.4.2 Subjective and Social Values of Time 574

18.4.3 Some Practical Results 575

18.4.4 Methods of Analysis 576

18.4.4.1 Estimation of Subjective Values of Time 576

18.4.4.2 Confidence Intervals for the Value of Time 577

18.4.4.3 A Deeper Look at Computing Measures of Uncertainty for WTP 580

18.4.4.4 Special Problems Brought in by the Use of More Flexible Models 582

18.4.4.5 The Transfer Price Approach 589

18.4.4.6 The Stated Preference Approach 590

18.5 Valuing External Effects of Transport 590

18.5.1 Introduction 590

18.5.2 Methods of Analysis 591

18.5.2.2 Contingent Valuation 593

Exercises 596

19 Pricing and Revenue 599

19.1 Pricing and Welfare 599

19.2 Correcting Prices for Externalities 600

19.3 The Perception of Travel Costs 601

19.4 Pricing Tools 601

19.4.1 Car Ownership Taxes 602

19.4.2 Fuel Taxes 602

19.4.3 Parking Charges 602

19.4.4 Tolled Facilities 603

19.4.5 Pay-As-You-Drive Insurance 604

19.4.6 Congestion and Road User Charging 604

19.5 The Experience of Private Sector Projects 605

19.5.1 Involvement of Private Sector in Transport Projects 605

19.5.2 Uncertainty and Risk 607

19.5.3 Risk Management and Mitigation 609

19.6 Demand Modelling 610

19.6.1 Willingness to Pay 610

19.6.2 Simple Projects 610

19.6.3 Complex Projects 611

19.6.4 Road User Charge Projects 613

19.6.5 Scheme Design 613

19.6.6 Ramp-Up, Leakage, and Discounts 615

19.7 Risk Analysis 616

19.7.1 Sensitivity and Sources of Risk 617

19.7.2 Stochastic Risk Analysis 618

19.7.3 Scenarios 619

19.8 Conclusions 620

Exercises 620

20 Modelling the Less Common 623

20.1 Introduction 623

20.2 New Scheduled Services 624

20.3 Walking 625

20.4 Cycling 625

20.5 Motorcycling 627

20.6 Parking 628

20.7 Demand-Responsive Transport 630

20.7.1 Introduction 630

20.7.2 Micro-Mobility Sharing 633

20.7.3 Car, Motorcycle, and Van Sharing 634

20.7.4 Connected and Automated Vehicles 635

20.7.5 Mobility as a Service 636

20.8 Modelling Demand-Responsive Mobility 636

20.8.1 The Challenge 636

20.8.2 Modelling Approaches 638

20.8.3 Model Outputs 640

20.9 Deliveries and Collections 640

20.10 Digital and Distant Presence 641

20.11 Soft Measures, Smarter Choices 642

References 645

Index 689