Transportation Systems Analysis: Models and Applications

Overview

Springer Optimization and Its Applications publishes undergraduate and graduate textbooks, monographs and state-of-the-art expository works that focus on algorithms for solving optimization problems and applications involving such problems. Some of the topics include optimization, network flow problems, optimal control, multi-objective programming, approximation and heuristic approaches.

This book provides a comprehensive and systematic presentation of the mathematical models ...

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Overview

Springer Optimization and Its Applications publishes undergraduate and graduate textbooks, monographs and state-of-the-art expository works that focus on algorithms for solving optimization problems and applications involving such problems. Some of the topics include optimization, network flow problems, optimal control, multi-objective programming, approximation and heuristic approaches.

This book provides a comprehensive and systematic presentation of the mathematical models for the analysis of transportation systems as well as the techniques for their design and appraisal. In particular, basic and advanced models are described for passenger/freight demand (traffic flows), transportation networks, and for traffic assignment. Theoretical and operational aspects are presented in a rigorous and exhaustive framework, addressing a broad range of applications performed by researchers and practitioners supporting strategic planning, feasibility studies, tactical planning and operations management programs at any scale.

In this 2nd edition the author extends and generalizes the contents of the previous edition entitled Transportation Systems Engineering: Theory and Methods published in 2001. In addition to entirely new material dealing with the recent developments in the field such as within-day Dynamic Traffic Assignment models suitable for large road networks and an exhaustive assessment of multi-criteria methods for project appraisal, the text has been revised to simplify the presentation. The Bibliography has also been expanded significantly. All the topics are presented with simple numerical examples as well as with references to real-life applications.

The material isstructured so as to offer different levels of complexity and different reading paths based on the reader's needs. It is suitable for graduate level courses on transportation analysis and planning. Due to the breadth and depth of topics covered, the book will also serve as an excellent reference guide for researchers, teachers and practitioners.

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Product Details

  • ISBN-13: 9781461424482
  • Publisher: Springer US
  • Publication date: 2/25/2012
  • Series: Springer Optimization and Its Applications Series, #29
  • Edition description: Softcover reprint of hardcover 2nd ed. 2009
  • Edition number: 2
  • Pages: 742
  • Product dimensions: 6.14 (w) x 9.21 (h) x 1.52 (d)

Table of Contents

1 Modeling Transportation Systems: Preliminary Concepts and Application Areas 1

1.1 Introduction 1

1.2 Transportation Systems 1

1.3 Transportation System Identification 5

1.3.1 Relevant Spatial Dimensions 6

1.3.2 Relevant Temporal Dimensions 9

1.3.3 Relevant Components of Travel Demand 13

1.4 Modeling Transportation Systems 17

1.5 Model Applications and Transportation Systems Engineering 20

1.5.1 Transportation Systems Design and the Decision-Making Process 20

1.5.2 Some Areas of Application 24

Reference Notes 27

2 Transportation Supply Models 29

2.1 Introduction 29

2.2 Fundamentals of Traffic Flow Theory 29

2.2.1 Uninterrupted Flows 30

2.2.1.1 Fundamental Variables 30

2.2.1.2 Model Formulation 32

2.2.2 Queuing Models 36

2.2.2.1 Fundamental Variables 37

2.2.2.2 Deterministic Models 39

2.2.2.3 Stochastic Models 43

2.3 Congested Network Models 45

2.3.1 Network Structure 45

2.3.2 Flows 46

2.3.3 Performance Variables and Transportation Costs 48

2.3.4 Link Performance and Cost Functions 53

2.3.5 Impacts and Impact Functions 54

2.3.6 General Formulation 55

2.4 Applications of Transportation Supply Models 56

2.4.1 Supply Models for Continuous Service Transportation Systems 59

2.4.1.1 Graph Models 59

2.4.1.2 Link Performance and Cost Functions 61

2.4.2 Supply Models for Scheduled Service Transportation Systems 82

2.4.2.1 Line-based Graph Models 83

2.4.2.2 Link Performance and Cost Functions 83

Reference Notes 87

3 Random Utility Theory 89

3.1 Introduction 89

3.2 Basic Assumptions 90

3.3 Some Random Utility Models 95

3.3.1 The Multinomial Logit Model 95

3.3.2 The Single-Level Hierarchical Logit Model100

3.3.3 The Multilevel Hierarchical Logit Model* 107

3.3.4 The Cross-nested Logit Model* 115

3.3.5 The Generalized Extreme Value (GEV) Model* 118

3.3.6 The Probit Model 121

3.3.7 The Mixed Logit Model* 130

3.4 Expected Maximum Perceived Utility and Mathematical Properties of Random Utility Models 133

3.5 Choice Set Modeling 139

3.6 Direct and Cross-elasticities of Random Utility Models 143

3.7 Aggregation Methods for Random Utility Models 148

3.A Derivation of Logit Models from the GEV Model 152

3.A.1 Derivation of the Multinomial Logit Model 153

3.A.2 Derivation of the Single-Level Hierarchical Logit Model 154

3.A.3 Derivation of the Multilevel Hierarchical Logit Model 156

3.A.4 Derivation of the Cross-nested Logit Model 159

3.B Random Variables Relevant for Random Utility Models 161

3.B.1 The Gumbel Random Variable 161

3.B.2 The Multivariate Normal Random Variable 164

Reference Notes 166

4 Travel-Demand Models 169

4.1 Introduction 169

4.2 Trip-based Demand Model Systems 172

4.2.1 Random Utility Models for Trip Demand 176

4.3 Examples of Trip-based Demand Models 181

4.3.1 Models of Spatial and Temporal Characteristics 181

4.3.1.1 Trip Production or Trip Frequency Models 181

4.3.1.2 Distribution Models 185

4.3.2 Mode Choice Models 192

4.3.3 Path Choice Models 195

4.3.3.1 Path Choice Models for Road Networks 197

4.3.3.2 Path Choice Models for Transit Systems 207

4.3.4 A System of Demand Models 215

4.4 Trip-Chaining Demand Models 219

4.5 Activity-Based Demand Models 228

4.5.1 A Theoretical Reference Framework 231

4.5.1.1 Weekly Household Activity Model 232

4.5.1.2 Daily Household Activity Model 233

4.5.1.3 Daily Individual Activity List Model 234

4.5.1.4 Activity Pattern and Trip-Chain Models 234

4.6 Applications of Demand Models 235

4.7 Freight Transportation Demand Models 238

4.7.1 Multiregional Input-Output (MRIO) models 240

4.7.2 Freight Mode Choice Models 253

Reference Notes 255

5 Basic Static Assignment to Transportation Networks 259

5.1 Introduction 259

5.1.1 Classification of Assignment Models 259

5.1.2 Fields of Application of Assignment Models 263

5.2 Definitions, Assumptions, and Basic Equations 265

5.2.1 Supply Model 266

5.2.2 Demand Model 269

5.2.3 Feasible Path and Link Flow Sets 274

5.2.4 Network Performance Indicators 275

5.3 Uncongested Networks 278

5.3.1 Models for Stochastic Assignment 280

5.3.2 Models for Deterministic Assignment 283

5.3.3 Algorithms Without Explicit Path Enumeration 286

5.4 Congested Networks: Equilibrium Assignment 304

5.4.1 Models for Stochastic User Equilibrium 307

5.4.2 Algorithms for Stochastic User Equilibrium 313

5.4.3 Models for Deterministic User Equilibrium 318

5.4.4 Algorithms for Deterministic User Equilibrium 324

5.4.5 Relationship Between Stochastic and Deterministic Equilibrium 329

5.4.6 System Optimum Assignment* 331

5.5 Result Interpretation and Parameter Calibration 338

5.5.1 Specification and Calibration of Assignment Models 341

5.A Optimization Models for Stochastic Assignment 341

5.A.1 Uncongested Network: Stochastic Assignment 342

5.A.2 Congested Network: Stochastic User Equilibrium 342

Reference Notes 344

Assignment Models 344

Assignment Algorithms 346

6 Advanced Models for Traffic Assignment to Transportation Networks 349

6.1 Introduction 349

6.2 Assignment with Pre-trip/En-route Path Choice 349

6.2.1 Definitions, Assumptions, and Basic Equations 349

6.2.2 Uncongested Networks 357

6.2.3 Congested Networks: Equilibrium Assignment 363

6.3 Equilibrium Assignment with Variable Demand 367

6.3.1 Single-Mode Assignment 368

6.3.1.1 Models for Stochastic User Equilibrium 372

6.3.1.2 Models for Deterministic User Equilibrium 375

6.3.1.3 Algorithms 379

6.3.2 Multimode Equilibrium Assignment 385

6.4 Multiclass Assignment 389

6.4.1 Undifferentiated Congestion Multiclass Assignment 392

6.4.2 Differentiated Congestion Multiclass Assignment 394

6.5 Interperiod Dynamic Process Assignment 396

6.5.1 Definitions, Assumptions, and Basic Equations 398

6.5.1.1 Supply Model 398

6.5.1.2 Demand Model 399

6.5.1.3 Approaches to Dynamic Process Modeling 402

6.5.2 Deterministic Process Models 403

6.5.3 Stochastic Process Models 410

6.6 Synthesis and Application Issues 419

Reference Notes 419

7 Intraperiod (Within-Day) Dynamic Models* 421

7.1 Introduction 421

7.2 Supply Models for Transport Systems with Continuous Service 423

7.2.1 Space-Discrete Macroscopic Models 426

7.2.1.1 Variables and Consistency Conditions 426

7.2.1.2 Network Flow Propagation Model 435

7.2.1.3 Link Performance and Travel Time Functions 438

7.2.1.4 Dynamic Network Loading 439

7.2.1.5 Path Performance and Travel Time Functions 440

7.2.1.6 Formalization of the Whole Supply Model 442

7.2.2 Mesoscopic Models 443

7.2.2.1 Variables and Consistency Conditions 444

7.2.2.2 Link Performance and Travel Time Functions 447

7.2.2.3 Path Performance and Travel Time Functions 448

7.2.2.4 Dynamic Network Loading 449

7.2.2.5 Formalization of the Whole Supply Model 450

7.3 Demand Models for Continuous Service Systems 451

7.4 Demand-Supply Interaction Models for Continuous Service Systems 455

7.4.1 Uncongested Network Assignment Models 455

7.4.2 User Equilibrium Assignment Models 458

7.4.3 Dynamic Process Assignment Models 461

7.5 Dynamic Traffic Assignment with Nonseparable Link Cost Functions and Queue Spillovers 464

7.5.1 Network Performance Model 467

7.5.1.1 Exit Capacity Model 472

7.5.1.2 Exit Flow and Travel Time Model 473

7.5.1.3 Entry Capacity Model 475

7.5.1.4 Fixed-Point Formulation of the NPM 477

7.5.2 Network Loading Map and Fixed-Point Formulation of the Equilibrium Model 477

7.6 Models for Transport Systems with Scheduled Services 480

7.6.1 Models for Regular Low-Frequency Services 482

7.6.1.1 Supply Models 482

7.6.1.2 Demand Models 487

7.6.1.3 Demand-Supply Interaction Models 489

7.6.2 Models for Irregular High-Frequency Services 489

7.6.2.1 Supply Models 489

7.6.2.2 Demand Models 490

7.6.2.3 Demand-Supply Interaction Models 495

7.A The Simplified Theory of Kinematic Waves Based on Cumulative Flows: Application to Macroscopic Link Performance Models 497

7.A.1 Bottlenecks 499

7.A.2 Segments 501

Reference Notes 510

8 Estimation of Travel Demand Flows 513

8.1 Introduction 513

8.2 Direct Estimation of Present Demand 514

8.2.1 Sampling Surveys 514

8.2.2 Sampling Estimators 516

8.3 Disaggregate Estimation of Demand Models 520

8.3.1 Model Specification 521

8.3.2 Model Calibration 522

8.3.3 Model Validation 530

8.4 Disaggregate Estimation of Demand Models with Stated Preference Surveys* 536

8.4.1 Definitions and Types of Survey 537

8.4.2 Survey Design 538

8.4.3 Model Calibration 545

8.5 Estimation of O-D Demand Flows Using Traffic Counts 549

8.5.1 Maximum Likelihood and GLS Estimators 555

8.5.2 Bayesian Estimators 560

8.5.3 Application Issues 562

8.5.4 Solution Methods 564

8.6 Aggregate Calibration of Demand Models Using Traffic Counts 569

8.7 Estimation of Within-Period Dynamic Demand Flows Using Traffic Counts 574

8.7.1 Simultaneous Estimators 578

8.7.2 Sequential Estimators 579

8.8 Real-Time Estimation and Prediction of Within-Period Dynamic Demand Flows Using Traffic Counts 580

8.9 Applications of Demand Estimation Methods 582

8.9.1 Estimation of Present Demand 582

8.9.2 Estimation of Demand Variations (Forecasting) 584

Reference Notes 586

9 Transportation Supply Design Models 589

9.1 Introduction 589

9.2 General Formulations of the Supply Design Problem 592

9.3 Applications of Supply Design Models 595

9.3.1 Models for Road Network Layout Design 596

9.3.2 Models for Road Network Capacity Design 598

9.3.3 Models for Transit Network Design 602

9.3.4 Models for Pricing Design 604

9.3.5 Models for Mixed Design 606

9.4 Some Algorithms for Supply Design Models 607

9.4.1 Algorithms for the Discrete SDP 607

9.4.2 Algorithms for the Continuous SDP 614

Reference Notes 619

10 Methods for the Evaluation and Comparison of Transportation System Projects 621

10.1 Introduction 621

10.2 Evaluation of Transportation System Projects 622

10.2.1 Identification of Relevant Impacts 623

10.2.2 Identification and Estimation of Impact Indicators 626

10.2.3 Computation of Users' Surplus Changes 628

10.3 Methods for the Comparison of Alternative Projects 641

10.3.1 Benefit-Cost Analysis 641

10.3.2 Revenue-Cost Analysis 647

10.3.3 Multi-criteria Analysis 648

10.3.3.1 Noncompensatory Methods* 658

10.3.3.2 Multiattribute Utility Theory Method (MAUT)* 660

10.3.3.3 Linear Additive Methods* 665

10.3.3.4 The Analytical Hierarchy Process (AHP)* 667

10.3.3.5 Outranking Methods* 673

10.3.3.6 Constrained Optimization Method* 677

Reference Notes 680

Appendix A Review of Numerical Analysis 683

A.1 Sets and Functions 683

A.1.1 Elements of Set Topology 683

A.1.2 Continuous and Differentiable Functions 685

A.1.3 Convex Functions 689

A.2 Solution Algorithms 690

A.3 Fixed-Point Problems 691

A.3.1 Properties of Fixed-Points 693

A.3.2 Solution Algorithms for Fixed-Point Problems 695

A.4 Optimization Problems 697

A.4.1 Properties of Minimum Points 697

A.4.1.1 Properties of Minimum Points on Open Sets 697

A.4.1.2 Properties of Minimum Points on Closed Sets 698

A.4.2 Solution Algorithms for Optimization Problems 699

A.4.2.1 Monodimensional Optimization Algorithms 699

A.4.2.2 Unconstrained Multidimensional Optimization Algorithms 703

A.4.2.3 Bounded Variables Multidimensional Optimization Algorithms 706

A.4.2.4 Linearly Constrained Multidimensional Optimization Algorithms 707

A.5 Variational Inequality Problems 709

A.5.1 Properties of Variational Inequalities 711

A.5.2 Solution Algorithms for Variational Inequality Problems 712

Index 715

References 725

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