Breakdown in Traffic Networks (eBook)

Preface 5
Acknowledgments 7
Contents 8
Acronyms and Symbols 21
1 Introduction—The Reason for Paradigm Shift in Transportation Science 28
1.1 Definitions of Free and Congested Traffic in Empirical Data 29
1.2 Bottlenecks 32
1.3 Definitions of Synchronized Flow and Wide Moving Jam Phases in Empirical Data for Congested Traffic 33
1.4 Traffic Breakdown 36
1.5 Empirical Phase Transitions in Traffic Flow 36
1.6 Empirical Fundamental of Transportation Science 39
1.7 The Origin of Failure of Classical Traffic and Transportation Theories 44
1.7.1 Nature of Stochastic Highway Capacity 44
1.7.2 Description of Traffic Breakdown with Classical Traffic Flow Models 45
1.7.2.1 About Applications of LWR-Model 46
1.7.2.2 About Traffic Flow Models of General Motors (GM) Model Class 46
1.7.2.3 Common Critical Statements to Classical Traffic Flow Models and Their Applications 47
1.7.2.4 About Achievements of Classical Traffic Flow Models 48
1.7.3 Deterioration of Traffic System Through Standard Dynamic Traffic Assignment in Networks 48
1.7.4 Failure of Applications of Intelligent Transportation Systems (ITS) Based on Classical Traffic Theories 50
1.8 Classical Ideas of Transportation Science and Nucleation Nature of Empirical Traffic Breakdown 52
1.9 Three-Phase Traffic Theory 52
1.10 Infinite Number of Stochastic Highway Capacities in Three-Phase Theory 56
1.11 Breakdown Minimization (BM) Principle 57
1.12 Mathematical Three-Phase Traffic Flow Models and ITS-Applications of Three-Phase Theory 58
1.13 Criticism of Three-Phase Traffic Theory 63
1.14 Incommensurability of Three-Phase Traffic Theory and Classical Traffic Theories 66
1.15 Objectives of the Book 67
1.16 Book's Structure 69
References 71
2 Achievements of Empirical Studies of Traffic Breakdown at Highway Bottlenecks 99
2.1 Introduction 99
2.2 Empirical Features of Traffic Breakdown 100
2.2.1 Traffic Breakdown—Transition from Free to Synchronized Flow at Highway Bottleneck 100
2.2.2 Time-Dependence of Flow Rate During Empirical Traffic Breakdown at Highway Bottleneck 101
2.3 Stochastic Behavior and Probability of Traffic Breakdown at Highway Bottleneck 103
2.4 Conclusions 106
References 107
3 Nucleation Nature of Traffic Breakdown—Empirical Fundamental of Transportation Science 113
3.1 Introduction 113
3.2 Definitions of Empirical Spontaneous and Empirical Induced Traffic Breakdowns at Highway Bottlenecks 114
3.3 Explanation of Term ``Nucleus'' for Traffic Breakdown 118
3.4 Nucleation of Empirical Spontaneous Traffic Breakdown at Highway Bottlenecks 120
3.4.1 Waves in Empirical Free Flow 120
3.4.2 Empirical Nucleation of Traffic Breakdown at On-Ramp Bottleneck 122
3.4.3 Empirical Nucleation of Traffic Breakdown at Off-Ramp Bottleneck 122
3.4.4 Empirical Permanent Speed Disturbance at Highway Bottleneck and Nucleation of Traffic Breakdown 126
3.4.5 Empirical Two-Dimensional (2D) Asymmetric Spatiotemporal Structure of Nuclei for Traffic Breakdown 130
3.5 Waves in Free Flow and Empirical Spontaneous Traffic Breakdown in Flow Without Trucks 133
3.6 Induced Traffic Breakdown—Empirical Proof of Nucleation Nature of Empirical Traffic Breakdown 133
3.6.1 Sources of Nucleus for Empirical Traffic Breakdown 134
3.6.2 Induced Traffic Breakdown as One of Different Consequences of Spillover in Real Traffic 142
3.7 Empirical Nucleation Nature of Traffic Breakdown as Origin of the Infinity of Highway Capacities 143
3.8 Conclusions 146
References 147
4 Failure of Generally Accepted Classical Traffic Flow Theories 149
4.1 Introduction 149
4.2 Fundamental Diagram of Traffic Flow 151
4.2.1 Empirical Features of Fundamental Diagram of Traffic Flow 151
4.2.2 Application of Fundamental Diagram for Traffic Flow Modelling 154
4.3 Traffic Breakdown at Bottleneck in Lighthill-Whitham-Richards (LWR) Model 154
4.3.1 Basic Assumption of LWR Model 154
4.3.2 Achievements of LWR Theory in Description of Traffic Breakdown 155
4.3.3 Failure of LWR Theory in Explanation of Empirical Nucleation Nature of Traffic Breakdown 157
4.4 Description of Traffic Breakdown with General Motors (GM) Model Class 160
4.4.1 Classical Traffic Flow Instability: Growing Wave of Local Speed Reduction in Traffic Flow Due to Over-Deceleration Effect 160
4.4.2 ``Boomerang'' Effect 162
4.4.3 Moving Jam Emergence at Bottleneck 165
4.5 Achievements of Generally Accepted ClassicalTraffic Models 166
4.5.1 Metastability of Free Flow with Respect to Moving Jam Emergence and Line J 167
4.5.1.1 Characteristic Parameters of Wide Moving Jam 168
4.5.1.2 Line J 171
4.5.2 Driver Behavioral Assumptions 173
4.6 Summary of Achievements of Classical Traffic Flow Models 174
4.7 Why Are Generally Accepted Classical Two-Phase Traffic Flow Models Inconsistent with Features of Real Traffic? 175
4.8 Model Validation with Empirical Data 177
4.9 Applications of Classical Traffic Flow Theories for Development of Intelligent Transportation systems (ITS) 180
4.9.1 Simulations of ITS Performance 180
4.9.2 On-Ramp Metering 182
4.9.3 Effect of Automatic Driving on Traffic Flow 183
4.10 Classical Understanding of Stochastic Highway Capacity 185
4.11 Strict Belief in Classical Theories as Reason for Defective Analysis of Empirical Traffic Phenomena 189
4.11.1 A Possible Origin of Failure of Classical Traffic Flow Models 189
4.11.2 Capacity Drop 191
4.11.3 Macroscopic Fundamental Diagram 193
4.11.4 Boomerang Effect, Homogeneous Congested Traffic, and Diagram of Congested Traffic States 194
4.11.5 Driver Behavioral Assumptions 196
4.12 Conclusions 198
References 199
5 Theoretical Fundamental of Transportation Science—The Three-Phase Theory 213
5.1 Introduction—Definition of Stochastic Highway Capacity 213
5.2 The Basic Assumption of Three-Phase Traffic Theory 217
5.3 Qualitative Theory of Critical Nucleus for Traffic Breakdown at Bottleneck 218
5.3.1 Permanent Speed Disturbance at Bottleneck 218
5.3.2 Critical Nucleus at Location of Permanent Speed Disturbance 220
5.3.3 Dependence of Critical Nucleus on Flow Rate 222
5.3.4 Z-Characteristic for Traffic Breakdown 225
5.4 Probabilistic Characteristics of Spontaneous Traffic Breakdown at Bottleneck 226
5.4.1 Theoretical Probability of Spontaneous Traffic Breakdown 226
5.4.2 Theoretical Z-Characteristic for Traffic Breakdown at Bottleneck 228
5.4.3 Flow-Rate Dependence of Characteristics of Spontaneous Traffic Breakdown 230
5.4.3.1 Flow-Rate Region I 230
5.4.3.2 Flow-Rate Region II 231
5.4.3.3 Flow-Rate Region III 232
5.4.3.4 Flow-Rate Region IV 233
5.4.4 Time-Delayed Traffic Breakdown and Calculation of Breakdown Probabilityat Bottleneck 233
5.4.5 Effect of Number of Simulation Realizations on Threshold Flow Rate and Maximum Highway Capacity 236
5.4.6 Mean Time Delay for Occurrence of TrafficBreakdown 237
5.4.7 Definition and Physical Meaning of Threshold Flow Rate for Spontaneous Traffic Breakdown 238
5.4.8 Definition and Physical Meaning of Maximum Highway Capacity of Free Flow at Bottleneck 239
5.4.9 Summary of Probabilistic Characteristics of Traffic Breakdown in Three-Phase Theory 240
5.5 Induced Traffic Breakdown at Bottleneck in Empirical Traffic Data and Numerical Simulations 240
5.6 Large Fluctuations in Free Flow: Minimum Highway Capacity as Threshold Flow Rate for Spontaneous Traffic Breakdown at Bottleneck 242
5.7 Stochastic Minimum and Maximum Highway Capacities 243
5.8 Competition of Driver Over-Acceleration and Driver Speed Adaptation: A Qualitative Model 246
5.9 Driver Speed Adaptation 247
5.9.1 Two-Dimensional (2D) Synchronized Flow States 247
5.9.2 Speed Adaptation Effect Within 2D-States of Synchronized Flow 252
5.9.3 About Mathematical Modeling of 2D-States of Synchronized Flow 253
5.10 Driver Over-Acceleration 257
5.10.1 Hypothesis About Discontinuous Character of Over-Acceleration 257
5.10.2 Mathematical Models of Over-Acceleration Effect on Single-Lane Road 261
5.10.3 Mathematical Simulation of Over-Acceleration Effect Due to Lane Changing 263
5.11 Microscopic Stochastic Features of S?F Instability Away of Bottlenecks 266
5.12 Microscopic Stochastic Features of S?F Instabilityat Bottleneck 270
5.12.1 ``Speed Peak''—Local Speed Disturbance in Synchronized Flow at Bottleneck Initiating S?F Instability 271
5.12.2 S?F Instability: Growing Speed Wave of Local Increase in Speed in Synchronized Flowat Bottleneck 274
5.12.3 Dissolving Speed Wave of Local Increase in Speed Within Synchronized Flow at Bottleneck 277
5.12.4 Nucleation Nature of S?F Instability 281
5.13 S?F Instability as Origin of Nucleation Nature of Traffic Breakdown at Bottleneck 282
5.13.1 Microscopic Nature of Permanent Local Speed Disturbance in Free Flow at Bottleneck 283
5.13.2 Sequence of F?S?F Transitions at Bottleneck 283
5.13.3 Nature of Random Time Delay of Traffic Breakdown at Bottleneck 285
5.14 Explanation of Empirical Features of Traffic Breakdown at Bottleneck with Three-Phase Theory 288
5.14.1 Nucleation of Traffic Breakdown at Road Bottleneck in Traffic Flow with Moving Bottleneck 289
5.14.2 Features of Flow-Rate Dependence of Probability of Traffic Breakdown at Bottleneck 292
5.15 Conclusions: Driver Behaviors Explaining Nucleation Nature of Real Traffic Breakdown at Highway Bottlenecks 297
References 299
6 Effect of Automatic Driving on Probability of Breakdown in Traffic Networks 301
6.1 Introduction 301
6.2 Operating Points and String Stability of Adaptive Cruise Control (ACC) 302
6.3 Decrease in Probability of Traffic Breakdown Through Automatic Driving Vehicles 306
6.4 Deterioration of Performance of Traffic System Through Automatic Driving Vehicles 313
6.5 Conclusions 320
References 320
7 Future Automatic Driving Based on Three-Phase Theory 322
7.1 Introduction 322
7.2 Automatic Driving Based on Three-Phase Theory 323
7.2.1 Infinite Number of Operating Points for Given Speed of Automatic Driving Vehicle 323
7.2.2 About Dynamic Behavior of Automatic Driving Vehicle Based on Three-Phase Theory 325
7.3 Driver Behaviors Facilitating Free Flow 327
7.4 Conclusions 330
References 331
8 The Reason for Incommensurability of Three-Phase Theory with Classical Traffic Flow Theories 332
8.1 Introduction 332
8.2 Classical Traffic Flow Instability Versus S?F Instability of Three-Phase Theory 334
8.3 Moving Jam Emergence in Classical Theories and Three-Phase Theory 335
8.3.1 Empirical Metastability of Free Flow with Respect to F?J Transition 335
8.3.2 Probability of Spontaneous F?J Transitions at On-Ramp Bottleneck in Two-Phase Model 340
8.3.3 S?J Transition in Two-Phase and Three-Phase Traffic Flow Models 343
8.4 General Congested Patterns Resulting from Sequence of Two Different Time-Delayed Transitions in Three-Phase Models 350
8.4.1 F?S?J Transitions 350
8.4.2 Complexity of Phase Transitions in Vehicular Traffic 354
8.5 The Fundamental Requirement for Reliability of ITS 357
8.6 Methodology of Study of Critical Nuclei Required for Phase Transitions 362
8.7 Induced F?J Transitions in Three-Phase and Two-Phase Traffic Flow Models 365
8.7.1 Induced F?J Transition at On-Ramp Bottleneck in Two-Phase Model 365
8.7.2 Induced F?J Transition at On-Ramp Bottleneck in Three-Phase Model 367
8.8 Effect of S?F Instability on Nuclei for Traffic Breakdown at Bottleneck 369
8.8.1 Induced Traffic Breakdown (Induced F?S Transition) at Bottleneck in Three-Phase Model 369
8.8.2 Two Different ``Critical Nuclei'' for Phase Transitions in Free Flow at Bottleneck in Three-Phase Theory 371
8.9 Basic Requirement for Three-Phase Traffic Flow Models 375
8.10 Basic Difference Between Three-Phase and Two-Phase Traffic Flow Models 379
8.11 Stochastic Highway Capacity: Classical Theory Versus Three-Phase Theory 383
8.12 Conclusions 386
References 389
9 Time-Delayed Breakdown at Traffic Signal in City Traffic 392
9.1 Introduction—When Can Classical Traffic Flow Theories Be Considered Special Cases of Three-PhaseTheory? 392
9.2 Traffic Breakdown at Signal in Classical Theory of CityTraffic 395
9.2.1 Vehicle Queue at Signal Versus Wide Moving Jam in Highway Traffic 396
9.2.2 ``Lost Time'' and Effective Green Phase Duration at Signal 398
9.2.3 Classical Signal Capacity 403
9.3 Time-Delayed Breakdown at Signal in Two-Phase and Three-Phase Traffic Flow Models: An Overview 406
9.3.1 Metastability of Under-Saturated Traffic at Signal 406
9.3.2 General Characteristics of Time-Delayed Traffic Breakdown at Signal 407
9.3.3 Effect of Large Fluctuations in Under-Saturated Traffic on Time-Delayed Traffic Breakdownat Signal 411
9.3.4 Stochastic Minimum and Maximum SignalCapacities 412
9.4 Breakdown of Green Wave (GW) in City Traffic in Framework of Three-Phase Theory 413
9.4.1 Model of GW 413
9.4.2 Two Basic Moving Patterns in Three-Phase Theory of City Traffic: Moving Synchronized Pattern (MSP) and Moving Queue 415
9.4.3 Physics of GW Breakdown at Signal 420
9.4.4 Probability of GW Breakdown at Signal 424
9.4.5 Flow–Flow Characteristic of GW Breakdownat Signal 425
9.4.6 Spatiotemporal Interaction of MSPs Induced by GW Propagation Though Sequence of CityIntersections 426
9.5 Effect of Time-Dependence of Arrival Flow Rate on Traffic Breakdown at Signal 430
9.5.1 Characteristics of Probability of Traffic Breakdown at Signal 431
9.5.2 Empirical Probability of Traffic Breakdown at Signal 433
9.5.3 Physical Reason for Dissolving Over-Saturated Traffic at Signal 434
9.6 Two-Phase Models of GM Model Class Versus Three-Phase Theory 436
9.7 Reasons for Metastable Under-Saturated Traffic at Signal 440
9.7.1 Arrival Flow Rate Exceeds Saturation Flow Rate During Green Signal Phase 441
9.7.1.1 Explanation of Condition (9.49) for Real City Traffic 441
9.7.1.2 Duration of Green Phase and Metastability of Under-Saturated Traffic 442
9.7.1.3 Qualitative Explanation of Metastability of Under-Saturated City Traffic 442
9.7.2 Arrival Flow Rate Is Smaller Than Saturation Flow Rate 445
9.7.2.1 Dissolving MSP in Under-Saturated Traffic 449
9.7.2.2 Compression of Under-Saturated Traffic at Signal Due to Formation of Dissolving MSP 449
9.7.2.3 Reason for Metastable Under-Saturated Traffic Under Condition (9.50) 452
9.8 ``Red Wave'' in City Traffic: Classical Theory of Traffic at Signal as Special Case of Three-Phase Theory 456
9.9 Conclusions 460
References 461
10 Theoretical Fundamental of Transportation Science—Breakdown Minimization (BM) Principle 464
10.1 Introduction—Motivation for BM Principle 464
10.2 Definition of BM Principle 465
10.3 Model of Traffic and Transportation Networks 466
10.4 A Mathematical Formulation of BM Principle 467
10.5 Constrain ``Alternative Network Routes'' 468
10.6 Basic Applications of BM Principle 470
10.7 Conclusions 471
References 472
11 Maximization of Network Throughput Ensuring Free Flow Conditions in Network 473
11.1 Introduction 473
11.2 Network Throughput Maximization Approach: The Maximization of Network Throughput by Prevention of Breakdown in Network 475
11.3 A Physical Measure of Traffic and Transportation Networks—Network Capacity 476
11.4 The Maximization of Network Throughput in Non-Steady State of Network 479
11.5 Behavior of Probability of Traffic Breakdown in Traffic and Transportation Networks 480
11.5.1 Fluctuations in Metastable Free Flow and Spontaneous Traffic Breakdown at Network Bottlenecks 480
11.5.2 Probability of Traffic Breakdown in Network Under Large Free Flow Fluctuations 483
11.6 Effect of Fluctuations on Prevention of Spontaneous Traffic Breakdown in Networks 484
11.6.1 Empirical Induced and Spontaneous Traffic Breakdowns in Networks 485
11.6.2 Network Throughput Maximization Preventing Spontaneous Breakdown Under Small Free Flow Fluctuations in Networks 487
11.6.3 Probability of Traffic Breakdown in Network Under Small Free Flow Fluctuations 488
11.6.4 Network Capacity Under Small Free FlowFluctuations 489
11.6.5 Heterogeneous Free Flow Fluctuations in Networks 490
11.6.6 ``Non-Isolated'' Traffic Networks 492
11.6.7 Prevention of Dissolving Over-Saturated Traffic at Traffic Signals in City Networks 492
11.7 Conclusions 493
References 494
12 Minimization of Traffic Congestion in Networks 496
12.1 Introduction 496
12.2 An Explicit Formulation for BM Principle 497
12.3 Empirical Spontaneous Traffic Breakdowns as Independent Events in Network 499
12.4 Simulations of Minimum Probability of Traffic Breakdown in Networks 503
12.4.1 General Characteristics of Applications of BM Principle for Simple Network Model 503
12.4.2 Two-Route and Three-Route Simple NetworkModels 504
12.4.3 Probabilistic Features of Traffic Breakdown in Networks 508
12.5 Effect of Application of BM Principle on Random Traffic Breakdown at Network Bottlenecks 511
12.6 Traffic Control in Framework of Three-Phase Theory 514
12.6.1 Congested Pattern Control Approach 514
12.6.2 ANCONA On-Ramp Metering 517
12.6.3 Enforcing Synchronized Flow Under Heavy Traffic Congestion 523
12.7 Conclusions 523
References 524
13 Deterioration of Traffic System Through Standard Dynamic Traffic Assignment in Networks 526
13.1 Introduction—Wardrop's User Equilibrium (UE) and System Optimum (SO) 526
13.2 BM Principle Versus Wardrop's Equilibria: General Results 528
13.3 Facilitation of Traffic Breakdown in Networks Through the Use of Wardrop's UE 531
13.3.1 Wardrop's UE in Simple Network Models 531
13.3.2 Dynamic Traffic Assignment with Congested Pattern Control Approach 537
13.3.3 Dynamic Traffic Assignment Under Time-Independent Total Network Inflow Rate 540
13.3.4 Dynamic Traffic Assignment Under Time-Dependent Total Network Inflow Rate 541
13.3.4.1 Application of Wardrop's UE 541
13.3.4.2 Application of Network Throughput Maximization Approach 542
13.4 Facilitation of Traffic Breakdown in Networks Through the Use of Wardrop's SO 542
13.5 Control of Traffic Breakdown in Networks: Wardrop's UE Versus BM Principle 546
13.6 Conclusions 549
References 551
14 Discussion of Future Dynamic Traffic Assignment and Control in Networks 555
14.1 Introduction 555
14.2 The Necessity of Applications of BM Principle 556
14.3 Benefits of Applications of BM Principle 558
14.4 Choice of Threshold for Constrain ``Alternative Network Routes (Paths)'' in Applications of BM Principle 559
14.5 Possible Applications of BM Principle for Real Traffic and Transportation Networks 560
14.5.1 Applications of Network Throughput Maximization Approach 561
14.5.2 Possible Applications of BM Principle Under Subsequent Increase in Total Network Inflow Rate 562
14.5.3 About Future Control of Heavy Traffic Congestion in Networks 563
14.6 Conclusions 564
15 Conclusions and Outlook 565
15.1 Empirical Fundamental of Transportation Science 566
15.2 Theoretical Fundamentals of Transportation Science 567
15.2.1 The Three-Phase Traffic Theory 567
15.2.2 The Breakdown Minimization (BM) Principle 569
15.3 Failure of Classical Traffic and Transportation Theories 570
15.4 Paradigm Shift in Transportation Science 572
15.5 Challenges for Transportation Science 572
Erratum to: The Reason for Incommensurability of Three-Phase Theory with Classical Traffic Flow Theories 574
A Kerner-Klenov Stochastic Microscopic Model in Framework of Three-Phase Theory 576
Additional List of Symbols Used in Appendices A and B 576
A.1 Motivation 578
A.2 Discrete Model Version 580
A.3 Update Rules of Vehicle Motion in Road Lane in Model of Identical Drivers and Vehicles 581
A.3.1 Synchronization Space Gap and Hypothetical Steady States of Synchronized Flow 582
A.3.2 Model Speed Fluctuations 583
A.3.3 Stochastic Time Delays of Acceleration and Deceleration 584
A.3.4 Simulations of Slow-to-Start Rule 585
A.3.5 Safe Speed 586
A.3.6 Boundary and Initial Conditions 587
A.4 Physical Meaning of State of Vehicle Motion 588
A.5 Lane Changing Rules for Two-Lane Road 589
A.6 Models of Road Bottlenecks 590
A.6.1 On-, Off-Ramp, and Merge Bottlenecks 590
A.6.2 Moving Bottleneck 591
A.6.3 Models of Vehicle Merging at Bottlenecks 591
A.6.3.1 Vehicle Speed Adaptation Within Merging Region of Bottleneck 591
A.6.3.2 Safety Conditions for Vehicle Merging 593
A.6.3.3 Speed and Coordinate of Vehicle After Vehicle Merging 594
A.6.4 ACC-Vehicle Merging at On-Ramp Bottleneck 594
A.7 Stochastic Simulation of ``Strong'' and ``Weak'' Speed Adaptation 595
A.7.1 Simulation of Driver Speed Adaptation Effect 595
A.7.2 Stochastic Driver's Choice of Space Gap in Synchronized Flow 597
A.7.3 ``Jam-Absorption'' Effect 599
A.8 Simulation Approaches to Over-Acceleration Effect 601
A.8.1 Implicit Simulation of Over-Acceleration Effect Through Driver Acceleration 602
A.8.2 Simulation of Over-Acceleration Effect Through Combination of Lane Changing to Faster Lane and Random Driver Acceleration 602
A.8.3 ``Boundary'' Over-Acceleration 602
A.8.4 Explicit Simulation of Over-Acceleration Effect Through Lane Changing to Faster Lane 603
A.9 A Markov Chain: Sequence of Numerical Calculationsof Model 605
A.9.1 Vehicles Moving Outside Merging Regions of Bottlenecks 605
A.9.2 Vehicles Moving Within Merging Regions of Bottlenecks 608
A.10 Model of Heterogeneous Traffic Flow 611
A.10.1 Vehicle Motion on Single-Lane Road 612
A.10.1.1 Steady States and Vehicle Motion 612
A.10.1.2 Fluctuations 614
A.10.1.3 Safe Speed 614
A.10.2 Lane Changing Rules in Model of Two-Lane Road 614
A.10.3 Boundary, Initial Conditions, and Models of Bottlenecks 617
A.11 Realistic Heterogeneous Traffic Flow 618
A.11.1 Dependence of Free Flow Speed on Space Gap 618
A.11.2 Simulations of Traffic Patterns on Realistic Three-Lane Highway 618
A.11.3 Update Rules of Vehicle Motion in Road Lane 621
A.11.4 Lane Changing Rules on Three-Lane Road 622
A.11.5 Models of On- and Off-Ramp Bottlenecks on Three-Lane Road 624
A.11.6 Some Results of Simulations 626
A.12 Traffic Flow Model for City Traffic 629
A.12.1 Adaptation of Model Parameters for City Traffic 629
A.12.2 Rules of Vehicle Motion 629
A.12.3 Reduction of Three-Phase Model to Two-PhaseModel 631
References 632
B Kerner-Klenov-Schreckenberg-Wolf (KKSW) Cellular Automaton (CA) Three-Phase Model 634
B.1 Motivation 634
B.2 Rules of Vehicle Motion in KKSW CA Model 635
B.3 Models of Bottlenecks for KKSW CA Model 641
B.3.1 On- and Off-Ramp Bottlenecks 641
B.3.2 Vehicle Motion Rules in Merging Regionof Bottlenecks 642
B.4 Comparison of KKSW CA Model with Nagel-Schreckenberg CA Model 645
References 646
C Dynamic Traffic Assignment Based on Wardrop's UE with Step-by-Step Method 647
Reference 649
Glossary 650
Index 666