Kerner Breakdown in Traffic Networks

Fundamentals of Transportation Science
1. Auflage 2017
ISBN: 978-3-662-54473-0
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 673 Seiten

This book offers a detailed investigation of breakdowns in traffic and transportation networks. It shows empirically that transitions from free flow to so-called synchronized flow, initiated by local disturbances at network bottlenecks, display a nucleation-type behavior: while small disturbances in free flow decay, larger ones grow further and lead to breakdowns at the bottlenecks. Further, it discusses in detail the significance of this nucleation effect for traffic and transportation theories, and the consequences this has for future automatic driving, traffic control, dynamic traffic assignment, and optimization in traffic and transportation networks. Starting from a large volume of field traffic data collected from various sources obtained solely through measurements in real world traffic, the author develops his insights, with an emphasis less on reviewing existing methodologies, models and theories, and more on providing a detailed analysis of empirical traffic data and drawing consequences regarding the minimum requirements for any traffic and transportation theories to be valid. The book - proves the empirical nucleation nature of traffic breakdown in networks - discusses the origin of the failure of classical traffic and transportation theories - shows that the three-phase theory is incommensurable with the classical traffic theories, and - explains why current state-of-the art dynamic traffic assignments tend to provoke heavy traffic congestion, making it a valuable reference resource for a wide audience of scientists and postgraduate students interested in the fundamental understanding of empirical traffic phenomena and related data-driven phenomenology, as well as for practitioners working in the fields of traffic and transportation engineering.

Autoren/Hrsg.

Kerner, Boris S.

Inhaltsverzeichnis

1;Preface;5
2;Acknowledgments;7
3;Contents;8
4;Acronyms and Symbols;21
5;1 Introduction—The Reason for Paradigm Shift in Transportation Science;28
5.1;1.1 Definitions of Free and Congested Traffic in Empirical Data;29
5.2;1.2 Bottlenecks;32
5.3;1.3 Definitions of Synchronized Flow and Wide Moving Jam Phases in Empirical Data for Congested Traffic;33
5.4;1.4 Traffic Breakdown;36
5.5;1.5 Empirical Phase Transitions in Traffic Flow;36
5.6;1.6 Empirical Fundamental of Transportation Science;39
5.7;1.7 The Origin of Failure of Classical Traffic and Transportation Theories;44
5.7.1;1.7.1 Nature of Stochastic Highway Capacity;44
5.7.2;1.7.2 Description of Traffic Breakdown with Classical Traffic Flow Models;45
5.7.2.1;1.7.2.1 About Applications of LWR-Model;46
5.7.2.2;1.7.2.2 About Traffic Flow Models of General Motors (GM) Model Class;46
5.7.2.3;1.7.2.3 Common Critical Statements to Classical Traffic Flow Models and Their Applications;47
5.7.2.4;1.7.2.4 About Achievements of Classical Traffic Flow Models;48
5.7.3;1.7.3 Deterioration of Traffic System Through Standard Dynamic Traffic Assignment in Networks;48
5.7.4;1.7.4 Failure of Applications of Intelligent Transportation Systems (ITS) Based on Classical Traffic Theories;50
5.8;1.8 Classical Ideas of Transportation Science and Nucleation Nature of Empirical Traffic Breakdown;52
5.9;1.9 Three-Phase Traffic Theory;52
5.10;1.10 Infinite Number of Stochastic Highway Capacities in Three-Phase Theory;56
5.11;1.11 Breakdown Minimization (BM) Principle;57
5.12;1.12 Mathematical Three-Phase Traffic Flow Models and ITS-Applications of Three-Phase Theory;58
5.13;1.13 Criticism of Three-Phase Traffic Theory;63
5.14;1.14 Incommensurability of Three-Phase Traffic Theory and Classical Traffic Theories;66
5.15;1.15 Objectives of the Book;67
5.16;1.16 Book's Structure;69
5.17;References;71
6;2 Achievements of Empirical Studies of Traffic Breakdown at Highway Bottlenecks;99
6.1;2.1 Introduction;99
6.2;2.2 Empirical Features of Traffic Breakdown;100
6.2.1;2.2.1 Traffic Breakdown—Transition from Free to Synchronized Flow at Highway Bottleneck;100
6.2.2;2.2.2 Time-Dependence of Flow Rate During Empirical Traffic Breakdown at Highway Bottleneck;101
6.3;2.3 Stochastic Behavior and Probability of Traffic Breakdown at Highway Bottleneck;103
6.4;2.4 Conclusions;106
6.5;References;107
7;3 Nucleation Nature of Traffic Breakdown—Empirical Fundamental of Transportation Science;113
7.1;3.1 Introduction;113
7.2;3.2 Definitions of Empirical Spontaneous and Empirical Induced Traffic Breakdowns at Highway Bottlenecks;114
7.3;3.3 Explanation of Term ``Nucleus'' for Traffic Breakdown;118
7.4;3.4 Nucleation of Empirical Spontaneous Traffic Breakdown at Highway Bottlenecks;120
7.4.1;3.4.1 Waves in Empirical Free Flow;120
7.4.2;3.4.2 Empirical Nucleation of Traffic Breakdown at On-Ramp Bottleneck;122
7.4.3;3.4.3 Empirical Nucleation of Traffic Breakdown at Off-Ramp Bottleneck;122
7.4.4;3.4.4 Empirical Permanent Speed Disturbance at Highway Bottleneck and Nucleation of Traffic Breakdown;126
7.4.5;3.4.5 Empirical Two-Dimensional (2D) Asymmetric Spatiotemporal Structure of Nuclei for Traffic Breakdown;130
7.5;3.5 Waves in Free Flow and Empirical Spontaneous Traffic Breakdown in Flow Without Trucks;133
7.6;3.6 Induced Traffic Breakdown—Empirical Proof of Nucleation Nature of Empirical Traffic Breakdown;133
7.6.1;3.6.1 Sources of Nucleus for Empirical Traffic Breakdown;134
7.6.2;3.6.2 Induced Traffic Breakdown as One of Different Consequences of Spillover in Real Traffic;142
7.7;3.7 Empirical Nucleation Nature of Traffic Breakdown as Origin of the Infinity of Highway Capacities;143
7.8;3.8 Conclusions;146
7.9;References;147
8;4 Failure of Generally Accepted Classical Traffic Flow Theories;149
8.1;4.1 Introduction;149
8.2;4.2 Fundamental Diagram of Traffic Flow;151
8.2.1;4.2.1 Empirical Features of Fundamental Diagram of Traffic Flow;151
8.2.2;4.2.2 Application of Fundamental Diagram for Traffic Flow Modelling;154
8.3;4.3 Traffic Breakdown at Bottleneck in Lighthill-Whitham-Richards (LWR) Model;154
8.3.1;4.3.1 Basic Assumption of LWR Model;154
8.3.2;4.3.2 Achievements of LWR Theory in Description of Traffic Breakdown;155
8.3.3;4.3.3 Failure of LWR Theory in Explanation of Empirical Nucleation Nature of Traffic Breakdown;157
8.4;4.4 Description of Traffic Breakdown with General Motors (GM) Model Class;160
8.4.1;4.4.1 Classical Traffic Flow Instability: Growing Wave of Local Speed Reduction in Traffic Flow Due to Over-Deceleration Effect;160
8.4.2;4.4.2 ``Boomerang'' Effect;162
8.4.3;4.4.3 Moving Jam Emergence at Bottleneck;165
8.5;4.5 Achievements of Generally Accepted ClassicalTraffic Models;166
8.5.1;4.5.1 Metastability of Free Flow with Respect to Moving Jam Emergence and Line J;167
8.5.1.1;4.5.1.1 Characteristic Parameters of Wide Moving Jam;168
8.5.1.2;4.5.1.2 Line J;171
8.5.2;4.5.2 Driver Behavioral Assumptions;173
8.6;4.6 Summary of Achievements of Classical Traffic Flow Models;174
8.7;4.7 Why Are Generally Accepted Classical Two-Phase Traffic Flow Models Inconsistent with Features of Real Traffic?;175
8.8;4.8 Model Validation with Empirical Data;177
8.9;4.9 Applications of Classical Traffic Flow Theories for Development of Intelligent Transportation systems (ITS);180
8.9.1;4.9.1 Simulations of ITS Performance;180
8.9.2;4.9.2 On-Ramp Metering;182
8.9.3;4.9.3 Effect of Automatic Driving on Traffic Flow;183
8.10;4.10 Classical Understanding of Stochastic Highway Capacity;185
8.11;4.11 Strict Belief in Classical Theories as Reason for Defective Analysis of Empirical Traffic Phenomena;189
8.11.1;4.11.1 A Possible Origin of Failure of Classical Traffic Flow Models;189
8.11.2;4.11.2 Capacity Drop;191
8.11.3;4.11.3 Macroscopic Fundamental Diagram;193
8.11.4;4.11.4 Boomerang Effect, Homogeneous Congested Traffic, and Diagram of Congested Traffic States;194
8.11.5;4.11.5 Driver Behavioral Assumptions;196
8.12;4.12 Conclusions;198
8.13;References;199
9;5 Theoretical Fundamental of Transportation Science—The Three-Phase Theory;213
9.1;5.1 Introduction—Definition of Stochastic Highway Capacity;213
9.2;5.2 The Basic Assumption of Three-Phase Traffic Theory;217
9.3;5.3 Qualitative Theory of Critical Nucleus for Traffic Breakdown at Bottleneck;218
9.3.1;5.3.1 Permanent Speed Disturbance at Bottleneck;218
9.3.2;5.3.2 Critical Nucleus at Location of Permanent Speed Disturbance;220
9.3.3;5.3.3 Dependence of Critical Nucleus on Flow Rate;222
9.3.4;5.3.4 Z-Characteristic for Traffic Breakdown;225
9.4;5.4 Probabilistic Characteristics of Spontaneous Traffic Breakdown at Bottleneck;226
9.4.1;5.4.1 Theoretical Probability of Spontaneous Traffic Breakdown;226
9.4.2;5.4.2 Theoretical Z-Characteristic for Traffic Breakdown at Bottleneck;228
9.4.3;5.4.3 Flow-Rate Dependence of Characteristics of Spontaneous Traffic Breakdown;230
9.4.3.1;5.4.3.1 Flow-Rate Region I;230
9.4.3.2;5.4.3.2 Flow-Rate Region II;231
9.4.3.3;5.4.3.3 Flow-Rate Region III;232
9.4.3.4;5.4.3.4 Flow-Rate Region IV;233
9.4.4;5.4.4 Time-Delayed Traffic Breakdown and Calculation of Breakdown Probabilityat Bottleneck;233
9.4.5;5.4.5 Effect of Number of Simulation Realizations on Threshold Flow Rate and Maximum Highway Capacity;236
9.4.6;5.4.6 Mean Time Delay for Occurrence of TrafficBreakdown;237
9.4.7;5.4.7 Definition and Physical Meaning of Threshold Flow Rate for Spontaneous Traffic Breakdown;238
9.4.8;5.4.8 Definition and Physical Meaning of Maximum Highway Capacity of Free Flow at Bottleneck;239
9.4.9;5.4.9 Summary of Probabilistic Characteristics of Traffic Breakdown in Three-Phase Theory;240
9.5;5.5 Induced Traffic Breakdown at Bottleneck in Empirical Traffic Data and Numerical Simulations;240
9.6;5.6 Large Fluctuations in Free Flow: Minimum Highway Capacity as Threshold Flow Rate for Spontaneous Traffic Breakdown at Bottleneck;242
9.7;5.7 Stochastic Minimum and Maximum Highway Capacities;243
9.8;5.8 Competition of Driver Over-Acceleration and Driver Speed Adaptation: A Qualitative Model;246
9.9;5.9 Driver Speed Adaptation;247
9.9.1;5.9.1 Two-Dimensional (2D) Synchronized Flow States;247
9.9.2;5.9.2 Speed Adaptation Effect Within 2D-States of Synchronized Flow;252
9.9.3;5.9.3 About Mathematical Modeling of 2D-States of Synchronized Flow;253
9.10;5.10 Driver Over-Acceleration;257
9.10.1;5.10.1 Hypothesis About Discontinuous Character of Over-Acceleration;257
9.10.2;5.10.2 Mathematical Models of Over-Acceleration Effect on Single-Lane Road;261
9.10.3;5.10.3 Mathematical Simulation of Over-Acceleration Effect Due to Lane Changing;263
9.11;5.11 Microscopic Stochastic Features of S?F Instability Away of Bottlenecks;266
9.12;5.12 Microscopic Stochastic Features of S?F Instabilityat Bottleneck;270
9.12.1;5.12.1 ``Speed Peak''—Local Speed Disturbance in Synchronized Flow at Bottleneck Initiating S?F Instability;271
9.12.2;5.12.2 S?F Instability: Growing Speed Wave of Local Increase in Speed in Synchronized Flowat Bottleneck;274
9.12.3;5.12.3 Dissolving Speed Wave of Local Increase in Speed Within Synchronized Flow at Bottleneck;277
9.12.4;5.12.4 Nucleation Nature of S?F Instability;281
9.13;5.13 S?F Instability as Origin of Nucleation Nature of Traffic Breakdown at Bottleneck;282
9.13.1;5.13.1 Microscopic Nature of Permanent Local Speed Disturbance in Free Flow at Bottleneck;283
9.13.2;5.13.2 Sequence of F?S?F Transitions at Bottleneck;283
9.13.3;5.13.3 Nature of Random Time Delay of Traffic Breakdown at Bottleneck;285
9.14;5.14 Explanation of Empirical Features of Traffic Breakdown at Bottleneck with Three-Phase Theory;288
9.14.1;5.14.1 Nucleation of Traffic Breakdown at Road Bottleneck in Traffic Flow with Moving Bottleneck;289
9.14.2;5.14.2 Features of Flow-Rate Dependence of Probability of Traffic Breakdown at Bottleneck;292
9.15;5.15 Conclusions: Driver Behaviors Explaining Nucleation Nature of Real Traffic Breakdown at Highway Bottlenecks;297
9.16;References;299
10;6 Effect of Automatic Driving on Probability of Breakdown in Traffic Networks;301
10.1;6.1 Introduction;301
10.2;6.2 Operating Points and String Stability of Adaptive Cruise Control (ACC);302
10.3;6.3 Decrease in Probability of Traffic Breakdown Through Automatic Driving Vehicles;306
10.4;6.4 Deterioration of Performance of Traffic System Through Automatic Driving Vehicles;313
10.5;6.5 Conclusions;320
10.6;References;320
11;7 Future Automatic Driving Based on Three-Phase Theory;322
11.1;7.1 Introduction;322
11.2;7.2 Automatic Driving Based on Three-Phase Theory;323
11.2.1;7.2.1 Infinite Number of Operating Points for Given Speed of Automatic Driving Vehicle;323
11.2.2;7.2.2 About Dynamic Behavior of Automatic Driving Vehicle Based on Three-Phase Theory;325
11.3;7.3 Driver Behaviors Facilitating Free Flow;327
11.4;7.4 Conclusions;330
11.5;References;331
12;8 The Reason for Incommensurability of Three-Phase Theory with Classical Traffic Flow Theories;332
12.1;8.1 Introduction;332
12.2;8.2 Classical Traffic Flow Instability Versus S?F Instability of Three-Phase Theory;334
12.3;8.3 Moving Jam Emergence in Classical Theories and Three-Phase Theory;335
12.3.1;8.3.1 Empirical Metastability of Free Flow with Respect to F?J Transition;335
12.3.2;8.3.2 Probability of Spontaneous F?J Transitions at On-Ramp Bottleneck in Two-Phase Model;340
12.3.3;8.3.3 S?J Transition in Two-Phase and Three-Phase Traffic Flow Models;343
12.4;8.4 General Congested Patterns Resulting from Sequence of Two Different Time-Delayed Transitions in Three-Phase Models;350
12.4.1;8.4.1 F?S?J Transitions;350
12.4.2;8.4.2 Complexity of Phase Transitions in Vehicular Traffic;354
12.5;8.5 The Fundamental Requirement for Reliability of ITS;357
12.6;8.6 Methodology of Study of Critical Nuclei Required for Phase Transitions;362
12.7;8.7 Induced F?J Transitions in Three-Phase and Two-Phase Traffic Flow Models;365
12.7.1;8.7.1 Induced F?J Transition at On-Ramp Bottleneck in Two-Phase Model;365
12.7.2;8.7.2 Induced F?J Transition at On-Ramp Bottleneck in Three-Phase Model;367
12.8;8.8 Effect of S?F Instability on Nuclei for Traffic Breakdown at Bottleneck;369
12.8.1;8.8.1 Induced Traffic Breakdown (Induced F?S Transition) at Bottleneck in Three-Phase Model;369
12.8.2;8.8.2 Two Different ``Critical Nuclei'' for Phase Transitions in Free Flow at Bottleneck in Three-Phase Theory;371
12.9;8.9 Basic Requirement for Three-Phase Traffic Flow Models;375
12.10;8.10 Basic Difference Between Three-Phase and Two-Phase Traffic Flow Models;379
12.11;8.11 Stochastic Highway Capacity: Classical Theory Versus Three-Phase Theory;383
12.12;8.12 Conclusions;386
12.13;References;389
13;9 Time-Delayed Breakdown at Traffic Signal in City Traffic;392
13.1;9.1 Introduction—When Can Classical Traffic Flow Theories Be Considered Special Cases of Three-PhaseTheory?;392
13.2;9.2 Traffic Breakdown at Signal in Classical Theory of CityTraffic;395
13.2.1;9.2.1 Vehicle Queue at Signal Versus Wide Moving Jam in Highway Traffic;396
13.2.2;9.2.2 ``Lost Time'' and Effective Green Phase Duration at Signal;398
13.2.3;9.2.3 Classical Signal Capacity;403
13.3;9.3 Time-Delayed Breakdown at Signal in Two-Phase and Three-Phase Traffic Flow Models: An Overview;406
13.3.1;9.3.1 Metastability of Under-Saturated Traffic at Signal;406
13.3.2;9.3.2 General Characteristics of Time-Delayed Traffic Breakdown at Signal;407
13.3.3;9.3.3 Effect of Large Fluctuations in Under-Saturated Traffic on Time-Delayed Traffic Breakdownat Signal;411
13.3.4;9.3.4 Stochastic Minimum and Maximum SignalCapacities;412
13.4;9.4 Breakdown of Green Wave (GW) in City Traffic in Framework of Three-Phase Theory;413
13.4.1;9.4.1 Model of GW;413
13.4.2;9.4.2 Two Basic Moving Patterns in Three-Phase Theory of City Traffic: Moving Synchronized Pattern (MSP) and Moving Queue;415
13.4.3;9.4.3 Physics of GW Breakdown at Signal;420
13.4.4;9.4.4 Probability of GW Breakdown at Signal;424
13.4.5;9.4.5 Flow–Flow Characteristic of GW Breakdownat Signal;425
13.4.6;9.4.6 Spatiotemporal Interaction of MSPs Induced by GW Propagation Though Sequence of CityIntersections;426
13.5;9.5 Effect of Time-Dependence of Arrival Flow Rate on Traffic Breakdown at Signal;430
13.5.1;9.5.1 Characteristics of Probability of Traffic Breakdown at Signal;431
13.5.2;9.5.2 Empirical Probability of Traffic Breakdown at Signal;433
13.5.3;9.5.3 Physical Reason for Dissolving Over-Saturated Traffic at Signal;434
13.6;9.6 Two-Phase Models of GM Model Class Versus Three-Phase Theory;436
13.7;9.7 Reasons for Metastable Under-Saturated Traffic at Signal;440
13.7.1;9.7.1 Arrival Flow Rate Exceeds Saturation Flow Rate During Green Signal Phase;441
13.7.1.1;9.7.1.1 Explanation of Condition (9.49) for Real City Traffic;441
13.7.1.2;9.7.1.2 Duration of Green Phase and Metastability of Under-Saturated Traffic;442
13.7.1.3;9.7.1.3 Qualitative Explanation of Metastability of Under-Saturated City Traffic;442
13.7.2;9.7.2 Arrival Flow Rate Is Smaller Than Saturation Flow Rate;445
13.7.2.1;9.7.2.1 Dissolving MSP in Under-Saturated Traffic;449
13.7.2.2;9.7.2.2 Compression of Under-Saturated Traffic at Signal Due to Formation of Dissolving MSP;449
13.7.2.3;9.7.2.3 Reason for Metastable Under-Saturated Traffic Under Condition (9.50);452
13.8;9.8 ``Red Wave'' in City Traffic: Classical Theory of Traffic at Signal as Special Case of Three-Phase Theory;456
13.9;9.9 Conclusions;460
13.10;References;461
14;10 Theoretical Fundamental of Transportation Science—Breakdown Minimization (BM) Principle;464
14.1;10.1 Introduction—Motivation for BM Principle;464
14.2;10.2 Definition of BM Principle;465
14.3;10.3 Model of Traffic and Transportation Networks;466
14.4;10.4 A Mathematical Formulation of BM Principle;467
14.5;10.5 Constrain ``Alternative Network Routes'';468
14.6;10.6 Basic Applications of BM Principle;470
14.7;10.7 Conclusions;471
14.8;References;472
15;11 Maximization of Network Throughput Ensuring Free Flow Conditions in Network;473
15.1;11.1 Introduction;473
15.2;11.2 Network Throughput Maximization Approach: The Maximization of Network Throughput by Prevention of Breakdown in Network;475
15.3;11.3 A Physical Measure of Traffic and Transportation Networks—Network Capacity;476
15.4;11.4 The Maximization of Network Throughput in Non-Steady State of Network;479
15.5;11.5 Behavior of Probability of Traffic Breakdown in Traffic and Transportation Networks;480
15.5.1;11.5.1 Fluctuations in Metastable Free Flow and Spontaneous Traffic Breakdown at Network Bottlenecks;480
15.5.2;11.5.2 Probability of Traffic Breakdown in Network Under Large Free Flow Fluctuations;483
15.6;11.6 Effect of Fluctuations on Prevention of Spontaneous Traffic Breakdown in Networks;484
15.6.1;11.6.1 Empirical Induced and Spontaneous Traffic Breakdowns in Networks;485
15.6.2;11.6.2 Network Throughput Maximization Preventing Spontaneous Breakdown Under Small Free Flow Fluctuations in Networks;487
15.6.3;11.6.3 Probability of Traffic Breakdown in Network Under Small Free Flow Fluctuations;488
15.6.4;11.6.4 Network Capacity Under Small Free FlowFluctuations;489
15.6.5;11.6.5 Heterogeneous Free Flow Fluctuations in Networks;490
15.6.6;11.6.6 ``Non-Isolated'' Traffic Networks;492
15.6.7;11.6.7 Prevention of Dissolving Over-Saturated Traffic at Traffic Signals in City Networks;492
15.7;11.7 Conclusions;493
15.8;References;494
16;12 Minimization of Traffic Congestion in Networks;496
16.1;12.1 Introduction;496
16.2;12.2 An Explicit Formulation for BM Principle;497
16.3;12.3 Empirical Spontaneous Traffic Breakdowns as Independent Events in Network;499
16.4;12.4 Simulations of Minimum Probability of Traffic Breakdown in Networks;503
16.4.1;12.4.1 General Characteristics of Applications of BM Principle for Simple Network Model;503
16.4.2;12.4.2 Two-Route and Three-Route Simple NetworkModels;504
16.4.3;12.4.3 Probabilistic Features of Traffic Breakdown in Networks;508
16.5;12.5 Effect of Application of BM Principle on Random Traffic Breakdown at Network Bottlenecks;511
16.6;12.6 Traffic Control in Framework of Three-Phase Theory;514
16.6.1;12.6.1 Congested Pattern Control Approach;514
16.6.2;12.6.2 ANCONA On-Ramp Metering;517
16.6.3;12.6.3 Enforcing Synchronized Flow Under Heavy Traffic Congestion;523
16.7;12.7 Conclusions;523
16.8;References;524
17;13 Deterioration of Traffic System Through Standard Dynamic Traffic Assignment in Networks;526
17.1;13.1 Introduction—Wardrop's User Equilibrium (UE) and System Optimum (SO);526
17.2;13.2 BM Principle Versus Wardrop's Equilibria: General Results;528
17.3;13.3 Facilitation of Traffic Breakdown in Networks Through the Use of Wardrop's UE;531
17.3.1;13.3.1 Wardrop's UE in Simple Network Models;531
17.3.2;13.3.2 Dynamic Traffic Assignment with Congested Pattern Control Approach;537
17.3.3;13.3.3 Dynamic Traffic Assignment Under Time-Independent Total Network Inflow Rate;540
17.3.4;13.3.4 Dynamic Traffic Assignment Under Time-Dependent Total Network Inflow Rate;541
17.3.4.1;13.3.4.1 Application of Wardrop's UE;541
17.3.4.2;13.3.4.2 Application of Network Throughput Maximization Approach;542
17.4;13.4 Facilitation of Traffic Breakdown in Networks Through the Use of Wardrop's SO;542
17.5;13.5 Control of Traffic Breakdown in Networks: Wardrop's UE Versus BM Principle;546
17.6;13.6 Conclusions;549
17.7;References;551
18;14 Discussion of Future Dynamic Traffic Assignment and Control in Networks;555
18.1;14.1 Introduction;555
18.2;14.2 The Necessity of Applications of BM Principle;556
18.3;14.3 Benefits of Applications of BM Principle;558
18.4;14.4 Choice of Threshold for Constrain ``Alternative Network Routes (Paths)'' in Applications of BM Principle;559
18.5;14.5 Possible Applications of BM Principle for Real Traffic and Transportation Networks;560
18.5.1;14.5.1 Applications of Network Throughput Maximization Approach;561
18.5.2;14.5.2 Possible Applications of BM Principle Under Subsequent Increase in Total Network Inflow Rate;562
18.5.3;14.5.3 About Future Control of Heavy Traffic Congestion in Networks;563
18.6;14.6 Conclusions;564
19;15 Conclusions and Outlook;565
19.1;15.1 Empirical Fundamental of Transportation Science;566
19.2;15.2 Theoretical Fundamentals of Transportation Science;567
19.2.1;15.2.1 The Three-Phase Traffic Theory;567
19.2.2;15.2.2 The Breakdown Minimization (BM) Principle;569
19.3;15.3 Failure of Classical Traffic and Transportation Theories;570
19.4;15.4 Paradigm Shift in Transportation Science;572
19.5;15.5 Challenges for Transportation Science;572
20;Erratum to: The Reason for Incommensurability of Three-Phase Theory with Classical Traffic Flow Theories;574
21;A Kerner-Klenov Stochastic Microscopic Model in Framework of Three-Phase Theory;576
21.1;Additional List of Symbols Used in Appendices A and B;576
21.2;A.1 Motivation;578
21.3;A.2 Discrete Model Version;580
21.4;A.3 Update Rules of Vehicle Motion in Road Lane in Model of Identical Drivers and Vehicles;581
21.4.1;A.3.1 Synchronization Space Gap and Hypothetical Steady States of Synchronized Flow;582
21.4.2;A.3.2 Model Speed Fluctuations;583
21.4.3;A.3.3 Stochastic Time Delays of Acceleration and Deceleration;584
21.4.4;A.3.4 Simulations of Slow-to-Start Rule;585
21.4.5;A.3.5 Safe Speed;586
21.4.6;A.3.6 Boundary and Initial Conditions;587
21.5;A.4 Physical Meaning of State of Vehicle Motion;588
21.6;A.5 Lane Changing Rules for Two-Lane Road;589
21.7;A.6 Models of Road Bottlenecks;590
21.7.1;A.6.1 On-, Off-Ramp, and Merge Bottlenecks;590
21.7.2;A.6.2 Moving Bottleneck;591
21.7.3;A.6.3 Models of Vehicle Merging at Bottlenecks;591
21.7.3.1;A.6.3.1 Vehicle Speed Adaptation Within Merging Region of Bottleneck;591
21.7.3.2;A.6.3.2 Safety Conditions for Vehicle Merging;593
21.7.3.3;A.6.3.3 Speed and Coordinate of Vehicle After Vehicle Merging;594
21.7.4;A.6.4 ACC-Vehicle Merging at On-Ramp Bottleneck;594
21.8;A.7 Stochastic Simulation of ``Strong'' and ``Weak'' Speed Adaptation;595
21.8.1;A.7.1 Simulation of Driver Speed Adaptation Effect;595
21.8.2;A.7.2 Stochastic Driver's Choice of Space Gap in Synchronized Flow;597
21.8.3;A.7.3 ``Jam-Absorption'' Effect;599
21.9;A.8 Simulation Approaches to Over-Acceleration Effect;601
21.9.1;A.8.1 Implicit Simulation of Over-Acceleration Effect Through Driver Acceleration;602
21.9.2;A.8.2 Simulation of Over-Acceleration Effect Through Combination of Lane Changing to Faster Lane and Random Driver Acceleration;602
21.9.3;A.8.3 ``Boundary'' Over-Acceleration;602
21.9.4;A.8.4 Explicit Simulation of Over-Acceleration Effect Through Lane Changing to Faster Lane;603
21.10;A.9 A Markov Chain: Sequence of Numerical Calculationsof Model;605
21.10.1;A.9.1 Vehicles Moving Outside Merging Regions of Bottlenecks;605
21.10.2;A.9.2 Vehicles Moving Within Merging Regions of Bottlenecks;608
21.11;A.10 Model of Heterogeneous Traffic Flow;611
21.11.1;A.10.1 Vehicle Motion on Single-Lane Road;612
21.11.1.1;A.10.1.1 Steady States and Vehicle Motion;612
21.11.1.2;A.10.1.2 Fluctuations;614
21.11.1.3;A.10.1.3 Safe Speed;614
21.11.2;A.10.2 Lane Changing Rules in Model of Two-Lane Road;614
21.11.3;A.10.3 Boundary, Initial Conditions, and Models of Bottlenecks;617
21.12;A.11 Realistic Heterogeneous Traffic Flow;618
21.12.1;A.11.1 Dependence of Free Flow Speed on Space Gap;618
21.12.2;A.11.2 Simulations of Traffic Patterns on Realistic Three-Lane Highway;618
21.12.3;A.11.3 Update Rules of Vehicle Motion in Road Lane;621
21.12.4;A.11.4 Lane Changing Rules on Three-Lane Road;622
21.12.5;A.11.5 Models of On- and Off-Ramp Bottlenecks on Three-Lane Road;624
21.12.6;A.11.6 Some Results of Simulations;626
21.13;A.12 Traffic Flow Model for City Traffic;629
21.13.1;A.12.1 Adaptation of Model Parameters for City Traffic;629
21.13.2;A.12.2 Rules of Vehicle Motion;629
21.13.3;A.12.3 Reduction of Three-Phase Model to Two-PhaseModel;631
21.14;References;632
22;B Kerner-Klenov-Schreckenberg-Wolf (KKSW) Cellular Automaton (CA) Three-Phase Model;634
22.1;B.1 Motivation;634
22.2;B.2 Rules of Vehicle Motion in KKSW CA Model;635
22.3;B.3 Models of Bottlenecks for KKSW CA Model;641
22.3.1;B.3.1 On- and Off-Ramp Bottlenecks;641
22.3.2;B.3.2 Vehicle Motion Rules in Merging Regionof Bottlenecks;642
22.4;B.4 Comparison of KKSW CA Model with Nagel-Schreckenberg CA Model;645
22.5;References;646
23;C Dynamic Traffic Assignment Based on Wardrop's UE with Step-by-Step Method;647
23.1;Reference;649
24;Glossary;650
25;Index;666