The Physics of Traffic

This book is devoted to the explanation of freeway traffic congestion, a fact of life for many car drivers. Results of empirical observations of freeway congestion, which exhibit diverse complex spatiotemporal patterns including moving traffic jams, are analyzed. Empirical features of these reproducible freeway traffic patterns only recently sufficiently well understood are reviewed. In the first part, three-phase traffic theory can be found, which is the basis for a physical theory of traffic phenomena and its applications in engineering. In the second part, the empirical spatiotemporal patterns are examined and, finally in parts III and IV, the mathematical model and the engineering applications are addressed. The Physics of Traffic addresses researchers and practitioners alike.

Texte du rabat

The core of ths book presents a theory developed by the author to combine the recent insight into empirical data with mathematical models in freeway traffic research based on dynamical non-linear processes.

Contenu

1 Introduction.- I Historical Overview and Three-Phase Traffic Theory.- 2 Spatiotemporal Pattern Formation in Freeway Traffic.- 2.1 Introduction.- 2.2 Traffic and Synergetics.- 2.3 Free and Congested Traffic.- 2.3.1 Local Measurements of Traffic Variables.- 2.3.2 Examples of Freeway Infrastructures and Detector Arrangements.- 2.3.3 Free Traffic Flow.- 2.3.4 Congested Traffic.- 2.3.5 Empirical Fundamental Diagram.- 2.3.6 Complex Local Dynamics of Congested Traffic.- 2.4 Main Empirical Features of Spatiotemporal Congested Patterns.- 2.4.1 Three Traffic Phases.- 2.4.2 Characteristic Parameters of Wide Moving Jams.- 2.4.3 Spontaneous Breakdown Phenomenon (Spontaneous F?S Transition).- 2.4.4 Induced Breakdown Phenomenon.- 2.4.5 Synchronized Flow Patterns.- 2.4.6 Catch Effect.- 2.4.7 Moving Jam Emergence in Synchronized Flow: General Pattern.- 2.4.8 Expanded Congested Patterns.- 2.4.9 Foreign Wide Moving Jams.- 2.4.10 Reproducible and Predictable Congested Patterns.- 2.4.11 Methodology for Empirical Congested Pattern Study.- 2.5 Conclusions Fundamental Empirical Features of Spatiotemporal Congested Patterns.- 3 Overview of Freeway Traffic Theories and Models: Fundamental Diagram Approach.- 3.1 Introduction: Hypothesis About Theoretical Fundamental Diagram.- 3.2 Achievements of Fundamental Diagram Approach to Traffic Flow Modeling and Theory.- 3.2.1 Conservation of Vehicle Number on Road and Front Velocity.- 3.2.2 The Lighthill-Whitham-Richards Model and Shock Wave Theory.- 3.2.3 Collective Flow Concept and Probability of Passing.- 3.2.4 Scenarios for Moving Jam Emergence.- 3.2.5 Wide Moving Jam Characteristics.- 3.2.6 Flow Rate in Wide Moving Jam Outflow The Line J.- 3.2.7 Metastable States of Free Flow with Respect to Moving Jam Emergence.- 3.3 Drawbacks of Fundamental Diagram Approach in Describing of Spatiotemporal Congested Freeway Patterns.- 3.3.1 Shock Wave Theory.- 3.3.2 Models and Theories of Moving Jam Emergence in Free Flow.- 3.3.3 Models and Theories with Variety of Vehicle and Driver Characteristics.- 3.3.4 Application of Classical Queuing Theories to Freeway Congested Traffic Patterns.- 3.4 Conclusions.- 4 Basis of Three-Phase Traffic Theory.- 4.1 Introduction and Remarks on Three-Phase Traffic Theory.- 4.2 Definition of Traffic Phases in Congested Traffic Based on Empirical Data.- 4.2.1 Objective Criteria for Traffic Phases in Congested Traffic.- 4.2.2 Explanation of Terms "Synchronized Flow" and "Wide Moving Jam".- 4.2.3 Mean Vehicle Trajectories.- 4.2.4 Flow Rate in Synchronized Flow.- 4.2.5 Empirical Line J.- 4.2.6 Propagation of Two Wide Moving Jams.- 4.3 Fundamental Hypothesis of Three-Phase Traffic Theory.- 4.3.1 Three-Phase Traffic Theory as Driver Behavioral Theory.- 4.3.2 Synchronization Distance and Speed Adaptation Effect in Synchronized Flow.- 4.3.3 Random Transformations ("Wandering") Within Synchronized Flow States.- 4.3.4 Dynamic Synchronized Flow States.- 4.4 Empirical Basis of Three-Phase Traffic Theory.- 4.5 Conclusions.- 5 Breakdown Phenomenon (F?S Transition) in Three-Phase Traffic Theory.- 5.1 Introduction.- 5.2 Breakdown Phenomenon on Homogeneous Road.- 5.2.1 Speed Breakdown at Limit Point of Free Flow.- 5.2.2 Critical Local Perturbation for Speed Breakdown.- 5.2.3 Probability for Breakdown Phenomenon.- 5.2.4 Threshold Flow Rate and Density, Metastability, and Nucleation Effects.- 5.2.5 Z-Shaped Speed-Density and Passing Probability Characteristics.- 5.2.6 Physics of Breakdown Phenomenon: Competition Between Over-Acceleration and Speed Adaptation.- 5.2.7 Physics of Threshold Point in Free Flow.- 5.2.8 Moving Synchronized Flow Pattern.- 5.3 Breakdown Phenomenon at Freeway Bottlenecks.- 5.3.1 Deterministic Local Perturbation.- 5.3.2 Deterministic F?S Transition.- 5.3.3 Physics of Deterministic Speed Breakdown at Bottleneck.- 5.3.4 Influence of Random Perturbations.- 5.3.5 Z-Characteristic for Speed Breakdown at Bottleneck.- 5.3.6 Physics of Speed Breakdown at Bottleneck.- 5.3.7 Time Delay of Speed Breakdown.- 5.4 Conclusions.- 6 Moving Jam Emergence in Three-Phase Traffic Theory.- 6.1 Introduction.- 6.2 Wide Moving Jam Emergence in Free Flow.- 6.3 Wide Moving Jam Emergence in Synchronized Flow.- 6.3.1 Hypothesis for Moving Jam Emergence in Synchronized Flow.- 6.3.2 Features of Metastable Synchronized Flow States.- 6.3.3 Stable High Density Synchronized Flow States.- 6.4 Double Z-Shaped Traffic Flow Characteristics.- 6.4.1 Z-Characteristic for S?J Transition.- 6.4.2 Cascade of Two Phase Transitions (F? S?J Transitions).- 6.4.3 Wide Moving Jam Emergence Within Initial Moving Synchronized Flow Pattern.- 6.5 Moving Jam Emergence in Synchronized Flow at Bottlenecks.- 6.5.1 Why Moving Jams Do not Emerge in Free Flow at Bottlenecks.- 6.5.2 Z-Characteristic for S?J Transition at Bottlenecks.- 6.5.3 Physics of Moving Jam Emergence in Synchronized Flow.- 6.5.4 Double Z-Characteristic and F?S?J Transitions at Bottlenecks.- 6.6 Conclusions.- 7 Congested Patterns at Freeway Bottlenecks in Three-Phase Traffic Theory.- 7.1 Introduction.- 7.2 Two Main Types of Spatiotemporal Congested Patterns.- 7.3 Simplified Diagram of Congested Patterns at Isolated Bottlenecks.- 7.4 Synchronized Flow Patterns.- 7.4.1 Influence of Fluctuations on Limit Point for Free Flow at Bottlenecks.- 7.4.2 Moving Synchronized Flow Pattern Emergence at Bottlenecks.- 7.4.3 Pinning of Downstream Front of Synchronized Flow at Bottlenecks.- 7.4.4 Transformation Between Widening and Localized Synchronized Flow Patterns.- 7.5 General Patterns.- 7.5.1 Spatiotemporal Structure of General Patterns.- 7.5.2 Dissolving General Pattern and Pattern Transformation.- 7.6 Physics of General Patterns.- 7.6.1 Region of Wide Moving Jams.- 7.6.2 Narrow Moving Jam Emergence in Pinch Region.- 7.6.3 Moving Jam Suppression Effect.- 7.6.4 Width of Pinch Region.- 7.6.5 Wide Moving Jam Propagation Through Bottlenecks.- 7.7 Conclusions.- 8 Freeway Capacity in Three-Phase Traffic Theory.- 8.1 Introduction.- 8.2 Homogeneous Road.- 8.3 Freeway Capacity in Free Flow at Bottlenecks.- 8.3.1 Definition of Freeway Capacity.- 8.3.2 Probability for Speed Breakdown at Bottlenecks.- 8.3.3 Threshold Boundary for Speed Breakdown.- 8.3.4 Features of Freeway Capacity at Bottlenecks.- 8.4 Z-Characteristic and Probability for Speed Breakdown.- 8.5 Congested Pattern Capacity at Bottlenecks.- 8.6 Main Behavioral Assumptions of Three-Phase Traffic Theory.- 8.7 Conclusions.- II Empirical Spatiotemporal Congested Traffic Patterns.- 9 Empirical Congested Patterns at Isolated Bottlenecks.- 9.1 Introduction.- 9.2 Effectual Bottlenecks and Effective Locations of Bottlenecks.- 9.2.1 Effectual Bottlenecks on Freeway A5-South.- 9.2.2 Effectual Bottlenecks on Freeway A5-North.- 9.2.3 Isolated Effectual Bottleneck.- 9.3 Empirical Synchronized Flow Patterns.- 9.3.1 Widening Synchronized Flow Pattern.- 9.3.2 Localized Synchronized Flow Pattern.- 9.3.3 Moving Synchronized Flow Pattern.- 9…