The Physics of Traffic

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.- 9.4 Empirical General Patterns.- 9.4.1 Empirical General Pattern of Type (1).- 9.4.2 Empirical General Pattern of Type (2).- 9.4.3 Dependence of Effective Location of Bottleneck on Time.- 9.5 Conclusions.- 10 Empirical Breakdown Phenomenon: Phase Transition from Free Flow to Synchronized Flow.- 10.1 Introduction.- 10.2 Spontaneous Breakdown Phenomenon (Spontaneous F?S Transition) at On-Ramp Bottlenecks.- 10.3 Probability for F?S Transition.- 10.3.1 Empirical and Theoretical Definitions of Freeway Capacities at Bottlenecks.- 10.3.2 Pre-Discharge Flow Rate.- 10.4 Induced Speed Breakdown at On-Ramp Bottlenecks.- 10.4.1 F?S Transition Induced by Wide Moving Jam Propagation Through Effectual Bottleneck.- 10.4.2 Induced Speed Breakdown at Bottlenecks Caused by Synchronized Flow Propagation.- 10.5 Breakdown Phenomenon at Off- Ramp Bottlenecks.- 10.6 Breakdown Phenomenon Away from Bottlenecks.- 10.7 Some Empirical Features of Synchronized Flow.- 10.7.1 Complex Behavior in Flow-Density Plane.- 10.7.2 Three Types of Synchronized Flow.- 10.7.3 Overlapping States of Free Flow and Synchronized Flow in Density.- 10.7.4 Analysis of Individual Vehicle Speeds.- 10.8 Conclusions.- 11 Empirical Features of Wide Moving Jam Propagation.- 11.1 Introduction.- 11.2 Characteristic Parameters of Wide Moving Jams.- 11.2.1 Empirical Determination of Line J.- 11.2.2 Dependence of Characteristic Jam Parameters on Traffic Conditions.- 11.2.3 Propagation of Wide Moving Jams Through Synchronized Flow.- 11.2.4 Moving Blanks Within Wide Moving Jams.- 11.3 Features of Foreign Wide Moving Jams.- 11.4 Conclusions.- 12 Empirical Features of Moving Jam Emergence.- 12.1 Introduction.- 12.2 Pinch Effect in Synchronized Flow.- 12.2.1 Narrow Moving Jam Emergence.- 12.2.2 Wide Moving Jam Emergence (S?J Transition).- 12.2.3 Correlation of Characteristics for Pinch Region and Wide Moving Jams.- 12.2.4 Frequency of Narrow Moving Jam Emergence.- 12.2.5 Saturation and Dynamic Features of Pinch Effect.- 12.2.6 Spatial Dependence of Speed Correlation Function.- 12.2.7 Effect of Wide Moving Jam Emergence in Pinch Region of General Pattern.- 12.3 Strong and Weak Congestion.- 12.4 Moving Jam Emergence in Synchronized Flow Away from Bottlenecks.- 12.5 Pattern Formation at Off-Ramp Bottlenecks.- 12.6 Induced F?J Transition.- 12.7 Conclusions.- 13 Empirical Pattern Evolution and Transformation at Isolated Bottlenecks.- 13.1 Introduction.- 13.2 Evolution of General Patterns at On-Ramp Bottlenecks.- 13.2.1 Transformation of General Pattern into Synchronized Flow Pattern.- 13.2.2 Alternation of Free Flow and Synchronized Flow in Congested Patterns.- 13.2.3 Hysteresis Effects Due to Pattern Formation and Dissolution.- 13.3 Transformations of Congested Patterns Under Weak Congestion.- 13.4 Discharge Flow Rate and Capacity Drop.- 13.5 Conclusions.- 14 Empirical Complex Pattern Formation Caused by Peculiarities of Freeway Infrastructure.- 14.1 Introduction.- 14.2 Expanded Congested Pattern.- 14.2.1 Common Features.- 14.2.2 Example of Expanded Congested Pattern.- 14.3 Dissolution of Moving Jams at Bottlenecks.- 14.3.1 Dynamics of Wide Moving Jam Outflow.- 14.3.2 Localized Synchronized Flow Patterns Resulting from Moving Jam Dissolution.- 14.4 Conclusions.- 15 Dependence of Empirical Fundamental Diagram on Congested Pattern Features.- 15.1 Introduction.- 15.1.1 Empirical Fundamental Diagram and Steady State Model Solutions.- 15.1.2 Two Branches of Empirical Fundamental Diagram.- 15.1.3 Line J and Wide Moving Jam Outflow.- 15.2 Empirical Fundamental Diagram and Line J.- 15.2.1 Asymptotic Behavior of Empirical Fundamental Diagrams.- 15.2.2 Influence of Different Vehicle Characteristics on Fundamental Diagrams.- 15.3 Dependence of Empirical Fundamental Diagram on Congested Pattern Type.- 15.4 Explanation of Reversed-?, Inverted-V, and Inverted-U Empirical Fundamental Diagrams.- 15.5 Conclusions.- III Microscopic Three-Phase Traffic Theory.- 16 Microscopic Traffic Flow Models for Spatiotemporal Congested Patterns.- 16.1 Introduction.- 16.2 Cellular Automata Approach to Three-Phase Traffic Theory.- 16.2.1 General Rules of Vehicle Motion.- 16.2.2 Synchronization Distance.- 16.2.3 Steady States.- 16.2.4 Fluctuations of Acceleration and Deceleration in Cellular Automata Models.- 16.2.5 Boundary Conditions and Model of On-Ramp.- 16.2.6 Summary of Model Equations and Parameters.- 16.3 Continuum in Space Model Approach to Three-Phase Traffic Theory.- 16.3.1 Vehicle Motion Rules.- 16.3.2 Speed Adaptation Effect Within Synchronization Distance.- 16.3.3 Motion State Model for Random Acceleration and Deceleration.- 16.3.4 Safe Speed.- 16.3.5 2D Region of Steady States.- 16.3.6 Physics of Driver Time Delays.- 16.3.7 Over-Acceleration and Over-Deceleration Effects ....- 16.3.8 Lane Changing Rules.- 16.3.9 Boundary Conditions and Models of Bottlenecks ....- 16.3.10 Summary of Model Equations and Parameters.- 16.4 Conclusions.- 17 Microscopic Theory of Phase Transitions in Freeway Traffic.- 17.1 Introduction.- 17.2 Microscopic Theory of Breakdown Phenomenon (F?S Transition).- 17.2.1 Homogeneous Road.- 17.2.2 Breakdown Phenomenon at On-Ramp Bottlenecks.- 17.3 Moving Jam Emergence and Double Z-Shaped Characteristics of Traffic Flow.- 17.3.1 F?J Transition on Homogeneous Road.- 17.3.2 S?J Transition on Homogeneous Road.- 17.3.3 Moving Jam Emergence in Synchronized Flow Upstream of Bottlenecks.- 17.4 Conclusions.- 18 Congested Patterns at Isolated Bottlenecks.- 18.1 Introduction.- 18.2 Diagram of Congested Patterns at Isolated On-Ramp Bottlenecks.- 18.2.1 Synchronized Flow Patterns.- 18.2.2 Single Vehicle Characteristics in Synchronized Flow.- 18.2.3 Maximum Freeway Capacities and Limit Point in Diagram.- 18.2.4 Pinch Effect in General Patterns.- 18.2.5 Peculiarities of General Patterns.- 18.3 Weak and Strong Congestion in General Patterns.- 18.3.1 Criteria for Strong and Weak Congestion.- 18.3.2 Strong Congestion Features.- 18.4 Evolution of Congested Patterns at On-Ramp Bottlenecks.- 18.5 Hysteresis and Nucleation Effects by Pattern Formation at On-Ramp Bottlenecks.- 18.5.1 Threshold Boundary for Synchronized Flow Patterns.- 18.5.2 Threshold Boundary for General Patterns.- 18.5.3 Overlap of Different Metastable Regions and Multiple Pattern Excitation.- 18.6 Strong Congestion at Merge Bottlenecks.- 18.6.1 Comparison of General Patterns at Merge Bottleneck and at On-Ramp Bottleneck.- 18.6.2 Diagram of Congested Patterns.- 18.7 Weak Congestion at Off- Ramp Bottlenecks.- 18.7.1 Diagram of Congested Patterns.- 18.7.2 Comparison of Pattern Features at Various Bottlenecks.- 18.8 Congested Pattern Capacity at On-Ramp Bottlenecks.- 18.8.1 Transformations of Congested Patterns at On-Ramp Bottlenecks.- 18.8.2 Temporal Evolution of Discharge Flow Rate.- 18.8.3 Dependence of Congested Pattern Capacity on On-Ramp Inflow.- 18.9 Conclusions.- 19 Complex Congested Pattern Interaction and Transformation.- 19.1 Introduction.- 19.2 Catch Effect and Induced Congested Pattern Formation.- 19.2.1 Induced Pattern Emergence.- 19.3 Complex Congested Patterns and Pattern Interaction.- 19.3.1 Foreign Wide Moving Jams.- 19.3.2 Expanded Congested Patterns.- 19.4 Intensification of Downstream Congestion Due to Upstream Congestion.- 19.5 Conclusions.- 20 Spatiotemporal Patterns in Heterogeneous Traffic Flow.- 20.1 Introduction.- 20.2 Microscopic Two-Lane Model for Heterogeneous Traffic Flow with Various Driver Behavioral Characteristics and Vehicle Parameters.- 20.2.1 Single-Lane Model.- 20.2.2 Two-Lane Model.- 20.2.3 Boundary, Initial Conditions, and Model of Bottleneck.- 20.2.4 Simulation Parameters.- 20.3 Patterns in Heterogeneous Traffic Flow with Different Driver Behavioral Characteristics.- 20.3.1 Vehicle Separation Effect in Free Flow.- 20.3.2 Onset of Congestion in Free Flow on Homogeneous Road.- 20.3.3 Lane Asymmetric Emergence of Moving Synchronized Flow Patterns.- 20.3.4 Congested Patterns at On-Ramp Bottlenecks.- 20.3.5 Wide Moving Jam Propagation.- 20.4 Patterns in Heterogeneous Traffic Flow with Different Vehicle Parameters.- 20.4.1 Peculiarity of Wide Moving Jam Propagation.- 20.4.2 Partial Destroying of Speed Synchronization.- 20.4.3 Extension of Free Flow Recovering and Vehicle Separation.- 20.5 Weak Heterogeneous Flow.- 20.5.1 Spontaneous Onset of Congestion Away from Bottlenecks.- 20.5.2 Lane Asymmetric Free Flow Distributions.- 20.6 Characteristics of Congested Pattern Propagation in Heterogeneous Traffic Flow.- 20.6.1 Velocity of Downstream Jam Front.- 20.6.2 Flow Rate in Jam Outflow.- 20.6.3 Velocity of Downstream Front of Moving Synchronized Flow Patterns.- 20.7 Conclusions.- IV Engineering Applications.- 21 ASDA and FOTO Models of Spatiotemporal Pattern Dynamics based on Local Traffic Flow Measurements.- 21.1 Introduction.- 21.2 Identification of Traffic Phases.- 21.3 Determination of Traffic Phases with FOTO Model.- 21.3.1 Fuzzy Rules for FOTO Model.- 21.4 Tracking Moving Jams with ASDA: Simplified Discussion.- 21.4.1 Tracking Synchronized Flow with FOTO Model.- 21.4.2 ASDA-Like Approach to Tracking Synchronized Flow.- 21.4.3 Cumulative Flow Rate Approach to Tracking Synchronized Flow.- 21.5 Conclusions.- 22 Spatiotemporal Pattern Recognition, Tracking, and Prediction.- 22.1 Introduction.- 22.2 FOTO and ASDA Application for Congested Pattern Recognition and Tracking.- 22.2.1 Validation of FOTO and ASDA Models at Traffic Control Center of German Federal State of Hessen.- 22.2.2 Application of FOTO and ASDA Models on Other Freeways in Germany and USA.- 22.3 Spatiotemporal Pattern Prediction.- 22.3.1 Historical Time Series.- 22.3.2 Database of Reproducible and Predictable Spatiotemporal Pattern Features.- 22.3.3 Vehicle Onboard Autonomous Spatiotemporal Congested Pattern Prediction.- 22.4 Traffic Analysis and Prediction in Urban Areas.- 22.4.1 Model for Traffic Prediction in City Networks.- 22.5 Conclusions.- 23 Control of Spatiotemporal Congested Patterns.- 23.1 Introduction.- 23.2 Scenarios for Traffic Management and Control.- 23.3 Spatiotemporal Pattern Control Through Ramp Metering.- 23.3.1 Free Flow Control Approach.- 23.3.2 Congested Pattern Control Approach.- 23.3.3 Comparison of Free Flow and Congested Pattern Control Approaches.- 23.3.4 Comparison of Different Control Rules in Congested Pattern Control Approach.- 23.4 Dissolution of Congested Patterns.- 23.5 Prevention of Induced Congestion.- 23.6 Influence of Automatic Cruise Control on Congested Patterns.- 23.6.1 Model of Automatic Cruise Control.- 23.6.2 Automatic Cruise Control with Quick Dynamic Adaptation.- 23.6.3 Automatic Cruise Control with Slow Dynamic Adaptation.- 23.7 Conclusions.- 24 Conclusion.- A Terms and Definitions.- A.1 Traffic States, Parameters, and Variables.- A.2 Traffic Phases.- A.3 Phase Transitions.- A.4 Bottleneck Characteristics.- A.5 Congested Patterns at Bottlenecks.- A.6 Local Perturbations.- A.7 Critical and Threshold Traffic Variables.- A.8 Some Features of Phase Transitions and Traffic State Stability.- B ASDA and FOTO Models for Practical Applications.- B.1 ASDA Model for Several Road Detectors.- B.1.1 Extensions of ASDA for On-Ramps, Off- Ramps, and Changing of Number of Freeway Lanes Upstream of Moving Jam.- B.1.2 Extensions of ASDA for On-Ramps, Off- Ramps, and Changing of Number of Freeway Lanes Downstream of Moving Jam.- B.1.3 FOTO Model for Several Road Detectors.- B.1.4 Extended Rules for FOTO Model.- B.2 Statistical Evaluation of Different Reduced Detector Configurations.- References.