Physics of Traffic

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November 2004



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.


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.- 9.4 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.



From the reviews:
"For the analysis of complex spatiotemporal behaviour of traffic on motorways Kerner's book severs as an important basis for freeway traffic science that can be valuable for traffic scientists and engineers in solving many tasks in traffic engineering." (Hartmut Keller, tec-Traffic Engineering and Control International Journal of Traffic Management and Transportation Planning 2005, vol. 46, page 72-73)
"I commend Boris Kerner on his pioneering research on a new traffic theory... [This] is the first book I have read that offers detailed discussions about traffic congestion on freeways." --Henry Lieu, in Physics Today, November 2005
"Key topic of the book is the description of empirical spatiotemporal behaviour of traffic based on the Kerner's three-phase traffic theory. The content of the book is based on research work, which Kerner has performed ... . The comprehensive bibliography ... is impressive whereby they are referred to almost solely as reference numbers in the text. ... Kerner's book serves as an important basis for freeway traffic science that can be valuable for traffic scientists and engineers in solving many tasks in traffic engineering." (Hartmut Keller, tec-Traffic Engineering and Control, Vol. 46 (2), 2005)
"Boris Kerner presents in his book an in-depth and comprehensive presentation of his three-phase theory of freeway traffic flow. ... It might well mark a milestone in the long-lasting discussion on modeling of freeway traffic flow. ... The book is didactically very well written, it guides the reader through the material by providing figurative descriptions whenever possible before diving into mathematics. Every chapter starts and ends with summaries ... ." (Peter Vortisch, IEEE Vehicular Technology Magazine, June, 2006)
EAN: 9783540207160
ISBN: 3540207163
Untertitel: Empirical Freeway Pattern Features, Engineering Applications, and Theory. 'Understanding Complex Systems'. Auflage 2004. Sprache: Englisch.
Verlag: Springer-Verlag GmbH
Erscheinungsdatum: November 2004
Seitenanzahl: XXIV
Format: gebunden
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