1 Introduction
1.1 Motivation
1.2 Objectives
1.3 Contributions
1.4 Organization
2 Literature Review
2.1 Introduction
2.2 Historical Development of Traffic Flow Theory
2.2.1 Macroscopic Modeling
2.2.2 Mesoscopic Modeling
2.2.3 Microscopic Modeling
2.2.4 Stochastic Modeling
2.3 Probabilistic HeadwaySpacing Distributions
2.3.1 Simple Univariable Distributions
2.3.2 Compositional Distributions
2.3.3 Mixed Distributions
2.3.4 Random Matrix Model
2.4 Summary
3 Empirical Observations of Stochastic and Dynamic Evolutions of Traffic Flow
3.1 Introduction
3.2 Characteristics of HeadwaySpacingVelocity
3.3 Congested Platoon Oscillations
3.4 Time-Frequency Properties
3.5 Summary
4 A Markov Model Based on HeadwaySpacing Distributions
4.1 Introduction
4.2 A Markov Model for HeadwaySpacing Distributions
4.2.1 Background
4.2.2 Markov-Process Simulation Models
4.2.3 Simulation Results
4.2.4 Discussions
4.3 Asymmetric Stochastic Tau Theory in Car-Following
4.3.1 Asymmetric Stochastic Extension of the Tau Theory
4.3.2 Testing Results
4.3.3 Discussions
5 Stochastic Fundamental Diagram Based on HeadwaySpacing Distributions
5.1 Introduction
5.2 Newell''s Simplified Model and Its Stochastic Extension
5.3 The Homogeneous Platoon Model
5.3.1 Basic Idea
5.3.2 Summation of Lognormal Random Variables
5.3.3 Average Headway Distribution
5.3.4 Model Validation
5.3.5 Sensitivity Analysis
5.4 The Heterogeneous Platoon Model
5.4.1 Average Headway Distribution
5.4.2 Validation
5.4.3 Boundaries of Congested Flows
5.5 Summary
6 Traffic Flow Breakdown Model Based on HeadwaySpacing Distributions
6.1 Introduction
6.2 Nonparametric Lifetime Statistics Approach
6.3 Queueing Models for Breakdown Probability
6.3.1 Backgrounds
6.3.2 Some Previous Models
6.3.3 GG1 Queueing Model
6.3.4 Discussions
6.3.5 Model Validation
6.3.6 Summary
6.4 Phase Diagram Analysis
6.4.1 Backgrounds
6.4.2 The Spatial-Temporal Queueing Model
6.4.3 The Analytical Solution for Phase Diagram
6.4.4 Numerical Example
6.5 Discussions
7 Conclusions and Future Work
Appendix A: Linear Stability Analysis of the Higher-Order Macroscopic Model
Appendix B: Linear Stability Analysis of the Multi-Anticipative Car-Following Models
References
Index
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