Feedback Ramp Metering in Intelligent Transportation Systems

Focusing on feedback control in ramp metering, this book provides traffic theory fundamentals and the design of feedback controllers for isolated and coordinated ramp metering problems. It provides software simulation code in Matlab and Paramics. It is useful for a senior or graduate level course on the subject.

1 Introduction.- 1. Introduction.- 2. Intelligent Approach to Congestion Problem: Ramp Metering.- 2.1 Local Ramp Metering Control Strategies.- 2.1.1 Demand Capacity Control.- 2.1.2 Upstream Occupancy Control.- 2.1.3 Gap Acceptance Control.- 2.1.4 Closed-Loop Local Control Strategies.- 2.2 System-wide Ramp Control Strategies.- 3. Ramp Metering Implementations in the USA.- 4. Benefits of Ramp Metering.- 5. Problem Description.- 6. Preliminary Considerations for Using Feedback Control for Ramp Metering.- 7. Effect of Ramp Metering.- 8. Feedback Control.- 8.1 Control Design Steps.- 8.2 Ordinary Differential Equations.- 8.3 Difference Equations.- 8.4 Feedback Control Example.- 9. Summary.- 10. Questions.- 11. Problems.- 12. References.- 2 Distributed Ramp Model.- 1. Conservation Equation.- 2. Density Flow Relationship.- 2.1 Greenshield''s Model.- 2.2 Greenberg''s Model.- 2.3 Underwood''s Model.- 2.4 Northwestern University Model.- 2.5 Drew Model.- 2.6 Pipes Munjal Model.- 2.7 Multi Regime Model.- 2.8 Diffusion Models.- 3. Microscopic Traffic Characteristics.- 4. Classification of PDEs.- 5. Existence of Solution.- 5.1 Traffic Problem.- 6. Method of Characteristics to Solve First order PDEs.- 7. Traffic Shock Wave Propagation.- 8. Traffic Measurements.- 8.1 Time Mean Speed.- 8.2 Space Mean Speed.- 8.3 Time Headway.- 8.4 Space Headway.- 8.5 Flow Measurements.- 8.6 Traffic Density Measurements.- 8.7 Occupancy.- 8.8 Distributed Measurements.- 8.9 Moving Observer Method.- 9. Summary.- 10. Exercises.- 11. References.- 3 Distributed Modeling and Problem Formulation.- 1. System.- 2. Control Objective.- 3. Limitations of the Model.- 3.1 Jam Density.- 3.2 Maximum Queue Length.- 3.3 Negative Density.- 3.4 Negative Queue Length.- 3.5 Traffic Jam Time.- 3.6 Projection Dynamics.- 3.6.1 Right Face.- 3.6.2 Left Face.- 3.6.3 Top face.- 3.6.4 Bottom Face.- 4. Summary.- 5. Questions.- 6. Problems.- 7. References.- 4 Simulation Software for Distributed Model.- 1. Basic Model.- 2. Numerical Algorithm.- 3. Matlab Software.- 4. Simulations.- 5. Limitations.- 5.1 Large Queue Length.- 5.2 Negative Queue Length.- 5.3 Negative Traffic Density on Mainline.- 5.4 Higher than Jam Density.- 5.5 Traffic Diffusion.- 6. Summary.- 7. Questions.- 8. Problems.- 9. References.- 5 Feedback Control Design Using the Distributed Model.- 1. Model Summary.- 2. Control Objective.- 3. Feedback Control Law for the Basic Model.- 3.1 Implementation of the Basic Feedback Control Law.- 3.2 Limitations on Achievable Performance.- 3.3 Software Simulation for the Closed-Loop System.- 3.4 Integral Term in Control.- 3.5 Parametric Effect on Simulations.- 4. Summary.- 5. Questions.- 6. Problems.- 7. References.- 6 Feedback Control Design Using the Distributed Model with Diffusion.- 1. Model Summary of the Diffusion Model.- 2.Control Objective.- 3. Feedback Control Law for the Diffusion Model.- 3.1 Implementation of the Basic Feedback Control Law.- 3.2 Control Discretization.- 3.3 Integral Term.- 3.4 Software Simulation for the Closed-Loop System.- 4. Summary.- 5. Questions.- 6. Problems.- 7. References.- 7 Feedback Control Design for the Distributed Model for Mixed Sensitivity.- 1. Summary of the Basic Model.- 2. Control Objective.- 3. Feedback Control Design.- 4. Software.- 5. Simulation Results.- 6. Summary.- 7. Questions.- 8. Problems.- 9. References.- 8 Feedback Control Design for Coordinated Ramps Using Distributed Modeling.- 1. Coordinated Ramp Metering.- 2. Motivation Example for Isolated Ramp Problem.- 2.1 Control Objective.- 2.2 Feedback Control Design.- 2.3 Simulation Program.- 2.4 Simulation Results.- 2.4.1 Basic Control Law on Basic Model.- 2.4.2 Basic Control Law on Diffusion Model.- 2.4.3 Diffusion Control Law on Diffusion Model.- 2.5 of the Control Objective and the Performance of the Controller.- 3. Coordinated Ramp Control.- 3.1 Control Objective.- 3.2 Feedback Control Design.- 4. Coordinated Mixed Sensitivity Feedback Ramp Control.- 4.1 Control Objective.- 4.2 Feedback Co...