Feedback Ramp Metering in Intelligent Transportation Systems

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 Control Design.- 5. Summary.- 6. Questions.- 7. Problems.- 8. References.- 9 Feedback Control Design Using the ODE Model.- 1. Mathematical Model.- 2. Control Objective.- 3. Control Design.- 214.- 3.1.1 Comparison with Wattle worth Model.- 3.1.2 Comparison with ALINEA Model.- 217.- 218.- 219.- 220.- 3.3.3 Overall Control.- 4. Software and Simulation Results.- 5. Coordinated Ramp Control in ODE Setting.- 5.1 Dynamics.- 5.2 Control Design.- 228.- 229.- 230.- 232.- 5.2.5 Overall Control.- 5.2.5.1 Decoupled Control.- 5.2.5.2 Coupled Control Laws.- 5.3 Simulation Files.- 5.4 Simulation Results.- 6. Summary.- 7. Questions.- 8. Problems.- 9. References.- 10 Feedback Control Design Using the Finite Difference Model.- 1. Finite Difference Model.- 2. Control Objective.- 3. Control Design.- 3.1 Control Objective.- 3.2 Control Objective.- 3.2.1 Region.- 3.2.2 Region.- 3.3.3 Overall Control.- 4. Coordinated Ramp Control in ODE Setting.- 4.1 Dynamics.- 4.2 Control Design.- 252.- 254.- 255.- 257.- 4.2.5 Overall Control.- 4.2.5.1 Decoupled Control.- 4.2.5.2 Coupled Control Laws.- 4.3 Simulation Files.- 4.4 Simulation Results.- 5. Summary.- 6. Questions.- 7. Problems.- 8. References.- 11 Nonlinear H?Feedback Control Design Using the ODE Model.- 1. Introduction.- 2. System Modeling.- 2.1 Discretized System Dynamics.- 3. Background (Nonlinear FL Control).- 4. Ramp Control Design.- 4.1 Continuous-Time Case.- 4.1.2 Nonlinear FL Solution for Two Cost Functions.- 4.1.2.1 Derivation of the Optimal Control for Ja.- 4.1.2.2 Derivation of the Optimal Control for Jb.- 4.1.2 Discretization of the Resulting System.- 4.2 Discrete-Time Case.- 5. Software and Simulation Results.- 6. Summary.- 7. Questions.- 8. Problems.- 9. References.- 12 Paramics.- 1. Introduction to PARAMICS.- 2. Advantages of PARAMICS Simulation.- 3. PARAMICS Applications and Validation Studies.- 4. PARAMICS Ramp Metering Applications.- 5. Simulation of the Study Network.- 6. Simulation Results.- 7. Conclusions.- 8. Summary.- 9. Questions.- 10. Problems.- 11. References.