Feedback Ramp Metering in Intelligent Transportation Systems

Frontmatter

Chapter 1. Introduction

Abstract

This chapter introduces the ramp-metering problem. It discusses the congestion problem on highways and how ramp metering is used to alleviate this problem. It also gives an overview of feedback control theory as we use it in this book. This is intended for those readers who do not have a background in that area.

Pushkin Kachroo, Kaan Ozbay

Chapter 2. Distributed Ramp Model

Abstract

This chapter introduces the conservation-based Partial Differential Equation (PDE) model for the highway ramp system. Various static and dynamic equations are used to describe the relationship between traffic velocity and traffic density. A numerical model for simulation is presented for the PDE and some basic simulation results are shown.

Pushkin Kachroo, Kaan Ozbay

Chapter 3. Distributed Modeling and Problem Formulation

Abstract

This chapter presents the modeling for the ramp metering problem in the distributed setting. It gives a detailed description of the dynamics and presents its limitations. The chapter also presents the control problem formulations in the distributed setting. The concept of projection dynamics is used to tackle the problems associated with the model.

Pushkin Kachroo, Kaan Ozbay

Chapter 4. Simulation Software for Distributed Model

Abstract

This chapter presents the numerical software we have developed to perform simulations using the distributed model of the ramp system. The software is developed in Matlab. We present a simple algorithm first. Then we show the limitations of that algorithm. Those limitations are removed by adding the projection dynamics elements discussed in the last chapter.

Pushkin Kachroo, Kaan Ozbay

Chapter 5. Feedback Control Design Using the Distributed Model

Abstract

This chapter presents the feedback control design of an isolated ramp metering problem where we use the distributed model of the ramp system that has been developed till now. We show the stability properties of the closed-loop system that is obtained by the application of the feedback control law on the ramp system. We verify the effectiveness of the feedback control law by running some simulation experiments using the designed feedback control law on the isolated ramp system.

Pushkin Kachroo, Kaan Ozbay

Chapter 6. Feedback Control Design Using the Distributed Model with Diffusion

Abstract

This chapter presents the feedback control design of an isolated ramp metering problem where we use the distributed model of the ramp system that also includes the diffusion term. Essentially, we are designing a feedback control law for the system whose model is the Burgers equation. We show the stability properties of the closed-loop system that is obtained by the application of the feedback control law on the ramp system. We verify the effectiveness of the feedback control law by running some simulation experiments using the designed feedback control law on the isolated ramp system.

Pushkin Kachroo, Kaan Ozbay

Chapter 7. Feedback Control Design for the Distributed Model for Mixed Sensitivity

Abstract

This chapter presents the feedback control design of an isolated ramp metering problem where we use the distributed model of the ramp system with the control designed not only to keep the flow on the highway at a critical value but also to keep the queue length on the ramp small. We show the stability properties of the closed-loop system that is obtained by the application of the feedback control law on the ramp system. We verify the effectiveness of the feedback control law by running some simulation experiments using the designed feedback control law on the isolated ramp system.

Pushkin Kachroo, Kaan Ozbay

Chapter 8. Feedback Control Design for Coordinated Ramps Using Distributed Modeling

Abstract

This chapter presents the feedback control design of a coordinated ramp metering problem where we use the distributed model of the ramp system. We show the stability properties of the closed-loop system that is obtained by the application of the feedback control laws on the ramp system. We verify the effectiveness of the feedback control law by running some simulation experiments using the designed feedback control law on the coordinated ramp system.

Pushkin Kachroo, Kaan Ozbay

Chapter 9. Feedback Control Design Using the Ode Model

Abstract

This chapter uses the ordinary differential equation (ODE) model of the ramp system for designing feedback control laws. We will design feedback control laws for isolated ramp metering problems, isolated with mixed sensitivity, and coordinated with and without mixed sensitivity. Software and simulation results will also be presented.

Pushkin Kachroo, Kaan Ozbay

Chapter 10. Feedback Control Design Using the Finite Difference Model

Abstract

This chapter uses the finite difference equation model of the ramp system for designing feedback control laws. This model is obtained by time discretization of the ODE model. We will design feedback control laws for isolated ramp metering problems, isolated with mixed sensitivity, and coordinated with and without mixed sensitivity. Software and simulation results will also be presented.

Pushkin Kachroo, Kaan Ozbay

Chapter 11. Nonlinear H∞ Feedback Control Design Using the Ode Model

Abstract

This chapter will solve the mixed sensitivity isolated ramp metering problem using nonlinear H∞ control theory. We will design the control law so that we achieve some optimization of an appropriately chosen criterion that is based on the traffic density on the highway and the queue lengths. We will also present simulation software and results.

Pushkin Kachroo, Kaan Ozbay

Chapter 12. Paramics

Abstract

This chapter introduces PARAMICS (PARAllel MICroscopic Simulation) software, a microscopic traffic simulation program, and discusses its use for testing and validating ramp metering algorithms discussed in the previous chapters of this book Chapters 9 (ALINEA), 10 (Mixed Control), 11 (New Control). The Quadstone website at www.paramics-online.com provides an overview of each module.

Pushkin Kachroo, Kaan Ozbay

Backmatter