A Compartmental Model for Traffic Networks and its Dynamical Behavior

TL;DR

This paper introduces a macroscopic traffic network model based on the Cell Transmission Model, analyzing its equilibrium and convergence properties, and demonstrating how non-cooperative dynamics can enhance traffic control strategies like ramp metering.

Contribution

It presents a novel dynamical system model for traffic networks that does not rely on cooperativity, enabling effective traffic control methods and optimal ramp metering solutions.

Findings

The model qualitatively analyzes equilibrium flows and convergence.

Non-cooperative properties facilitate effective traffic control.

Develops a linear program for optimal ramp metering.

Abstract

We propose a macroscopic traffic network flow model suitable for analysis as a dynamical system, and we qualitatively analyze equilibrium flows as well as convergence. Flows at a junction are determined by downstream supply of capacity as well as upstream demand of traffic wishing to flow through the junction. This approach is rooted in the celebrated Cell Transmission Model for freeway traffic flow. Unlike related results which rely on certain system cooperativity properties, our model generally does not possess these properties. We show that the lack of cooperativity is in fact a useful feature that allows traffic control methods, such as ramp metering, to be effective. Finally, we leverage the results of the paper to develop a linear program for optimal ramp metering.