A Continuous-Time Optimal Control Approach to Congestion Control

TL;DR

This paper introduces a continuous-time optimal control method for traffic congestion management, modeling traffic flow with mass conservation laws and optimizing boundary flows to reduce congestion in urban networks.

Contribution

It presents a novel continuous-time control framework for traffic congestion using mass-flow conservation and quadratic programming, applied to interconnected road networks.

Findings

Successful simulation on a network of interconnected roads

Effective boundary flow optimization reduces congestion

Framework applicable to real-world traffic management

Abstract

Traffic congestion has become a nightmare to modern life in metropolitan cities. On average, a driver spending X hours a year stuck in traffic is one of most common sentences we often read regarding traffic congestion. Our aim in this article is to provide a method to control this seemingly ever-growing problem of traffic congestion. We model traffic dynamics using a continuous-time mass-flow conservation law, and apply optimal control techniques to control traffic congestion. First, we apply the mass-flow conservation law to specify traffic feasibility and present continuous-time dynamics for modeling traffic as a network problem by defining a network of interconnected roads (NOIR). The traffic congestion control is formulated as a boundary control problem and we use the concept of statetransition matrix to help with the optimization of boundary flow by solving a constrained optimal control problem using quadratic programming. Finally, we show that the proposed algorithm is successful by simulating on a NOIR.