A measure theoretic approach to traffic flow optimization on networks

TL;DR

This paper introduces a measure-theoretic framework for optimizing traffic flow on networks, enabling the control of macroscopic traffic quantities through local and nonlocal interactions, with an adjoint-based method demonstrated on traffic lights.

Contribution

It develops a novel measure-theoretic approach for traffic control problems, unifying local and nonlocal driver interactions and deriving a gradient-based optimization method.

Findings

Effective control of traffic flow using measure-based models

Numerical experiments on smart traffic lights at a junction

Potential for improved traffic management strategies

Abstract

We consider a class of optimal control problems for measure-valued nonlinear transport equations describing traffic flow problems on networks. The objective isto minimise/maximise macroscopic quantities, such as traffic volume or average speed,controlling few agents, for example smart traffic lights and automated cars. The measuretheoretic approach allows to study in a same setting local and nonlocal drivers interactionsand to consider the control variables as additional measures interacting with the driversdistribution. We also propose a gradient descent adjoint-based optimization method, ob-tained by deriving first-order optimality conditions for the control problem, and we providesome numerical experiments in the case of smart traffic lights for a 2-1 junction.