Symmetry breaking in optimal timing of traffic signals on an idealized two-way street

TL;DR

This paper develops an analytical theory for optimal traffic signal timing on a two-way street, revealing asymmetric solutions and analyzing their robustness under varying traffic conditions.

Contribution

It introduces a novel analytical framework for understanding optimal traffic signal timing in an idealized two-way street model, highlighting asymmetric solutions.

Findings

Optimal signal timing can be derived analytically.

Asymmetric solutions emerge as optimal in certain conditions.

Solutions degrade with increased traffic density.

Abstract

Simple physical models based on fluid mechanics have long been used to understand the flow of vehicular traffic on freeways; analytically tractable models of flow on an urban grid, however, have not been as extensively explored. In an ideal world, traffic signals would be timed such that consecutive lights turned green just as vehicles arrived, eliminating the need to stop at each block. Unfortunately, this "green wave" scenario is generally unworkable due to frustration imposed by competing demands of traffic moving in different directions. Until now this has typically been resolved by numerical simulation and optimization. Here, we develop a theory for the flow in an idealized system consisting of a long two-way road with periodic intersections. We show that optimal signal timing can be understood analytically and that there are counter-intuitive asymmetric solutions to this signal coordination problem. We further explore how these theoretical solutions degrade as traffic conditions vary and automotive density increases.