A Riemann solver at a junction compatible with a homogenization limit

TL;DR

This paper justifies a Riemann solver at traffic junctions with traffic lights by analyzing a phase transition traffic model, extending classical models to account for driver speed variability, and connecting it to a homogenization limit.

Contribution

It provides a rigorous derivation of a Riemann solver for traffic flow at junctions with traffic lights using a phase transition model and homogenization techniques.

Findings

Justification of the Riemann solver at traffic junctions

Connection between phase transition model and classical traffic models

Derivation of maximal speed rule in outgoing road

Abstract

We consider a junction regulated by a traffic lights, with n incoming roads and only one outgoing road. On each road the Phase Transition traffic model, proposed in [6], describes the evolution of car traffic. Such model is an extension of the classic Lighthill-Whitham-Richards one, obtained by assuming that different drivers may have different maximal speed. By sending to infinity the number of cycles of the traffic lights, we obtain a justification of the Riemann solver introduced in [9] and in particular of the rule for determining the maximal speed in the outgoing road.