Relaxation models for scalar traffic networks and zero relaxation limit

TL;DR

This paper develops coupling conditions for a relaxation traffic model on networks and demonstrates how they converge to classical LWR network conditions through asymptotic analysis and numerical experiments.

Contribution

It introduces a new relaxation model for traffic networks and derives classical LWR coupling conditions via asymptotic analysis in the macroscopic limit.

Findings

Relaxation model converges to LWR network in the macroscopic limit.

Numerical experiments validate the convergence and compare different coupling conditions.

Asymptotic analysis of interface layers enhances understanding of boundary behaviors.

Abstract

In this paper we propose coupling conditions for a relaxation model for vehicular traffic on networks. We present a matched asymptotic expansion procedure to derive a LWR- network with well-known classical coupling conditions from the relaxation network in the macroscopic limit. Similar to the asymptotic limit of boundary value problems, we perform an asymptotic analysis of the interface layers at the nodes and a matching procedure using half-Riemann problems for the limit conservation law. Moreover, we present numerical experiments comparing the relaxation network with the LWR network for a broader range of coupling conditions.