Localisation of perturbations of a constant state in a traffic flow model

TL;DR

This paper studies the stability and localization of perturbations in a traffic flow model, extending previous results and providing a method to predict where perturbations concentrate over time.

Contribution

It introduces a perturbative approach that broadens the stability analysis space and enables localization predictions in the Aw-Rascle-Zhang traffic model.

Findings

Proves asymptotic stability of constant flows in a larger perturbation space.

Provides a method to compute the spatial localization of perturbations over time.

Applicable to various hyperbolic conservation law models with relaxations.

Abstract

We consider, in the Aw-Rascle-Zhang traffic flow model, the problem of the asymptotic stability of constant flows. By using a perturbative approach, we show the stability in a larger space of perturbation than previous results. Furthermore, we are able to compute where the perturbation is mainly localised in space for a given time, based on the localisation of the perturbation initially. These new ideas can be applied to various other models of hyperbolic conservation laws with relaxations.