A model for the evolution of traffic jams in multi-lane

TL;DR

This paper enhances a traffic jam model by incorporating multi-lane roads and variable speed limits, providing a more realistic description of traffic dynamics and proving the existence of solutions.

Contribution

It introduces a multi-lane extension of an existing pressureless gas dynamics traffic model with lane-dependent constraints and speed parameters.

Findings

Model captures formation and evolution of traffic jams in multi-lane settings.

Proves existence of weak solutions for the extended model.

Provides analysis of cluster dynamics in traffic flow.

Abstract

In [7], Berthelin, Degond, Delitala and Rascle introduced a traffic flow model describing the formation and the dynamics of traffic jams. This model consists of a Pressureless Gas Dynamics system under a maximal constraint on the density and is derived through a singular limit of the Aw-Rascle model. In the present paper we propose an improvement of this model by allowing the road to be multi-lane piecewise. The idea is to use the maximal constraint to modelize the number of lanes. We also add in the model a parameter {\alpha} which modelize the various speed limitations according to the number of lanes. We present the dynamical behaviour of clusters (traffic jams) and by approximation with such solutions, we obtain an existence result of weak solutions for any initial data.