A model for traffic flow on a road with variable widths

TL;DR

This paper introduces a modified Aw-Rascle traffic flow model for roads with variable widths, analyzing wave solutions and solving Riemann problems with numerical results aligning with theory.

Contribution

It presents a novel non-conservative traffic flow model accounting for variable road widths and derives its wave solutions and Riemann problem solutions.

Findings

Derived elementary waves including rarefaction, shock, contact, stationary waves

Solved Riemann problems for the new model

Numerical results match theoretical predictions

Abstract

We propose a model describing the traffic flow on a road with variable widths in this paper. The model, which is modified the Aw-Rascle model, is not conservative because of the source term. We obtain the elementary waves of the new traffic flow model, including rarefaction waves, shock waves, contact discontinuities and stationary waves. The Riemann problems of the system for the traffic flow are solved and some numerical results are given, which are almost the same as the theoretical ones.