A nonlinear discrete-velocity relaxation model for traffic flow

TL;DR

This paper introduces a new nonlinear discrete-velocity traffic flow model derived from kinetic theory, which converges to classical traffic equations, exhibits an invariant domain, and is simpler than existing models, supported by analytical and numerical results.

Contribution

The paper presents a novel nonlinear 2-equation discrete-velocity model for traffic flow, derived from kinetic models, with convergence properties and numerical validation, offering a simpler alternative to existing models.

Findings

Model converges to scalar Lighthill-Whitham equations

Invariant domain suitable for traffic modeling

Numerical results validate analytical findings

Abstract

We derive a nonlinear 2-equation discrete-velocity model for traffic flow from a continuous kinetic model. The model converges to scalar Lighthill-Whitham type equations in the relaxation limit for all ranges of traffic data. Moreover, the model has an invariant domain appropriate for traffic flow modeling. It shows some similarities with the Aw-Rascle traffic model. However, the new model is simpler and yields, in case of a concave fundamental diagram, an example for a totally linear degenerate hyperbolic relaxation model. We discuss the details of the hyperbolic main part and consider boundary conditions for the limit equations derived from the relaxation model. Moreover, we investigate the cluster dynamics of the model for vanishing braking distance and consider a relaxation scheme build on the kinetic discrete velocity model. Finally, numerical results for various situations are presented, illustrating the analytical results.