Influence of a slow moving vehicle on traffic: Well-posedness and approximation for a mildly non-local model

TL;DR

This paper introduces a macroscopic traffic model incorporating a slow-moving vehicle's influence through a non-local flux constraint, proving well-posedness, developing a convergent numerical scheme, and exploring its relation to local models.

Contribution

The paper presents a novel non-local traffic model with a vehicle-dependent flux constraint, along with a rigorous analysis and numerical validation.

Findings

Proved well-posedness of the model.

Developed a convergent finite volume scheme.

Numerically linked the non-local model to local traffic models.

Abstract

In this paper, we propose a macroscopic model that describes the influence of a slow moving large vehicle on road traffic. The model consists of a scalar conservation law with a non-local constraint on the flux. The constraint level depends on the trajectory of the slower vehicle which is given by an ODE depending on the downstream traffic density. After proving well-posedness, we first build a finite volume scheme and prove its convergence, and then investigate numerically this model by performing a series of tests. In particular, the link with the limit local problem of [M. L. Delle Monache and P. Goatin, J. Differ. Equ. 257 (2014), 4015--4029] is explored numerically.