Nonlocal approaches for multilane traffic models

TL;DR

This paper introduces a multilane traffic model using nonlocal source terms to better capture lane-changing behavior, supported by rigorous mathematical analysis and numerical simulations.

Contribution

It develops a novel multilane traffic model incorporating nonlocal effects and provides mathematical proofs of existence and uniqueness of solutions.

Findings

Nonlocal flux functions significantly affect traffic flow dynamics.

The model demonstrates improved realism over local flux models.

Numerical results highlight the impact of nonlocal interactions.

Abstract

We present a multilane traffic model based on balance laws, where the nonlocal source term is used to describe the lane changing rate. The modelling framework includes the consideration of local and nonlocal flux functions. Based on a Godunov type numerical scheme, we provide BV estimates and a discrete entropy inequality. Together with the $L^1$-contractivity property, we prove existence and uniqueness of weak solutions. Numerical examples show the nonlocal impact compared to local flux functions and local sources.