Communications in Mathematical Sciences

Volume 19 (2021)

Number 8

Nonlocal approaches for multilane traffic models

Pages: 2291 – 2317



Jan Friedrich (Department of Mathematics, University of Mannheim, Germany)

Simone Göttlich (Department of Mathematics, University of Mannheim, Germany)

Elena Rossi (Department of Sciences and Methods for Engineering, University of Modena and Reggio Emilia, Italy)


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 $\mathsf{L}^1$‑contractivity property, we prove existence and uniqueness of weak solutions. Numerical examples show the nonlocal impact compared to local flux functions and local sources.


nonlocal balance laws, multilane traffic flow, Godunov scheme

2010 Mathematics Subject Classification

35L65, 65M12, 90B20

Received 10 December 2020

Accepted 29 May 2021

Published 7 October 2021