# Nonlocal approaches for multilane traffic models

@article{Friedrich2021NonlocalAF, title={Nonlocal approaches for multilane traffic models}, author={Jan Friedrich and Simone G{\"o}ttlich and Elena Rossi}, journal={ArXiv}, year={2021}, volume={abs/2012.05794} }

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…

#### 2 Citations

Nonlocal reaction traffic flow model with on-off ramps

- Computer Science, MathematicsArXiv
- 2021

A new nonlocal traffic model which includes the effects of on and offramps is proposed which is based on a local reaction traffic model proposed in [16] and [16], and which is compatible with existing conservation laws with nonlocal flux.

Network models for nonlocal traffic flow

- Computer Science, MathematicsArXiv
- 2021

The maximum principle and the existence of weak solutions on networks are proved and the limiting behavior of the proposed models when the nonlocal influence tends to infinity are investigated.

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