Network models for nonlocal traffic flow

TL;DR

This paper introduces a network-based traffic flow model with nonlocal velocity effects, providing new coupling conditions at intersections, mathematical proofs, and numerical comparisons to existing models.

Contribution

It develops a novel network formulation for nonlocal traffic flow, including coupling conditions and analysis of limiting behavior, advancing the modeling and mathematical understanding.

Findings

Proves maximum principle and existence of weak solutions.

Shows differences between proposed coupling conditions and classical models.

Analyzes the limiting behavior as nonlocal influence increases.

Abstract

We present a network formulation for a traffic flow model with nonlocal velocity in the flux function. The modeling framework includes suitable coupling conditions at intersections to either ensure maximum flux or distribution parameters. Based on an upwind type numerical scheme, we prove the maximum principle and the existence of weak solutions on networks. We also investigate the limiting behavior of the proposed models when the nonlocal influence tends to infinity. Numerical examples show the difference between the proposed coupling conditions and a comparison to the Lighthill-Whitham-Richards network model.