Stability estimates for nonlocal balance laws arising in traffic modelling

TL;DR

This paper establishes the stability of entropy weak solutions for a nonlocal traffic flow model with on- and off-ramps, providing L1-dependence estimates and numerical experiments for flow optimization.

Contribution

It proves the stability of solutions with respect to initial data and kernel functions, and introduces numerical methods for traffic flow optimization.

Findings

L1-dependence estimates for solutions

Stability with respect to kernel functions

Numerical experiments for traffic optimization

Abstract

This paper focuses on the proof of the stability of entropy weak solutions of a nonlocal balance law modeling vehicular traffic flow on a road with on- and off-ramps. The stability is obtained with respect to a kernel function in the source term. We get an estimate of the L1-dependence of the solution with respect to the initial datum, the on-ramp rate, the off-ramp rate and the mentioned kernel function. We also show numerical experiments in order to perform an optimization problem in traffic flow with on-ramps.