A nonlocal traffic flow model with stochastic velocity

TL;DR

This paper introduces a stochastic nonlocal traffic flow model based on scalar conservation laws, analyzing its theoretical properties, well-posedness, and the impact of stochasticity through numerical simulations.

Contribution

It presents a novel stochastic nonlocal traffic flow model with theoretical analysis and numerical insights into the effects of randomness on traffic density evolution.

Findings

Stochasticity influences traffic density evolution significantly.

The model is well-posed under certain conditions.

Numerical examples demonstrate the mean behavior and parameter effects.

Abstract

In this paper, we investigate a nonlocal traffic flow model based on a scalar conservation law, where a stochastic velocity function is assumed. In addition to the modeling, theoretical properties of the stochastic nonlocal model are provided, also addressing the question of well-posedness. A detailed numerical analysis offers insights how the stochasticity affects the evolution of densities. Finally, numerical examples illustrate the mean behavior of solutions and the influence of parameters for a large number of realizations.