Stochastic Perturbation of the Lighthill-Whitham-Richards Model via the Method of Stochastic Characteristics

TL;DR

This paper introduces a stochastic perturbation approach to the Lighthill-Whitham-Richards traffic flow model using stochastic characteristics, analyzing effects of measurement errors modeled by Brownian motions.

Contribution

It applies the method of stochastic characteristics to incorporate stochastic perturbations into the traffic flow model, providing explicit solutions for specific stochastic processes.

Findings

Derived solutions for the perturbed model with standard Brownian motion.

Analyzed the model with geometric Brownian motion without drift.

Demonstrated the impact of measurement errors on traffic density predictions.

Abstract

In this paper we apply the method of stochastic characteristics to a Lighthill-Whitham-Richards model. The stochastic perturbation can be seen as errors in measurement of the traffic density. For concrete examples we solve the equation perturbed by a standard Brownian motion and the geometric Brownian motion without drift.