Microscopic and Macroscopic Traffic Flow Models including Random Accidents

TL;DR

This paper develops microscopic and macroscopic stochastic traffic flow models that incorporate random accidents, demonstrating their convergence and comparing their behaviors through numerical simulations.

Contribution

It introduces a novel stochastic framework for traffic modeling that includes accidents and proves the convergence of microscopic to macroscopic models.

Findings

Microscopic and macroscopic models are effectively linked through convergence.

Numerical simulations validate the models and their convergence behavior.

Accidents are modeled as interruptions linked to traffic conditions.

Abstract

We introduce microscopic and macroscopic stochastic traffic models including traffic accidents. The microscopic model is based on a Follow-the-Leader approach whereas the macroscopic model is described by a scalar conservation law with space dependent flux function. Accidents are introduced as interruptions of a deterministic evolution and are directly linked to the traffic situation. Based on a Lax-Friedrichs discretization convergence of the microscopic model to the macroscopic model is shown. Numerical simulations are presented to compare the above models and show their convergence behaviour.