# Modeling random traffic accidents by conservation laws

## TL;DR

This paper presents a stochastic traffic flow model incorporating accidents, based on conservation laws, with theoretical analysis and numerical methods to understand the impact of accidents on traffic dynamics.

## Contribution

It introduces a novel stochastic model for traffic accidents using conservation laws, with bounded variation analysis and a numerical solution algorithm.

## Key findings

- Total variation remains bounded over finite time
- The model effectively captures random accidents in traffic flow
- A numerical algorithm for simulating the model is developed

## Abstract

We introduce a stochastic traffic flow model to describe random traffic accidents on a single road. The model is a piecewise deterministic process incorporating traffic accidents and is based on a scalar conservation law with space-dependent flux function. Using a Lax-Friedrichs discretization, we show that the total variation is bounded in finite time and provide a theoretical framework to embed the stochastic process. Additionally, a solution algorithm is introduced to also investigate the model numerically.