Citation

Göttlich S, Knapp S. Math. Biosci. Eng. 2019; 17(2): 1677-1701.

Affiliation

Department of Mathematics, University of Mannheim, 68159 Mannheim, Germany.

Copyright

(Copyright © 2019, American Institute of Mathematical Sciences)

DOI

10.3934/mbe.2020088

PMID

32233602

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.

Language: en

Keywords

conservation laws ; piecewise deterministic processes ; random accidents ; traffic flow