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Modeling random traffic accidents by conservation laws

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

Special Issues: Mathematical Modeling with Measures

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

Citation: Simone Göttlich, Stephan Knapp. Modeling random traffic accidents by conservation laws. Mathematical Biosciences and Engineering, 2020, 17(2): 1677-1701. doi: 10.3934/mbe.2020088

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