Modeling random traffic accidents by conservation laws

Simone Göttlich; Stephan Knapp; Simone Göttlich; Stephan Knapp

doi:10.3934/mbe.2020088

Mathematical Biosciences and Engineering

2020, Volume 17, Issue 2: 1677-1701. doi: 10.3934/mbe.2020088

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Modeling random traffic accidents by conservation laws

Simone Göttlich ,
Stephan Knapp ^,

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

Received: 31 July 2019 Accepted: 27 November 2019 Published: 11 December 2019

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

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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.

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