Modeling random traffic accidents by conservation laws

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DOI:	https://doi.org/10.3934/mbe.2020088
URL:	https://madoc.bib.uni-mannheim.de/55238
Additional URL:	http://www.aimspress.com/article/10.3934/mbe.20200...
URN:	urn:nbn:de:bsz:180-madoc-552384
Document Type:	Article
Year of publication:	2020
The title of a journal, publication series:	Mathematical Biosciences and Engineering : MBE
Volume:	17
Issue number:	2
Page range:	1677-1701
Place of publication:	Springfield, MO
Publishing house:	American Institute of Mathematical Sciences
ISSN:	1547-1063 , 1551-0018
Related URLs:	https://www.researchgate.net/publication... https://arxiv.org/abs/1907.13544
Publication language:	English
Institution:	School of Business Informatics and Mathematics > Scientific Computing (Göttlich 2011-)
Pre-existing license:	Creative Commons Attribution 4.0 International (CC BY 4.0)
Subject:	510 Mathematics
Abstract:	We introduce a stochastic traffic flow model to describe random traffic accidents on a singleroad. The model is a piecewise deterministic process incorporating traffic accidents and is based on ascalar conservation law with space-dependent flux function. Using a Lax-Friedrichs discretization, weshow that the total variation is bounded in finite time and provide a theoretical framework to embedthe stochastic process. Additionally, a solution algorithm is introduced to also investigate the modelnumerically.