A non-local traffic flow model for 1-to-1 junctions

Chiarello, Felisia Angela ; Friedrich, Jan ; Goatin, Paola ; Göttlich, Simone ; Kolb, Oliver

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DOI: https://doi.org/10.1017/S095679251900038X
URL: https://www.cambridge.org/core/journals/european-j...
Additional URL: https://www.researchgate.net/publication/337959057...
URN: urn:nbn:de:bsz:180-madoc-552950
Document Type: Article
Year of publication: 2020
The title of a journal, publication series: European Journal of Applied Mathematics
Volume: 31
Issue number: 6
Page range: 1029-1049
Place of publication: Cambridge
Publishing house: Cambridge Univ. Press
ISSN: 0956-7925
Publication language: English
Institution: School of Business Informatics and Mathematics > Scientific Computing (Göttlich 2011-)
Subject: 510 Mathematics
600 Technology
Abstract: We present a model for a class of non-local conservation laws arising in traffic flow modelling at road junctions. Instead of a single velocity function for the whole road, we consider two different road segments, which may differ for their speed law and number of lanes (hence their maximal vehicle density). We use an upwind type numerical scheme to construct a sequence of approximate solutions, and we provide uniform L∞ and total variation estimates. In particular, the solutions of the proposed model stay positive and below the maximum density of each road segment. Using a Lax–Wendroff type argument and the doubling of variables technique, we prove the well-posedness of the proposed model. Finally, some numerical simulations are provided and compared with the corresponding (discontinuous) local model.
Additional information: Online-Ressource

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