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

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

DOI: https://doi.org/10.1017/S095679251900038X
URL: https://www.cambridge.org/core/journals/european-j...
Additional URL: https://www.researchgate.net/publication/337959057...
Document Type: Article
Year of publication Online: 2019
The title of a journal, publication series: European Journal of Applied Mathematics
Page range: 1-21
Place of publication: Cambridge
Publishing house: Cambridge Univ. Press
ISSN: 0956-7925
Publication language: English
Institution: School of Business Informatics and Mathematics > Wissenschaftliches Rechnen (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.

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Chiarello, Felisia Angela ; Friedrich, Jan ; Goatin, Paola ; Göttlich, Simone ORCID: 0000-0002-8512-4525 ; Kolb, Oliver ORCID: 0000-0001-6947-5520 (2019) A non-local traffic flow model for 1-to-1 junctions. European Journal of Applied Mathematics Cambridge 1-21 [Article]

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