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


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


URL: https://hal.archives-ouvertes.fr/hal-02142345
Document Type: Working paper
Year of publication: 2019
Place of publication: Mannheim [u.a.]
Publication language: English
Institution: School of Business Informatics and Mathematics > Wissenschaftliches Rechnen (Göttlich 2011-)
Subject: 510 Mathematics
Abstract: We present a model for a class of non-local conservation laws arising in traffic flow modeling 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.

Dieser Eintrag ist Teil der Universitätsbibliographie.




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Chiarello, Felisia Angela ; Friedrich, Jan ; Goatin, Paola ; Göttlich, Simone ORCID: 0000-0002-8512-4525 (2019) A non-local traffic flow model for 1-to-1 junctions. Mannheim [u.a.] [Working paper]


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