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

Part of: Hyperbolic equations and systems Operations research and management science Partial differential equations, initial value and time-dependent initial-boundary value problems

Published online by Cambridge University Press:  16 December 2019

F. A. CHIARELLO Open the ORCID record for F. A. CHIARELLO [Opens in a new window] ,
J. FRIEDRICH ,
P. GOATIN Open the ORCID record for P. GOATIN [Opens in a new window] ,
S. GÖTTLICH  and
O. KOLB Open the ORCID record for O. KOLB [Opens in a new window]
F. A. CHIARELLO
Affiliation:
Inria Sophia Antipolis - Méditerranée, Université Côte d’Azur, Inria, CNRS, LJAD, 2004 route des Lucioles - BP 93, 06902 Sophia Antipolis Cedex, France emails: felisia.chiarello@inria.fr; paola.goatin@inria.fr
J. FRIEDRICH
Affiliation:
Department of Mathematics, University of Mannheim, 68131Mannheim, Germany emails: jan.friedrich@uni-mannheim.de; goettlich@uni-mannheim.de; kolb@uni-mannheim.de
P. GOATIN
Affiliation:
Inria Sophia Antipolis - Méditerranée, Université Côte d’Azur, Inria, CNRS, LJAD, 2004 route des Lucioles - BP 93, 06902 Sophia Antipolis Cedex, France emails: felisia.chiarello@inria.fr; paola.goatin@inria.fr
S. GÖTTLICH
Affiliation:
Department of Mathematics, University of Mannheim, 68131Mannheim, Germany emails: jan.friedrich@uni-mannheim.de; goettlich@uni-mannheim.de; kolb@uni-mannheim.de
O. KOLB
Affiliation:
Department of Mathematics, University of Mannheim, 68131Mannheim, Germany emails: jan.friedrich@uni-mannheim.de; goettlich@uni-mannheim.de; kolb@uni-mannheim.de
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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.

Keywords

Non-local scalar conservation lawsupwind schememacroscopic traffic flow models on networks

MSC classification

Primary: 35L65: Conservation laws
Secondary: 65M12: Stability and convergence of numerical methods 90B20: Traffic problems
Type
Papers
Information
European Journal of Applied Mathematics , Volume 31 , Issue 6 , December 2020 , pp. 1029 - 1049
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Copyright
© The Authors 2019. Published by Cambridge University Press

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