Traffic flow models on a network of roads

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Abstract

Macroscopic models of traffic flow on a network of roads can be formulated in terms of a scalar conservation law on each road, together with boundary conditions, determining the flow at junctions. Some of these intersection models are reviewed in this note, discussing the well posedness of the resulting initial value problems. From a practical point of view, one can also study traffic patterns as the outcome of many decision problems, where each driver chooses his departure time and route to destination, in order to minimize the sum of a departure and an arrival cost. For the new models including a buffer at each intersection, one can prove: (i) the existence of a globally optimal solution, minimizing the total cost to all drivers, and (ii) the existence of a Nash equilibrium solution, where no driver can lower his own cost by changing his departure time or the route taken to reach destination.

Original languageEnglish (US)
Title of host publicationTheory, Numerics and Applications of Hyperbolic Problems I - Aachen, Germany, 2016
EditorsMichael Westdickenberg, Christian Klingenberg
PublisherSpringer New York LLC
Pages237-248
Number of pages12
ISBN (Print)9783319915449
DOIs
Publication statusPublished - Jan 1 2018
Event16th International Conference on Hyperbolic Problems: Theory, Numerics and Applications, 2016 - Aachen, Germany
Duration: Aug 1 2016Aug 5 2016

Publication series

NameSpringer Proceedings in Mathematics and Statistics
Volume236
ISSN (Print)2194-1009
ISSN (Electronic)2194-1017

Other

Other16th International Conference on Hyperbolic Problems: Theory, Numerics and Applications, 2016
CountryGermany
CityAachen
Period8/1/168/5/16

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All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Cite this

Bressan, A. (2018). Traffic flow models on a network of roads. In M. Westdickenberg, & C. Klingenberg (Eds.), Theory, Numerics and Applications of Hyperbolic Problems I - Aachen, Germany, 2016 (pp. 237-248). (Springer Proceedings in Mathematics and Statistics; Vol. 236). Springer New York LLC. https://doi.org/10.1007/978-3-319-91545-6_19