Analytical and grid-free solutions to the Lighthill-Whitham-Richards traffic flow model

Handle URI:
http://hdl.handle.net/10754/561940
Title:
Analytical and grid-free solutions to the Lighthill-Whitham-Richards traffic flow model
Authors:
Mazaré, Pierre Emmanuel; Dehwah, Ahmad H.; Claudel, Christian G. ( 0000-0003-0702-6548 ) ; Bayen, Alexandre M.
Abstract:
In this article, we propose a computational method for solving the Lighthill-Whitham-Richards (LWR) partial differential equation (PDE) semi-analytically for arbitrary piecewise-constant initial and boundary conditions, and for arbitrary concave fundamental diagrams. With these assumptions, we show that the solution to the LWR PDE at any location and time can be computed exactly and semi-analytically for a very low computational cost using the cumulative number of vehicles formulation of the problem. We implement the proposed computational method on a representative traffic flow scenario to illustrate the exactness of the analytical solution. We also show that the proposed scheme can handle more complex scenarios including traffic lights or moving bottlenecks. The computational cost of the method is very favorable, and is compared with existing algorithms. A toolbox implementation available for public download is briefly described, and posted at http://traffic.berkeley.edu/project/downloads/lwrsolver. © 2011 Elsevier Ltd.
KAUST Department:
Electrical Engineering Program; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division; Distributed Sensing Systems Laboratory (DSS)
Publisher:
Elsevier BV
Journal:
Transportation Research Part B: Methodological
Issue Date:
Dec-2011
DOI:
10.1016/j.trb.2011.07.004
Type:
Article
ISSN:
01912615
Appears in Collections:
Articles; Electrical Engineering Program; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.authorMazaré, Pierre Emmanuelen
dc.contributor.authorDehwah, Ahmad H.en
dc.contributor.authorClaudel, Christian G.en
dc.contributor.authorBayen, Alexandre M.en
dc.date.accessioned2015-08-03T09:34:35Zen
dc.date.available2015-08-03T09:34:35Zen
dc.date.issued2011-12en
dc.identifier.issn01912615en
dc.identifier.doi10.1016/j.trb.2011.07.004en
dc.identifier.urihttp://hdl.handle.net/10754/561940en
dc.description.abstractIn this article, we propose a computational method for solving the Lighthill-Whitham-Richards (LWR) partial differential equation (PDE) semi-analytically for arbitrary piecewise-constant initial and boundary conditions, and for arbitrary concave fundamental diagrams. With these assumptions, we show that the solution to the LWR PDE at any location and time can be computed exactly and semi-analytically for a very low computational cost using the cumulative number of vehicles formulation of the problem. We implement the proposed computational method on a representative traffic flow scenario to illustrate the exactness of the analytical solution. We also show that the proposed scheme can handle more complex scenarios including traffic lights or moving bottlenecks. The computational cost of the method is very favorable, and is compared with existing algorithms. A toolbox implementation available for public download is briefly described, and posted at http://traffic.berkeley.edu/project/downloads/lwrsolver. © 2011 Elsevier Ltd.en
dc.publisherElsevier BVen
dc.subjectGrid-free numerical schemeen
dc.subjectLWR modelen
dc.subjectTraffic flowen
dc.subjectVariational methoden
dc.titleAnalytical and grid-free solutions to the Lighthill-Whitham-Richards traffic flow modelen
dc.typeArticleen
dc.contributor.departmentElectrical Engineering Programen
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
dc.contributor.departmentDistributed Sensing Systems Laboratory (DSS)en
dc.identifier.journalTransportation Research Part B: Methodologicalen
dc.contributor.institutionUniversity of California at Berkeley, Department of Civil and Environmental Engineering, UC Berkeley, Sutardja Hall 642, Berkeley, CA 94720-1710, United Statesen
kaust.authorDehwah, Ahmad H.en
kaust.authorClaudel, Christian G.en
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