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dc.contributor.authorMazaré, Pierre Emmanuel
dc.contributor.authorDehwah, Ahmad H.
dc.contributor.authorClaudel, Christian G.
dc.contributor.authorBayen, Alexandre M.
dc.date.accessioned2015-08-03T09:34:35Z
dc.date.available2015-08-03T09:34:35Z
dc.date.issued2011-12
dc.identifier.issn01912615
dc.identifier.doi10.1016/j.trb.2011.07.004
dc.identifier.urihttp://hdl.handle.net/10754/561940
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.
dc.publisherElsevier BV
dc.subjectGrid-free numerical scheme
dc.subjectLWR model
dc.subjectTraffic flow
dc.subjectVariational method
dc.titleAnalytical and grid-free solutions to the Lighthill-Whitham-Richards traffic flow model
dc.typeArticle
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
dc.contributor.departmentDistributed Sensing Systems Laboratory (DSS)
dc.contributor.departmentElectrical Engineering Program
dc.contributor.departmentPhysical Sciences and Engineering (PSE) Division
dc.identifier.journalTransportation Research Part B: Methodological
dc.contributor.institutionUniversity of California at Berkeley, Department of Civil and Environmental Engineering, UC Berkeley, Sutardja Hall 642, Berkeley, CA 94720-1710, United States
kaust.personDehwah, Ahmad H.
kaust.personClaudel, Christian G.


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