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

Pierre Emmanuel Mazaré, Ahmad H. Dehwah, Christian G. Claudel, Alexandre M. Bayen

Research output: Contribution to journalArticlepeer-review

61 Scopus citations

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.
Original languageEnglish (US)
Pages (from-to)1727-1748
Number of pages22
JournalTransportation Research Part B: Methodological
Volume45
Issue number10
DOIs
StatePublished - Dec 2011

ASJC Scopus subject areas

  • Management Science and Operations Research
  • Transportation

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