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

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.

• Record URL:
  http://www.sciencedirect.com/science/article/pii/S0191261511001044
• Availability:
  • Find a library where document is available. Order URL: http://worldcat.org/issn/01912615
• Supplemental Notes:
  • Abstract reprinted with permission from Elsevier.
• Authors:
  • Mazare, Pierre-Emmanuel
  • Dehwah, Ahmad H
  • Claudel, Christian G
  • Bayen, Alexandre M
  • 0000-0002-6697-222X
• Publication Date: 2011-12

Language

• English

Media Info

• Media Type: Print
• Features: Appendices; Figures; References;
• Pagination: pp 1727-1748
• Serial:
  • Transportation Research Part B: Methodological
  • Volume: 45
  • Issue Number: 10
  • Publisher: Elsevier
  • ISSN: 0191-2615
  • Serial URL: http://www.sciencedirect.com/science/journal/01912615

Subject/Index Terms

• TRT Terms: Forecasting; Numerical analysis; Partial differential equations; Traffic flow; Traffic models
• Identifier Terms: Lighthill-Whitham-Richards traffic flow model
• Subject Areas: Highways; Planning and Forecasting; I71: Traffic Theory;

Filing Info

• Accession Number: 01359512
• Record Type: Publication
• Files: TRIS, ATRI
• Created Date: Dec 22 2011 2:08PM