Space-Time Inhomogeneity of Lighthill-Whitham and Richards Model: Modeling, Numerical Treatment, and Implications

In this paper, the space-time inhomogeneity associated with the kinematic wave (LWR) model is considered. The notion of space-time inhomogeneity refers to the fact that governing laws of traffic, essentially dictated by fundamental diagrams (FD), differ from each other in distinct space-time regions. Such a scenario is common when exogenous inputs, e.g. a group of slow moving vehicles, emerge in the modeling process. The well-posedness of this class of problems is proven. More importantly, it is shown that if the boundary delineating two neighboring regions is continuous and has bounded speed, this problem can be greatly simplified by introducing a piecewise linear approximation to the boundary. In particular, the variational formulation of kinematic wave model is utilized and it is proven that this approximation results in uniformly bounded errors in cumulative flow N which are proportional to the L-infinity deviation of the approximation. The numerical solution of a simplified problem is well understood, so it is ultimately implied that a kinematic wave model with space-time inhomogeneity can be solved accurately with any existing Godunov type scheme. Besides the solution theory, one concrete example is given that illustrates the application of inhomogeneous LWR model, which explains the capacity drop phenomenon as a natural result of space-time inhomogeneity.

• Supplemental Notes:
  • This paper was sponsored by TRB committee AHB45 Traffic Flow Theory and Characteristics
• Corporate Authors:

  Transportation Research Board

  500 Fifth Street, NW
  Washington, DC  United States  20001
• Authors:
  • Li, Jia
  • Zhang, H Michael
• Conference:
  • Transportation Research Board 91st Annual Meeting
  • Location: Washington DC, United States
  • Date: 2012-1-22 to 2012-1-26
• Date: 2012

Language

• English

Media Info

• Media Type: Digital/other
• Features: Appendices; Figures; References;
• Pagination: 22p
• Monograph Title: TRB 91st Annual Meeting Compendium of Papers DVD

Subject/Index Terms

• TRT Terms: Lane changing; Traffic models; Traffic speed; Travel time
• Identifier Terms: Lighthill-Whitham-Richards traffic flow model
• Uncontrolled Terms: Fundamental diagram
• Subject Areas: Data and Information Technology; Highways; I71: Traffic Theory;

Filing Info

• Accession Number: 01370295
• Record Type: Publication
• Report/Paper Numbers: 12-4060
• Files: TRIS, TRB
• Created Date: May 16 2012 4:09PM