Modeling space–time inhomogeneities with the kinematic wave theory

In this paper, the authors are concerned with modeling space–time inhomogeneities with the kinematic wave (Lighthill-Whitham-Richards(LWR)) model. 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 slowly moving vehicles, emerge in the modeling process. The authors will prove the well-posedness of this class of problems. More importantly, the authors show 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 authors utilize the variational formulation of the kinematic wave model and prove that this approximation results in uniformly bounded errors in cumulative flow N which are proportional to the L8 deviation of the approximation. The numerical solution of this simplified problem is well understood, and this result means that a kinematic wave model with space–time inhomogeneity can be solved accurately with any existing Godunov type scheme. Finally, using the inhomogeneous LWR model, the authors explain the capacity drop as a natural result of space–time inhomogeneity.

• Record URL:
  • https://doi.org/10.1016/j.trb.2013.03.005
• Record URL:
  • http://www.sciencedirect.com/science/article/pii/S0191261513000453
• Availability:
  • Find a library where document is available. Order URL: http://worldcat.org/issn/01912615
• Supplemental Notes:
  • Abstract reprinted with permission from Elsevier.
• Authors:
  • Li, Jia
  • Zhang, H M
• Publication Date: 2013-8

Language

• English

Media Info

• Media Type: Print
• Features: Figures; References;
• Pagination: pp 113-125
• Serial:
  • Transportation Research Part B: Methodological
  • Volume: 54
  • Issue Number: 0
  • Publisher: Elsevier
  • ISSN: 0191-2615
  • Serial URL: http://www.sciencedirect.com/science/journal/01912615

Subject/Index Terms

• TRT Terms: Highway capacity; Kinematics; Multilane highways; 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: 01487312
• Record Type: Publication
• Files: TRIS
• Created Date: Jul 18 2013 1:54PM