A variational formulation for higher order macroscopic traffic flow models of the GSOM family

The GSOM (Generic second order modelling) family of traffic flow models combines the Lighthill and Whitman, Richards (LWR) model with dynamics of driver-specific attributes and can be expressed as a system of conservation laws. The object of the paper is to show that a proper Lagrangian formulation of the GSOM model can be recast as a Hamilton–Jacobi equation, the solution of which can be expressed as the value function of an optimal control problem. This value function is interpreted as the position of vehicles, and the optimal trajectories of the optimal control formulation can be identified with the characteristics. Further the paper analyzes the initial and boundary conditions, proposes a generalization of the inf-morphism and the Lax–Hopf formulas to the GSOM model, and considers numerical aspects.

• Record URL:
  • https://doi.org/10.1016/j.trb.2013.07.005
• Record URL:
  • http://www.sciencedirect.com/science/article/pii/S0191261513001203
• Availability:
  • Find a library where document is available. Order URL: http://worldcat.org/issn/01912615
• Supplemental Notes:
  • Abstract reprinted with permission by Elsevier.
• Authors:
  • Lebacque, Jean-Patrick
  • Khoshyaran, Megan M
• Publication Date: 2013-11

Language

• English

Media Info

• Media Type: Print
• Features: Figures; References;
• Pagination: pp 245-265
• Serial:
  • Transportation Research Part B: Methodological
  • Volume: 57
  • Issue Number: 0
  • Publisher: Elsevier
  • ISSN: 0191-2615
  • Serial URL: http://www.sciencedirect.com/science/journal/01912615

Subject/Index Terms

• TRT Terms: Lagrangian functions; Macroscopic traffic flow; Numerical analysis; Traffic flow theory
• Identifier Terms: Lighthill-Whitham-Richards traffic flow model
• Subject Areas: Highways; Planning and Forecasting; I71: Traffic Theory;

Filing Info

• Accession Number: 01505131
• Record Type: Publication
• Files: TRIS
• Created Date: Jan 27 2014 10:45AM