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A variational formulation of kinematic waves: Solution methods

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  • Daganzo, Carlos F.

Abstract

This paper presents improved solution methods for kinematic wave traffic problems with concave flow-density relations. As explained in part I of this work, the solution of a kinematic wave problem is a set of continuum least-cost paths in space-time. The least cost to reach a point is the vehicle number. The idea here consists in overlaying a dense but discrete network with appropriate costs in the solution region and then using a shortest-path algorithm to estimate vehicle numbers. With properly designed networks, this procedure is more accurate than existing methods and can be applied to more complicated problems. In many important cases its results are exact.

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  • Daganzo, Carlos F., 2005. "A variational formulation of kinematic waves: Solution methods," Transportation Research Part B: Methodological, Elsevier, vol. 39(10), pages 934-950, December.
    • Handle: RePEc:eee:transb:v:39:y:2005:i:10:p:934-950
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    References listed on IDEAS

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    1. Daganzo, Carlos F. & Laval, Jorge A., 2003. "Moving Bottlenecks: A Numerical Method that Converges in Flows," Institute of Transportation Studies, Research Reports, Working Papers, Proceedings qt1hp588xx, Institute of Transportation Studies, UC Berkeley.
    2. Daganzo, Carlos F., 2003. "A Variational Formulation for a Class of First Order PDE's," Institute of Transportation Studies, Research Reports, Working Papers, Proceedings qt5p54n38q, Institute of Transportation Studies, UC Berkeley.
    3. Daganzo, Carlos F., 2005. "A variational formulation of kinematic waves: basic theory and complex boundary conditions," Transportation Research Part B: Methodological, Elsevier, vol. 39(2), pages 187-196, February.
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