A Variational Formulation of Kinematic Wave Theory

Carlos F. Daganzo

Institute of Transportation Studies, Research Reports, Working Papers, Proceedings from Institute of Transportation Studies, UC Berkeley

Abstract: This paper proves that kinematic wave (KW) problems with concave (or convex) equations of state can be formulated as calculus of variations problems. Every well-posed problem of this type, no matter how complicated, is reduced to the determination of a shortest tree in a relevant region of spacetime where cost is predefined. A duality between KW theory and /least cost networks is thus unveiled. In the new formulation space-time curves that constrain flow, such as sets of moving bottlenecks, become space-time shortcuts. These shortcuts become part of the network and affect the nature of the solution but not the speed with which it can be obtained. Complex boundary conditions are naturally handled in the new formulation as constraints/shortcuts of this type.

Date: 2003-05-01
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

Downloads: (external link)
https://www.escholarship.org/uc/item/02q9d45c.pdf;origin=repeccitec (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:cdl:itsrrp:qt02q9d45c

Access Statistics for this paper

More papers in Institute of Transportation Studies, Research Reports, Working Papers, Proceedings from Institute of Transportation Studies, UC Berkeley Contact information at EDIRC.
Bibliographic data for series maintained by Lisa Schiff ().