Solving the dynamic network user equilibrium problem with state-dependent time shifts

Terry L. Friesz, Reetabrata Mookherjee

Research output: Contribution to journalArticlepeer-review

70 Scopus citations


In this paper we consider the infinite dimensional variational inequality (VI) formulation of dynamic user equilibrium (DUE) put forward by Friesz et al. (1993) [A variational inequality formulation of the dynamic network user equilibrium problem. Operations Research 41, 179-191] as well as the differential variational inequality (DVI) version reported in Friesz et al. (2001) [Dynamic network user equilibrium with state-dependent time lags. Networks and Spatial Economics 1, 319-347]. We show how the theory of optimal control and the theory of infinite dimensional variational inequalities may be combined to create a simple and effective fixed point algorithm for calculating DUE network flows that are solutions of both formulations. A numerical example is provided.

Original languageEnglish (US)
Pages (from-to)207-229
Number of pages23
JournalTransportation Research Part B: Methodological
Issue number3
StatePublished - Mar 2006

All Science Journal Classification (ASJC) codes

  • Civil and Structural Engineering
  • Transportation


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