Dynamic user optimal traffic assignment on congested multidestination networks

Byung Wook Wie, Terry Lee Friesz, Roger L. Tobin

Research output: Contribution to journalArticlepeer-review

74 Scopus citations


An equivalent continuous time optimal control problem is formulated to predict the temporal evolution of traffic flow pattern on a congested multiple origin-destination network, corresponding to a dynamic generalization of Wardropian user equilibrium. Optimality conditions are derived using the Pontryagin minimum principle and given economic interpretations, which are generalizations of similar results previously reported for single-destination networks. Analyses of sufficient conditions for optimality and of singular controls are also given. Under the steady-state assumptions, the model is shown to be a proper dynamic extension of Beckmann's mathematical programming problem for a static user equilibrium traffic assignment.

Original languageEnglish (US)
Pages (from-to)431-442
Number of pages12
JournalTransportation Research Part B
Issue number6
StatePublished - Jan 1 1990

All Science Journal Classification (ASJC) codes

  • Civil and Structural Engineering
  • Transportation


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