Dynamic network traffic assignment considered as a continuous time optimal control problem

Terry L. Friesz, Javier Luque, Roger L. Tobin, Byung Wook Wie

Research output: Contribution to journalArticlepeer-review

278 Scopus citations


Two continuous time formulations of the dynamic traffic assignment problem are considered, one that corresponds to system optimization and the other to a version of user optimization on a single mode network using optimal control theory. Pontryagin's necessary conditions are analyzed and given economic interpretations that correspond to intuitive notions regarding dynamic system optimized and dynamic user optimized traffic flow patterns. Notably, we offer the first dynamic generalization of Beckmann's equivalent optimization problem for static user optimized traffic assignment in the form of an optimal control problem. The analysis further establishes that a constraint qualification and convexity requirements for the Hamiltonian, which together ensure that the necessary conditions are also sufficient, are satisfied under commonly encountered regularity conditions.

Original languageEnglish (US)
Pages (from-to)893-901
Number of pages9
JournalOperations Research
Issue number6
StatePublished - 1989

All Science Journal Classification (ASJC) codes

  • Computer Science Applications
  • Management Science and Operations Research


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