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

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

Research output: Contribution to journalArticle

247 Citations (Scopus)

Abstract

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
Volume37
Issue number6
DOIs
StatePublished - Jan 1 1989

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Hamiltonians
Control theory
Flow patterns
Dynamical systems
Economics
Continuous time
Assignment
Network dynamics
Optimal control
Traffic flow
Optimal control theory
Optimization problem
Dynamic traffic assignment
Regularity
Convexity
Dynamic systems
Assignment problem
Qualification

All Science Journal Classification (ASJC) codes

  • Computer Science Applications
  • Management Science and Operations Research

Cite this

Friesz, Terry Lee ; Luque, Javier ; Tobin, Roger L. ; Wie, Byung Wook. / Dynamic network traffic assignment considered as a continuous time optimal control problem. In: Operations Research. 1989 ; Vol. 37, No. 6. pp. 893-901.
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Dynamic network traffic assignment considered as a continuous time optimal control problem. / Friesz, Terry Lee; Luque, Javier; Tobin, Roger L.; Wie, Byung Wook.

In: Operations Research, Vol. 37, No. 6, 01.01.1989, p. 893-901.

Research output: Contribution to journalArticle

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