This paper deals with the user equilibrium problem (flow assignment with equal journey time by alternative routes) and system optimum (flow assignment with minimal average journey time) in a network consisting of parallel routes with a single origin-destination pair. The travel time is simulated by arbitrary smooth nondecreasing functions. We prove that the equilibrium and optimal assignment problems for such a network can be reduced to the fixed point problem expressed explicitly. A simple iterative method of finding equilibriumand optimal flow assignment is developed. The method is proved to converge geometrically; under some fairly natural conditions the method is proved to converge quadratically.
Original languageEnglish
Pages (from-to)243-256
JournalJournal of Applied and Industrial Mathematics
Volume10
Issue number2
StatePublished - 2016

    Research areas

  • user equilibrium, system optimum, fixed point, network routes

ID: 7568542