Two-direction methods for variable demand traffic assignment

Research output: Chapter in Book/Report/Conference proceedingConference contribution


  • A. Gordon
  • J. Springham
  • G. Skrobanski
  • M. Smith
  • A. Woods
  • Q. Lv
  • A Salis
  • Benjamin Heydecker (Editor)


Publication details

Title of host publicationFourth IMA International Conference on Mathematics in Transport
DatePublished - 2005
Number of pages25
Original languageEnglish
ISBN (Print)9780080450926


The estimation of equilibria within variable demand transport models is a central requirement for the assessment of transport proposals. Currently, given a transport model, the process of finding equilibria invariably now involves following a single search direction within the model repeatedly; aiming to reduce a measure of disequilibirium to approximately zero. This paper introduces two-direction methods for finding traffic equilibria; in these methods two directions are followed alternately instead of just one repeatedly. For each two-direction method described it is shown that, away from equilibrium and under natural standard conditions, one of the two directions certainly reduces a natural measure of disequilibrium. The paper also gives a counterexample showing that under these same natural conditions the search direction utilized is an algorithm called algorithm 1 is not guaranteed to reduce the degree of disequilibrium.

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