Multiple equilibria in a dynamic traffic network

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24 Citations (Scopus)


This study provides an example in which the dynamic user equilibrium (DUE) assignment of a congested road network with bottlenecks is non-unique. In previous studies, the uniqueness of DUE assignments with the bottleneck model has been shown in limited cases such as single-origin and single-destination networks. Consequently, it is still an important issue whether or not uniqueness is a general property of DUE assignments. The present study describes a network in which multiple patterns of link travel time are found, thus providing a negative answer to this question. The network has a loopy structure with multiple bottlenecks and multiple origin-destination (OD) pairs. Given a certain demand pattern of departure times for vehicles leaving their origins, a non-convex set of equilibria with a non-unique pattern of link travel times is shown to exist.

Original languageEnglish
Pages (from-to)867-879
Number of pages13
JournalTransportation Research Part B: Methodological
Issue number6
Publication statusPublished - 2011 Jul
Externally publishedYes


  • Bottleneck model
  • Dynamic traffic assignment
  • Dynamic user equilibrium
  • Uniqueness

ASJC Scopus subject areas

  • Civil and Structural Engineering
  • Transportation


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