A splitting rate model of traffic re-routeing and traffic control

Mike Smith*, Richard Mounce

*Corresponding author for this work

Research output: Contribution to journalArticle

9 Citations (Scopus)
5 Downloads (Pure)


The paper presents an idealised dynamical model of day-to-day or within-day re-routeing using splitting rates at nodes, or node-exit flows, rather than route-flows. It is shown that under certain conditions repeated application of the dynamical model gives rise to a sequence of link flow vectors which converges to a set of approximate Wardrop equilibria. A special dynamical signal green-time re-allocation model is added; the combination is shown (in outline) to converge to the set of approximate consistent equilibria under certain conditions. Finally the paper uses model network results to illustrate a method of designing fixed time signal timings to meet different scenarios. The paper sets the scene by giving a simple motivating model, involving both routeing changes and green-time changes following the equisaturation policy, in which unpredictable discontinuous behaviour, including a pitchfork bifurcation, occurs as a result of the interaction between re-routeing and responsive control. (C) 2010 Published by Elsevier Ltd.

Original languageEnglish
Pages (from-to)316-340
Number of pages25
JournalProcedia – Social and Behavioral Sciences
Publication statusPublished - 2011
Event19th International Symposium on Transportation and Traffic Theory (ISTTT) in honor of Carlos F. Daganzo - Berkeley, Canada
Duration: 18 Jul 201120 Jul 2011


  • user equilibrium assignment
  • variational-inequalities
  • signal control
  • road network
  • algorithms
  • transportation
  • enumeration
  • stability


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