A Two-direction Method of Solving Variable Demand Equilibrium Models with and without Signal Control

  • Mike Smith


   A two direction method of solving variable demand equilibrium models is considered. Throughout an equilibration using this method, if the first direction fails to reduce disequilibrium, use the second. A proof of convergence under fairly weak conditions is provided. The paper shows how the method works on models without and with responsive signal controls. In the former case the method may replace the iteration of an assignment and a demand model. In the latter case the method may replace the iteration of an assignment and a control model; and may then be utilized to design new fixed time signal timings suitable for a variety of situations. In both cases there will be a reasonable convergence guarantee if the two-direction method is utilized.


Incidence Matrix Descent Direction Proximal Point Algorithm Traffic Assignment Alternate Direction Method 
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I am grateful to all partners in the FREEFLOW project; and especially to Jim Austin and John Polak. The drawing shown in Fig. 1 above originated with Jim and naturally fits the thinking of John when he set up and gained support for the FREEFLOW project. Partners in the FREEFLOW project are: Transport for London, City of York Council, Kent County Council, QinetiQ, Mindsheet, ACIS, Trakm8, Kizoom, Imperial College London, Loughborough University and the University of York. The Ian Routledge Consultancy is a sub-contractor to the University of York.


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Copyright information

© Springer-Verlag US 2009

Authors and Affiliations

  • Mike Smith
    • 1
  1. 1.University of YorkLondonU.K

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