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

In: Transportation and Traffic Theory 2009: Golden Jubilee

Author

Listed:
  • Mike Smith

    (University of York)

Abstract

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.

Suggested Citation

  • Mike Smith, 2009. "A Two-direction Method of Solving Variable Demand Equilibrium Models with and without Signal Control," Springer Books, in: William H. K. Lam & S. C. Wong & Hong K. Lo (ed.), Transportation and Traffic Theory 2009: Golden Jubilee, chapter 0, pages 365-386, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4419-0820-9_18
    DOI: 10.1007/978-1-4419-0820-9_18
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    Cited by:

    1. Smith, Mike & Mounce, Richard, 2011. "A splitting rate model of traffic re-routeing and traffic control," Transportation Research Part B: Methodological, Elsevier, vol. 45(9), pages 1389-1409.
    2. Liu, Ronghui & Smith, Mike, 2015. "Route choice and traffic signal control: A study of the stability and instability of a new dynamical model of route choice and traffic signal control," Transportation Research Part B: Methodological, Elsevier, vol. 77(C), pages 123-145.
    3. Cantarella, Giulio Erberto & Cartenì, Armando & de Luca, Stefano, 2015. "Stochastic equilibrium assignment with variable demand: Theoretical and implementation issues," European Journal of Operational Research, Elsevier, vol. 241(2), pages 330-347.

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