IDEAS home Printed from https://ideas.repec.org/h/spr/sprchp/978-1-4419-0820-9_16.html
   My bibliography  Save this book chapter

Existence of Equilibrium in a Continuous Dynamic Queueing Model for Traffic Networks with Responsive Signal Control

In: Transportation and Traffic Theory 2009: Golden Jubilee

Author

Listed:
  • Richard Mounce

    (Queen’s University)

Abstract

Many real-life traffic systems incorporate responsive traffic signal control, i.e. where the green time assigned to a stage at a junction depends on the queue lengths on the various approaches. By making signals responsive one might expect the queueing pattern to approach equilibrium, i.e. a queueing pattern for which the responsive policy tells us to leave the signal settings unchanged. However, changing junction signal settings changes the costs of traversing the approaches to the junction and traffic may change route in the light of this. Hence, a responsive signal system is really at equilibrium only if it is at equilibrium with respect to its own rules and also with respect to the re-routing of traffic. The paper gives a framework for responsive signal control in the dynamic queueing model in terms of stage pressures. Three responsive signal policies are considered: delay-minimisation, equisaturation and P 0. A dynamical system is specified that describes both changes to signals due to the responsive signal policy and changes to route inflows due to the re-routing of traffic. An implicit function theorem is utilised in showing that the swap vector for the dynamical system is a continuous function of the route flow vector and green time vector. Then by Schauder's fixed point theorem, there exists equilibrium of the dynamical system. Finally, the responsive policies are compared with fixed signals in network simulations.

Suggested Citation

  • Richard Mounce, 2009. "Existence of Equilibrium in a Continuous Dynamic Queueing Model for Traffic Networks with Responsive 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 327-344, Springer.
  • Handle: RePEc:spr:sprchp:978-1-4419-0820-9_16
    DOI: 10.1007/978-1-4419-0820-9_16
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a search for a similarly titled item that would be available.

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    2. Smith, M.J. & Liu, R. & Mounce, R., 2015. "Traffic control and route choice: Capacity maximisation and stability," Transportation Research Part B: Methodological, Elsevier, vol. 81(P3), pages 863-885.
    3. 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.
    4. Wada, Kentaro & Satsukawa, Koki & Smith, Mike & Akamatsu, Takashi, 2019. "Network throughput under dynamic user equilibrium: Queue spillback, paradox and traffic control," Transportation Research Part B: Methodological, Elsevier, vol. 126(C), pages 391-413.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:sprchp:978-1-4419-0820-9_16. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.