IDEAS home Printed from https://ideas.repec.org/a/spr/annopr/v198y2012i1p185-21810.1007-s10479-011-0960-x.html
   My bibliography  Save this article

Continuous polling models and application to ferry assisted WLAN

Author

Listed:
  • Veeraruna Kavitha
  • Eitan Altman

Abstract

In this paper we focus on a class of polling systems encountered while modeling the ferry based wireless local area network (FWLAN). A moving ferry, while walking in a predetermined cyclic path, communicates with the static nodes (or users) of the network via a wireless link. The ferry is assumed to stop and communicate with a node that has a packet to send or to receive, when it is closest to that node. The location distribution of the node to which or from which a packet arrives is assumed to have a support of positive Lebesgue measure. These features imply that polling models with finite number of queues cannot be used to model the system. We study in this paper the continuous polling systems with service disciplines that model the use of the FWLAN (and that are more complex than the classical exhaustive or gated services). Our approach is based on discretization of the continuous polling model. We propose a special way of discretizing the continuous system such that: (1) the known Pseudo conservation laws can be applied to obtain the stationary expected workload of the discrete systems; (2) the limit, of these ‘discretized' expected workloads, equals the stationary expected workload of the continuous system. Our results rely heavily on fixed point analysis of infinite dimensional operators. Copyright Springer Science+Business Media, LLC 2012

Suggested Citation

  • Veeraruna Kavitha & Eitan Altman, 2012. "Continuous polling models and application to ferry assisted WLAN," Annals of Operations Research, Springer, vol. 198(1), pages 185-218, September.
    • Handle: RePEc:spr:annopr:v:198:y:2012:i:1:p:185-218:10.1007/s10479-011-0960-x
    DOI: 10.1007/s10479-011-0960-x
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s10479-011-0960-x
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s10479-011-0960-x?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Robert, Philippe, 2010. "The evolution of a spatial stochastic network," Stochastic Processes and their Applications, Elsevier, vol. 120(7), pages 1342-1363, July.
    2. Dirk P. Kroese & Volker Schmidt, 1996. "Light-Traffic Analysis for Queues with Spatially Distributed Arrivals," Mathematics of Operations Research, INFORMS, vol. 21(1), pages 135-157, February.
    Full references (including those not matched with items on IDEAS)

    Citations

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


    Cited by:

    1. Sem Borst & Onno Boxma, 2018. "Polling: past, present, and perspective," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 26(3), pages 335-369, October.
    2. Dieter Fiems, 2023. "Retrial queues with constant retrial times," Queueing Systems: Theory and Applications, Springer, vol. 103(3), pages 347-365, April.
    3. Vladimir Vishnevsky & Olga Semenova, 2021. "Polling Systems and Their Application to Telecommunication Networks," Mathematics, MDPI, vol. 9(2), pages 1-30, January.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Lasse Leskelä & Falk Unger, 2012. "Stability of a spatial polling system with greedy myopic service," Annals of Operations Research, Springer, vol. 198(1), pages 165-183, September.
    2. Peter Taylor, 2022. "Spatial queues with a moving server," Queueing Systems: Theory and Applications, Springer, vol. 100(3), pages 261-263, April.
    3. Sergey Foss, 2018. "Comments on: Polling: past, present and perspective," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 26(3), pages 374-378, October.

    More about this item

    Statistics

    Access and download statistics

    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:annopr:v:198:y:2012:i:1:p:185-218:10.1007/s10479-011-0960-x. 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.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with 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.