IDEAS home Printed from https://ideas.repec.org/a/spr/annopr/v198y2012i1p145-16410.1007-s10479-012-1093-6.html
   My bibliography  Save this article

Gated polling with stationary ergodic walking times, Markovian routing and random feedback

Author

Listed:
  • Dieter Fiems
  • Eitan Altman

Abstract

We investigate a gated polling system with semi-linear feedback and Markovian routing. We thereby relax the classical independence assumption on the walking times; the walking times constitute a sequence of stationary ergodic random variables. It is shown that the dynamics of this polling system can be described by semi-linear stochastic recursive equations in a Markovian environment. We obtain expressions for the first and second order moments of the workload and queue content at polling instants and for the mean queue content and workload at random instants. Copyright Springer Science+Business Media, LLC 2012

Suggested Citation

  • Dieter Fiems & Eitan Altman, 2012. "Gated polling with stationary ergodic walking times, Markovian routing and random feedback," Annals of Operations Research, Springer, vol. 198(1), pages 145-164, September.
    • Handle: RePEc:spr:annopr:v:198:y:2012:i:1:p:145-164:10.1007/s10479-012-1093-6
    DOI: 10.1007/s10479-012-1093-6
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s10479-012-1093-6
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s10479-012-1093-6?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. Leonard Kleinrock & Hanoch Levy, 1988. "The Analysis of Random Polling Systems," Operations Research, INFORMS, vol. 36(5), pages 716-732, October.
    2. Mandyam M. Srinivasan, 1991. "Nondeterministic Polling Systems," Management Science, INFORMS, vol. 37(6), pages 667-681, June.
    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. Dieter Fiems & Koen De Turck, 2023. "Analysis of Discrete-Time Queues with Branching Arrivals," Mathematics, MDPI, vol. 11(4), pages 1-13, February.
    2. 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. Tetsuji Hirayama, 2012. "Analysis of multiclass Markovian polling systems with feedback and composite scheduling algorithms," Annals of Operations Research, Springer, vol. 198(1), pages 83-123, September.
    2. Mahender P. Singh & Mandyam M. Srinivasan, 2007. "Performance Bounds for Flexible Systems Requiring Setups," Management Science, INFORMS, vol. 53(6), pages 991-1004, June.
    3. Bertsimas, Dimitris., 1995. "The achievable region method in the optimal control of queueing systems : formulations, bounds and policies," Working papers 3837-95., Massachusetts Institute of Technology (MIT), Sloan School of Management.
    4. Herwig Bruneel & Arnaud Devos, 2024. "Explicit Solutions for Coupled Parallel Queues," Mathematics, MDPI, vol. 12(15), pages 1-31, July.
    5. Dimitris Bertsimas & José Niño-Mora, 1996. "Optimization of multiclass queueing networks with changeover times via the achievable region approach: Part I, the single-station case," Economics Working Papers 302, Department of Economics and Business, Universitat Pompeu Fabra, revised Jul 1998.
    6. Christos Langaris, 1999. "Markovian polling systems with mixed service disciplines and retrial customers," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 7(2), pages 305-322, December.
    7. Boysen, Nils & de Koster, René & Weidinger, Felix, 2019. "Warehousing in the e-commerce era: A survey," European Journal of Operational Research, Elsevier, vol. 277(2), pages 396-411.
    8. Germs, Remco & Van Foreest, Nicky D., 2011. "Admission policies for the customized stochastic lot scheduling problem with strict due-dates," European Journal of Operational Research, Elsevier, vol. 213(2), pages 375-383, September.
    9. Jelmer P. Gaast & Ivo J. B. F. Adan & René B. M. Koster, 2017. "The analysis of batch sojourn-times in polling systems," Queueing Systems: Theory and Applications, Springer, vol. 85(3), pages 313-335, April.
    10. Chydzinski, Andrzej, 2016. "Analysis of the scheduling mechanism for virtualization of links with partial isolation," Applied Mathematics and Computation, Elsevier, vol. 281(C), pages 39-54.

    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:145-164:10.1007/s10479-012-1093-6. 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.