IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v197y2009i1p188-195.html
   My bibliography  Save this article

Stability of periodic polling system with BMAP arrivals

Author

Listed:
  • Saffer, Zsolt
  • Telek, Miklós

Abstract

This paper considers the stability of BMAP/GI/1 periodic polling models with mixed service disciplines. The server attends the N stations in a repeating sequence of stages. Customers arrive to the stations according to batch Markov arrival processes (BMAPs). The service times of the stations are general independent and identically distributed. The characterization of global stability of the system, the order of instability of stations and the necessary and sufficient condition for the stability are given. Our stability analysis is based on the investigation of the embedded Markovian chains at the polling epochs, which allows a much simpler discussion than the formerly applied approaches. This work can also be seen as a survey on stability of a quite general set of polling models, since the majority of the known results of the field is a special case of the presented ones.

Suggested Citation

  • Saffer, Zsolt & Telek, Miklós, 2009. "Stability of periodic polling system with BMAP arrivals," European Journal of Operational Research, Elsevier, vol. 197(1), pages 188-195, August.
    • Handle: RePEc:eee:ejores:v:197:y:2009:i:1:p:188-195
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377-2217(08)00425-6
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    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. Borovkov, A. A. & Schassberger, R., 1994. "Ergodicity of a polling network," Stochastic Processes and their Applications, Elsevier, vol. 50(2), pages 253-262, April.
    2. Martin Eisenberg, 1972. "Queues with Periodic Service and Changeover Time," Operations Research, INFORMS, vol. 20(2), pages 440-451, April.
    3. Lillo, Rosa E., 2005. "Ergodicity and analysis of the process describing the system state in polling systems with two queues," European Journal of Operational Research, Elsevier, vol. 167(1), pages 144-162, November.
    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. Vladimir Vishnevsky & Olga Semenova, 2021. "Polling Systems and Their Application to Telecommunication Networks," Mathematics, MDPI, vol. 9(2), pages 1-30, January.
    2. Jianyu Cao & Weixin Xie, 2017. "Stability of a two-queue cyclic polling system with BMAPs under gated service and state-dependent time-limited service disciplines," Queueing Systems: Theory and Applications, Springer, vol. 85(1), pages 117-147, February.

    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. 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.
    2. Jan-Kees Ommeren & Ahmad Al Hanbali & Richard J. Boucherie, 2020. "Analysis of polling models with a self-ruling server," Queueing Systems: Theory and Applications, Springer, vol. 94(1), pages 77-107, February.
    3. Marko A. A. Boon & Onno J. Boxma & Offer Kella & Masakiyo Miyazawa, 2017. "Queue-length balance equations in multiclass multiserver queues and their generalizations," Queueing Systems: Theory and Applications, Springer, vol. 86(3), pages 277-299, August.
    4. 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.
    5. M. Boon, 2012. "A polling model with reneging at polling instants," Annals of Operations Research, Springer, vol. 198(1), pages 5-23, September.
    6. Wu, Kan, 2014. "Taxonomy of batch queueing models in manufacturing systems," European Journal of Operational Research, Elsevier, vol. 237(1), pages 129-135.
    7. Lillo, Rosa E., 2005. "Ergodicity and analysis of the process describing the system state in polling systems with two queues," European Journal of Operational Research, Elsevier, vol. 167(1), pages 144-162, November.
    8. 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.
    9. Tayfur Altiok & Goang An Shiue, 1995. "Single‐stage, multi‐product production/inventory systems with lost sales," Naval Research Logistics (NRL), John Wiley & Sons, vol. 42(6), pages 889-913, September.
    10. Chen, Jung-Tai, 2008. "Queueing models of certain manufacturing cells under product-mix sequencing rules," European Journal of Operational Research, Elsevier, vol. 188(3), pages 826-837, August.
    11. Shaler Stidham, 2002. "Analysis, Design, and Control of Queueing Systems," Operations Research, INFORMS, vol. 50(1), pages 197-216, February.
    12. Ahmad Hanbali & Roland Haan & Richard Boucherie & Jan-Kees Ommeren, 2012. "Time-limited polling systems with batch arrivals and phase-type service times," Annals of Operations Research, Springer, vol. 198(1), pages 57-82, September.
    13. Menshikov, Mikhail & Zuyev, Sergei, 2001. "Polling systems in the critical regime," Stochastic Processes and their Applications, Elsevier, vol. 92(2), pages 201-218, April.
    14. 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.
    15. Gil Shapira & Hanoch Levy, 2022. "On fairness in polling systems," Annals of Operations Research, Springer, vol. 317(1), pages 253-285, October.

    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:eee:ejores:v:197:y:2009:i:1:p:188-195. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/eor .

    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.