IDEAS home Printed from https://ideas.repec.org/a/spr/topjnl/v24y2016i3d10.1007_s11750-015-0408-6.html
   My bibliography  Save this article

Finite-buffer polling systems with threshold-based switching policy

Author

Listed:
  • Kostia Avrachenkov

    (Inria, Sophia Antipolis)

  • Efrat Perel

    (Afeka, Tel-Aviv Academic College of Engineering
    School of Mathematical Sciences, Tel-Aviv University)

  • Uri Yechiali

    (School of Mathematical Sciences, Tel-Aviv University)

Abstract

We consider a system of two separate finite-buffer M / M / 1 queues served by a single server, where the switching mechanism between the queues is threshold-based, determined by the queue which is not being served. Applications may be found in data centers, smart traffic-light control and human behavior. Specifically, whenever the server attends queue i ( $$Q_i$$ Q i ) and the number of customers in the other queue, $$Q_j$$ Q j ( $$i,j=1,2$$ i , j = 1 , 2 ; $$j\ne i$$ j ≠ i ), reaches its threshold level, the server immediately switches to $$Q_j$$ Q j whenever $$Q_i$$ Q i is below its threshold. When a served $$Q_i$$ Q i becomes empty we consider two scenarios: (i) non-work-conserving; and (ii) work-conserving. We present occasions where the non-work-conserving policy is more economical than the work-conserving policy when high switching costs are involved. An intrinsic feature of the process is an oscillation phenomenon: when the occupancy of $$Q_i$$ Q i decreases the occupancy of the other queue increases. This fact is illustrated and discussed. By formulating the system as a three-dimensional continuous-time Markov chain we provide a probabilistic analysis of the system and investigate the effects of buffer sizes and arrival rates, as well as service rates, on the system’s performance. Numerical examples are presented and extreme cases are investigated.

Suggested Citation

  • Kostia Avrachenkov & Efrat Perel & Uri Yechiali, 2016. "Finite-buffer polling systems with threshold-based switching policy," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 24(3), pages 541-571, October.
    • Handle: RePEc:spr:topjnl:v:24:y:2016:i:3:d:10.1007_s11750-015-0408-6
    DOI: 10.1007/s11750-015-0408-6
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11750-015-0408-6
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s11750-015-0408-6?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. Boxma, O. J. & Down, D. G., 1997. "Dynamic server assignment in a two-queue model," European Journal of Operational Research, Elsevier, vol. 103(3), pages 595-609, December.
    2. Arnon Arazi & Eshel Ben-Jacob & Uri Yechiali, 2005. "Controlling an oscillating Jackson-type network having state-dependent service rates," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 62(3), pages 453-466, December.
    3. Efrat Perel & Uri Yechiali, 2013. "On Customers Acting As Servers," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 30(05), pages 1-23.
    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. Nimrod Dvir & Refael Hassin & Uri Yechiali, 2020. "Strategic behaviour in a tandem queue with alternating server," Queueing Systems: Theory and Applications, Springer, vol. 96(3), pages 205-244, December.
    2. Jewgeni H. Dshalalow & Ahmed Merie & Ryan T. White, 2020. "Fluctuation Analysis in Parallel Queues with Hysteretic Control," Methodology and Computing in Applied Probability, Springer, vol. 22(1), pages 295-327, March.
    3. Jewgeni H. Dshalalow & Ahmed Merie, 2018. "Fluctuation analysis in queues with several operational modes and priority customers," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 26(2), pages 309-333, July.
    4. Kevin Granville & Steve Drekic, 2021. "The unobserved waiting customer approximation," Queueing Systems: Theory and Applications, Springer, vol. 99(3), pages 345-396, December.
    5. Vladimir Vishnevsky & Olga Semenova, 2021. "Polling Systems and Their Application to Telecommunication Networks," Mathematics, MDPI, vol. 9(2), pages 1-30, January.
    6. 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.
    7. Kevin Granville & Steve Drekic, 2020. "A 2-class maintenance model with dynamic server behavior," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(1), pages 34-96, April.

    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. 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. Bedford, A. & Zeephongsekul, P., 2005. "On a dual queueing system with preemptive priority service discipline," European Journal of Operational Research, Elsevier, vol. 161(1), pages 224-239, February.
    3. Zeephongsekul, P. & Bedford, A., 2006. "Waiting time analysis of the multiple priority dual queue with a preemptive priority service discipline," European Journal of Operational Research, Elsevier, vol. 172(3), pages 886-908, August.
    4. 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.
    5. Mor Armony & Efrat Perel & Nir Perel & Uri Yechiali, 2019. "Exact analysis for multiserver queueing systems with cross selling," Annals of Operations Research, Springer, vol. 274(1), pages 75-100, March.
    6. Hanukov, Gabi, 2022. "A service system where junior servers approach a senior server on behalf of customers," International Journal of Production Economics, Elsevier, vol. 244(C).
    7. Feng, Wei & Adachi, Kouichi & Kowada, Masashi, 2002. "A two-queue and two-server model with a threshold-based control service policy," European Journal of Operational Research, Elsevier, vol. 137(3), pages 593-611, March.
    8. Leite, Saul C. & Fragoso, Marcelo D., 2013. "Diffusion approximation for signaling stochastic networks," Stochastic Processes and their Applications, Elsevier, vol. 123(8), pages 2957-2982.
    9. 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.
    10. Ioannis Dimitriou, 2021. "On partially homogeneous nearest-neighbour random walks in the quarter plane and their application in the analysis of two-dimensional queues with limited state-dependency," Queueing Systems: Theory and Applications, Springer, vol. 98(1), pages 95-143, June.
    11. Wei-Min Lan & Tava Lennon Olsen, 2006. "Multiproduct Systems with Both Setup Times and Costs: Fluid Bounds and Schedules," Operations Research, INFORMS, vol. 54(3), pages 505-522, June.

    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:topjnl:v:24:y:2016:i:3:d:10.1007_s11750-015-0408-6. 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.