IDEAS home Printed from https://ideas.repec.org/a/spr/topjnl/v26y2018i3d10.1007_s11750-018-0484-5.html
   My bibliography  Save this article

Polling: past, present, and perspective

Author

Listed:
  • Sem Borst

    (Eindhoven University of Technology
    Nokia Bell Labs)

  • Onno Boxma

    (Eindhoven University of Technology)

Abstract

This is a survey on polling systems, focussing on the basic single-server multi-queue polling system in which the server visits the queues in cyclic order. The main goals of the paper are: (i) to discuss a number of the key methodologies in analyzing polling models; (ii) to give an overview of recent polling developments; and (iii) to present a number of challenging open problems.

Suggested Citation

  • 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.
  • Handle: RePEc:spr:topjnl:v:26:y:2018:i:3:d:10.1007_s11750-018-0484-5
    DOI: 10.1007/s11750-018-0484-5
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11750-018-0484-5
    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/s11750-018-0484-5?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. 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.
    2. Blanc, J.P.C., 1990. "The power-series algorithm applied to cyclic polling systems," Research Memorandum FEW 445, Tilburg University, School of Economics and Management.
    3. Gamse, Beryl & Newell, G. F., 1982. "An analysis of elevator operation in moderate height buildings--I : A single elevator," Transportation Research Part B: Methodological, Elsevier, vol. 16(4), pages 303-319, August.
    4. S. W. Fuhrmann & Robert B. Cooper, 1985. "Stochastic Decompositions in the M / G /1 Queue with Generalized Vacations," Operations Research, INFORMS, vol. 33(5), pages 1117-1129, October.
    5. E. G. Coffman & A. A. Puhalskii & M. I. Reiman, 1998. "Polling Systems in Heavy Traffic: A Bessel Process Limit," Mathematics of Operations Research, INFORMS, vol. 23(2), pages 257-304, May.
    6. 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.
    7. Blanc, J.P.C. & van der Mei, R.D., 1992. "Optimization of polling systems with Bernoulli schedules," Research Memorandum FEW 563, Tilburg University, School of Economics and Management.
    8. 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.
    9. Ivo J. B. F. Adan & Onno J. Boxma & Stella Kapodistria & Vidyadhar G. Kulkarni, 2016. "The shorter queue polling model," Annals of Operations Research, Springer, vol. 241(1), pages 167-200, June.
    10. Robert B. Cooper & Shun-Chen Niu & Mandyam M. Srinivasan, 1996. "A Decomposition Theorem for Polling Models: The Switchover Times are Effectively Additive," Operations Research, INFORMS, vol. 44(4), pages 629-633, August.
    11. G. Celik & S. C. Borst & P. A. Whiting & E. Modiano, 2016. "Dynamic scheduling with reconfiguration delays," Queueing Systems: Theory and Applications, Springer, vol. 83(1), pages 87-129, June.
    12. Martin Eisenberg, 1972. "Queues with Periodic Service and Changeover Time," Operations Research, INFORMS, vol. 20(2), pages 440-451, April.
    13. David M. Markowitz & Martin I. Reiman & Lawrence M. Wein, 2000. "The Stochastic Economic Lot Scheduling Problem: Heavy Traffic Analysis of Dynamic Cyclic Policies," Operations Research, INFORMS, vol. 48(1), pages 136-154, February.
    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. Naishuo Tian & Zhe George Zhang, 2006. "Vacation Queueing Models Theory and Applications," International Series in Operations Research and Management Science, Springer, number 978-0-387-33723-4, September.
    16. Otis B. Jennings, 2010. "Averaging Principles for a Diffusion-Scaled, Heavy-Traffic Polling Station with K Job Classes," Mathematics of Operations Research, INFORMS, vol. 35(3), pages 669-703, August.
    17. Martin I. Reiman & Lawrence M. Wein, 1999. "Heavy Traffic Analysis of Polling Systems in Tandem," Operations Research, INFORMS, vol. 47(4), pages 524-534, August.
    18. S. C. Borst & O. J. Boxma, 1997. "Polling Models With and Without Switchover Times," Operations Research, INFORMS, vol. 45(4), pages 536-543, August.
    19. 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.
    20. Sid Browne & Offer Kella, 1995. "Parallel Service with Vacations," Operations Research, INFORMS, vol. 43(5), pages 870-878, October.
    21. Gamse, Beryl & Newell, G. F., 1982. "An analysis of elevator operation in moderate height buildings--II : Multiple elevators," Transportation Research Part B: Methodological, Elsevier, vol. 16(4), pages 321-335, August.
    22. Meilijson, Isaac & Yechiali, Uri, 1977. "On optimal right-of-way policies at a single-server station when insertion of idle times is permitted," Stochastic Processes and their Applications, Elsevier, vol. 6(1), pages 25-32, 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. 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.

    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. 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.
    2. Zsolt Saffer & Sergey Andreev & Yevgeni Koucheryavy, 2016. "$$M/D^{[y]}/1$$ M / D [ y ] / 1 Periodically gated vacation model and its application to IEEE 802.16 network," Annals of Operations Research, Springer, vol. 239(2), pages 497-520, April.
    3. Vladimir Vishnevsky & Olga Semenova, 2021. "Polling Systems and Their Application to Telecommunication Networks," Mathematics, MDPI, vol. 9(2), pages 1-30, January.
    4. David M. Markowitz & Lawrence M. Wein, 2001. "Heavy Traffic Analysis of Dynamic Cyclic Policies: A Unified Treatment of the Single Machine Scheduling Problem," Operations Research, INFORMS, vol. 49(2), pages 246-270, April.
    5. Otis B. Jennings, 2008. "Heavy-Traffic Limits of Queueing Networks with Polling Stations: Brownian Motion in a Wedge," Mathematics of Operations Research, INFORMS, vol. 33(1), pages 12-35, February.
    6. 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.
    7. 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.
    8. R. Mei & A. Roubos, 2012. "Polling models with multi-phase gated service," Annals of Operations Research, Springer, vol. 198(1), pages 25-56, September.
    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. 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.
    11. Priyanka Kalita & Gautam Choudhury & Dharmaraja Selvamuthu, 2020. "Analysis of Single Server Queue with Modified Vacation Policy," Methodology and Computing in Applied Probability, Springer, vol. 22(2), pages 511-553, June.
    12. Madhu Jain & Sandeep Kaur & Parminder Singh, 2021. "Supplementary variable technique (SVT) for non-Markovian single server queue with service interruption (QSI)," Operational Research, Springer, vol. 21(4), pages 2203-2246, December.
    13. Ioannis Dimitriou, 2016. "Queueing analysis of the DRX power saving mechanism in fault-tolerant 3GPP LTE wireless networks," Annals of Operations Research, Springer, vol. 239(2), pages 521-552, April.
    14. Yi Peng & Jinbiao Wu, 2020. "A Lévy-Driven Stochastic Queueing System with Server Breakdowns and Vacations," Mathematics, MDPI, vol. 8(8), pages 1-12, July.
    15. Jianjun Li & Liwei Liu & Tao Jiang, 2018. "Analysis of an M/G/1 queue with vacations and multiple phases of operation," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 87(1), pages 51-72, February.
    16. Robert B. Cooper & Shun-Chen Niu & Mandyam M. Srinivasan, 1998. "When Does Forced Idle Time Improve Performance in Polling Models?," Management Science, INFORMS, vol. 44(8), pages 1079-1086, August.
    17. 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.
    18. Chakravarthy, Srinivas R. & Shruti, & Kulshrestha, Rakhee, 2020. "A queueing model with server breakdowns, repairs, vacations, and backup server," Operations Research Perspectives, Elsevier, vol. 7(C).
    19. Tuan Phung-Duc, 2017. "Exact solutions for M/M/c/Setup queues," Telecommunication Systems: Modelling, Analysis, Design and Management, Springer, vol. 64(2), pages 309-324, February.
    20. Rhonda Righter & J. George Shanthikumar, 1998. "Multiclass Production Systems with Setup Times," Operations Research, INFORMS, vol. 46(3-supplem), pages 146-153, 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:26:y:2018:i:3:d:10.1007_s11750-018-0484-5. 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.