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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
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. 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.
    4. Blanc, J.P.C. & van der Mei, R.D., 1992. "Optimization of polling systems with Bernoulli schedules," Other publications TiSEM dd631dbc-d81c-4b05-9539-7, Tilburg University, School of Economics and Management.
    5. 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.
    6. Martin Eisenberg, 1972. "Queues with Periodic Service and Changeover Time," Operations Research, INFORMS, vol. 20(2), pages 440-451, April.
    7. 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.
    8. 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.
    9. 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.
    10. 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.
    11. 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.
    12. 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.
    13. 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.
    14. 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.
    15. 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.
    16. 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.
    17. 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, April.
    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. 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.
    21. 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.
    22. Sid Browne & Offer Kella, 1995. "Parallel Service with Vacations," Operations Research, INFORMS, vol. 43(5), pages 870-878, October.
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    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.

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