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Queues with Periodic Service and Changeover Time

Author

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  • Martin Eisenberg

    (Bell Telephone Laboratories, Holmdel, New Jersey)

Abstract

This paper analyzes a queuing model consisting of a system of queues that are attended periodically (in a given order) by a single server. The server empties each queue before proceeding to the next queue in sequence. A changeover time is required whenever the server switches from one queue to another. For a stationary process expressions are obtained for the Laplace-Stieltjes transforms of the waiting-time and intervisit-time distributions at each queue. It is also shown how the moments of these distributions can be calculated.

Suggested Citation

  • Martin Eisenberg, 1972. "Queues with Periodic Service and Changeover Time," Operations Research, INFORMS, vol. 20(2), pages 440-451, April.
    • Handle: RePEc:inm:oropre:v:20:y:1972:i:2:p:440-451
    DOI: 10.1287/opre.20.2.440
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    Cited by:

    1. Gil Shapira & Hanoch Levy, 2022. "On fairness in polling systems," Annals of Operations Research, Springer, vol. 317(1), pages 253-285, October.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. Shaler Stidham, 2002. "Analysis, Design, and Control of Queueing Systems," Operations Research, INFORMS, vol. 50(1), pages 197-216, February.
    7. 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.
    8. 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.
    9. 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.
    10. M. Boon, 2012. "A polling model with reneging at polling instants," Annals of Operations Research, Springer, vol. 198(1), pages 5-23, September.
    11. 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.
    12. Wu, Kan, 2014. "Taxonomy of batch queueing models in manufacturing systems," European Journal of Operational Research, Elsevier, vol. 237(1), pages 129-135.
    13. 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.
    14. 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.

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