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Time-limited polling systems with batch arrivals and phase-type service times

Author

Listed:
  • Ahmad Hanbali
  • Roland Haan
  • Richard Boucherie
  • Jan-Kees Ommeren

Abstract

In this paper, we develop a general framework to analyze polling systems with either the autonomous-server or the time-limited service discipline. According to the autonomous-server discipline, the server continues servicing a queue for a certain period of time. According to the time-limited service discipline, the server continues servicing a queue for a certain period of time or until the queue becomes empty, whichever occurs first. We consider Poisson batch arrivals and phase-type service times. It is known that these disciplines do not satisfy the well-known branching property in polling systems. Therefore, hardly any exact results exist in the literature. Our strategy is to apply an iterative scheme that is based on relating in closed-form the joint queue-lengths at the beginning and the end of a server visit to a queue. These kernel relations are derived using the theory of absorbing Markov chains. Copyright The Author(s) 2012

Suggested Citation

  • 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.
    • Handle: RePEc:spr:annopr:v:198:y:2012:i:1:p:57-82:10.1007/s10479-011-0846-y
    DOI: 10.1007/s10479-011-0846-y
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    References listed on IDEAS

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    1. Blanc, J.P.C., 1990. "Performance evaluation of polling systems by means of the power-series algorithm," Other publications TiSEM a5f5fb56-c17c-4c46-8d5e-b, Tilburg University, School of Economics and Management.
    2. Martin Eisenberg, 1972. "Queues with Periodic Service and Changeover Time," Operations Research, INFORMS, vol. 20(2), pages 440-451, April.
    3. Blanc, J.P.C., 1998. "The power-series algorithm for polling systems with time limits," Other publications TiSEM 3366bad3-964d-4039-82cc-a, Tilburg University, School of Economics and Management.
    4. Bernard Philippe & Youcef Saad & William J. Stewart, 1992. "Numerical Methods in Markov Chain Modeling," Operations Research, INFORMS, vol. 40(6), pages 1156-1179, December.
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    Cited by:

    1. Herwig Bruneel & Arnaud Devos, 2024. "Explicit Solutions for Coupled Parallel Queues," Mathematics, MDPI, vol. 12(15), pages 1-31, July.
    2. Chesoong Kim & Alexander Dudin & Olga Dudina & Valentina Klimenok, 2020. "Analysis of Queueing System with Non-Preemptive Time Limited Service and Impatient Customers," Methodology and Computing in Applied Probability, Springer, vol. 22(2), pages 401-432, June.
    3. Vladimir Vishnevsky & Olga Semenova, 2021. "Polling Systems and Their Application to Telecommunication Networks," Mathematics, MDPI, vol. 9(2), pages 1-30, January.
    4. Arnaud Devos & Joris Walraevens & Dieter Fiems & Herwig Bruneel, 2022. "Approximations for the performance evaluation of a discrete-time two-class queue with an alternating service discipline," Annals of Operations Research, Springer, vol. 310(2), pages 477-503, March.
    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. Wanlu Gu & Neng Fan & Haitao Liao, 2019. "Evaluating readmission rates and discharge planning by analyzing the length-of-stay of patients," Annals of Operations Research, Springer, vol. 276(1), pages 89-108, May.
    7. A. Oblakova & A. Al Hanbali & R. J. Boucherie & J. C. W. Ommeren & W. H. M. Zijm, 2019. "An exact root-free method for the expected queue length for a class of discrete-time queueing systems," Queueing Systems: Theory and Applications, Springer, vol. 92(3), pages 257-292, August.

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