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Analysis of a queue with general service demands and correlated service capacities

Author

Listed:
  • Michiel Muynck

    (Ghent University)

  • Herwig Bruneel

    (Ghent University)

  • Sabine Wittevrongel

    (Ghent University)

Abstract

We present the study of a non-classical discrete-time queueing model in which the customers each request a variable amount of service, called their “service demand”, from a server which is able to execute a variable amount of work, called its “service capacity”, during each time slot. We assume that the numbers of arrivals in consecutive time slots and the service demands of consecutive customers form two independent and identically distributed sequences. However, we allow the service capacities in consecutive time slots to be correlated according to a discrete-batch Markovian process. We study this model analytically and obtain expressions for the probability generating function of the steady-state system content and customer delay, as well as their moments and an approximation for their tail probabilities. The results are illustrated with several numerical examples.

Suggested Citation

  • Michiel Muynck & Herwig Bruneel & Sabine Wittevrongel, 2020. "Analysis of a queue with general service demands and correlated service capacities," Annals of Operations Research, Springer, vol. 293(1), pages 73-99, October.
    • Handle: RePEc:spr:annopr:v:293:y:2020:i:1:d:10.1007_s10479-019-03396-8
    DOI: 10.1007/s10479-019-03396-8
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    References listed on IDEAS

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    1. Michiel Muynck & Sabine Wittevrongel & Herwig Bruneel, 2017. "Analysis of discrete-time queues with general service demands and finite-support service capacities," Annals of Operations Research, Springer, vol. 252(1), pages 3-28, May.
    2. Giri, B. C. & Yun, W. Y. & Dohi, T., 2005. "Optimal design of unreliable production-inventory systems with variable production rate," European Journal of Operational Research, Elsevier, vol. 162(2), pages 372-386, April.
    3. M. L. Chaudhry & Gagandeep Singh & U. C. Gupta, 2013. "A Simple and Complete Computational Analysis of MAP/R/1 Queue Using Roots," Methodology and Computing in Applied Probability, Springer, vol. 15(3), pages 563-582, September.
    4. Herwig Bruneel & Sabine Wittevrongel & Dieter Claeys & Joris Walraevens, 2016. "Discrete-time queues with variable service capacity: a basic model and its analysis," Annals of Operations Research, Springer, vol. 239(2), pages 359-380, April.
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    Cited by:

    1. Freek Verdonck & Herwig Bruneel & Sabine Wittevrongel, 2021. "Delay in a 2-State Discrete-Time Queue with Stochastic State-Period Lengths and State-Dependent Server Availability and Arrivals," Mathematics, MDPI, vol. 9(14), pages 1-17, July.
    2. Michiel De Muynck & Herwig Bruneel & Sabine Wittevrongel, 2023. "Analysis of a Queue with General Service Demands and Multiple Servers with Variable Service Capacities," Mathematics, MDPI, vol. 11(4), pages 1-21, February.

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