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Discrete-time queues with variable service capacity: a basic model and its analysis

Author

Listed:
  • Herwig Bruneel

    (Ghent University—UGent)

  • Sabine Wittevrongel

    (Ghent University—UGent)

  • Dieter Claeys

    (Ghent University—UGent)

  • Joris Walraevens

    (Ghent University—UGent)

Abstract

In this paper, we present a basic discrete-time queueing model whereby the service process is decomposed in two (variable) components: the demand of each customer, expressed in a number of work units needed to provide full service of the customer, and the capacity of the server, i.e., the number of work units that the service facility is able to perform per time unit. The model is closely related to multi-server queueing models with server interruptions, in the sense that the service facility is able to deliver more than one unit of work per time unit, and that the number of work units that can be executed per time unit is not constant over time. Although multi-server queueing models with server interruptions—to some extent—allow us to study the concept of variable capacity, these models have a major disadvantage. The models are notoriously hard to analyze and even when explicit expressions are obtained, these contain various unknown probabilities that have to be calculated numerically, which makes the expressions difficult to interpret. For the model in this paper, on the other hand, we are able to obtain explicit closed-form expressions for the main performance measures of interest. Possible applications of this type of queueing model are numerous: the variable service capacity could model variable available bandwidths in communication networks, a varying production capacity in factories, a variable number of workers in an HR-environment, varying capacity in road traffic, etc.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:annopr:v:239:y:2016:i:2:d:10.1007_s10479-013-1428-y
    DOI: 10.1007/s10479-013-1428-y
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    References listed on IDEAS

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    1. Srinivas R. Chakravarthy, 2009. "Analysis Of A Multi-Server Queue With Markovian Arrivals And Synchronous Phase Type Vacations," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 26(01), pages 85-113.
    2. Bruneel, Herwig, 1984. "A general model for the behaviour of infinite buffers with periodic service opportunities," European Journal of Operational Research, Elsevier, vol. 16(1), pages 98-106, April.
    3. Bruneel, Herwig, 1984. "A mathematical model for discrete-time buffer systems with correlated output process," European Journal of Operational Research, Elsevier, vol. 18(1), pages 98-110, October.
    4. Glock, C. H., 2010. "Batch sizing with controllable production rates," Publications of Darmstadt Technical University, Institute for Business Studies (BWL) 57823, Darmstadt Technical University, Department of Business Administration, Economics and Law, Institute for Business Studies (BWL).
    5. Bruneel, Herwig, 1986. "A general treatment of discrete-time buffers with one randomly interrupted output line," European Journal of Operational Research, Elsevier, vol. 27(1), pages 67-81, October.
    6. Maertens, Tom & Walraevens, Joris & Bruneel, Herwig, 2007. "A modified HOL priority scheduling discipline: Performance analysis," European Journal of Operational Research, Elsevier, vol. 180(3), pages 1168-1185, August.
    7. 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.
    8. Laevens, Koenraad & Bruneel, Herwig, 1995. "Delay analysis for discrete-time queueing systems with multiple randomly interrupted servers," European Journal of Operational Research, Elsevier, vol. 85(1), pages 161-177, August.
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    Cited by:

    1. Nitin Kumar & U. C. Gupta, 2020. "A Renewal Generated Geometric Catastrophe Model with Discrete-Time Markovian Arrival Process," Methodology and Computing in Applied Probability, Springer, vol. 22(3), pages 1293-1324, September.
    2. Nitin Kumar & U. C. Gupta, 2020. "Analysis of batch Bernoulli process subject to discrete-time renewal generated binomial catastrophes," Annals of Operations Research, Springer, vol. 287(1), pages 257-283, April.
    3. 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.
    4. 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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