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System occupancy in a multiclass batch-service queueing system with limited variable service capacity

Author

Listed:
  • Jens Baetens

    (Ghent University)

  • Bart Steyaert

    (Ghent University)

  • Dieter Claeys

    (Ghent University
    Flanders Make)

  • Herwig Bruneel

    (Ghent University)

Abstract

In multi-class telecommunications or manufacturing systems, customers belonging to the same class can often be processed together. This results in a service capacity that depends on the classes of the customers in the queue. In this paper, we analyse a discrete-time batch-service queue with two customer classes. The single batch server can group all same-class customers at the head of the queue up to a constant class-dependent maximum service capacity. We focus on the analysis of the system occupancy at service initiation opportunities, and also compute both a light- and heavy traffic approximation in order to reduce the numerical complexity introduced by the maximum service capacities. Additionally, we propose a method for interpolating between these approximations in order to study the behaviour in the intermediate region. We also deduce the system occupancy and its approximations at random slot boundaries. In the numerical experiments, we examine the conditions under which these proposed approximations are accurate.

Suggested Citation

  • Jens Baetens & Bart Steyaert & Dieter Claeys & Herwig Bruneel, 2020. "System occupancy in a multiclass batch-service queueing system with limited variable service capacity," Annals of Operations Research, Springer, vol. 293(1), pages 3-26, October.
    • Handle: RePEc:spr:annopr:v:293:y:2020:i:1:d:10.1007_s10479-019-03470-1
    DOI: 10.1007/s10479-019-03470-1
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    References listed on IDEAS

    as
    1. Ward Whitt, 1989. "An Interpolation Approximation for the Mean Workload in a GI/G/1 Queue," Operations Research, INFORMS, vol. 37(6), pages 936-952, December.
    2. Bruneel, Herwig & Mélange, Willem & Steyaert, Bart & Claeys, Dieter & Walraevens, Joris, 2012. "A two-class discrete-time queueing model with two dedicated servers and global FCFS service discipline," European Journal of Operational Research, Elsevier, vol. 223(1), pages 123-132.
    3. Yi, Xeung W. & Kim, Nam K. & Yoon, Bong K. & Chae, Kyung C., 2007. "Analysis of the queue-length distribution for the discrete-time batch-service Geo/Ga,Y/1/K queue," European Journal of Operational Research, Elsevier, vol. 181(2), pages 787-792, September.
    4. Jens Baetens & Bart Steyaert & Dieter Claeys & Herwig Bruneel, 2018. "Delay analysis of a two-class batch-service queue with class-dependent variable server capacity," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 88(1), pages 37-57, August.
    5. Martin I. Reiman & Burton Simon, 1988. "An Interpolation Approximation for Queueing Systems with Poisson Input," Operations Research, INFORMS, vol. 36(3), pages 454-469, June.
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