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Delay analysis of a two-class batch-service queue with class-dependent variable server capacity

Author

Listed:
  • Jens Baetens

    (Ghent University)

  • Bart Steyaert

    (Ghent University)

  • Dieter Claeys

    (Ghent University
    Ghent University)

  • Herwig Bruneel

    (Ghent University)

Abstract

In this paper, we analyse the delay of a random customer in a two-class batch-service queueing model with variable server capacity, where all customers are accommodated in a common single-server first-come-first-served queue. The server can only process customers that belong to the same class, so that the size of a batch is determined by the length of a sequence of same-class customers. This type of batch server can be found in telecommunications systems and production environments. We first determine the steady state partial probability generating function of the queue occupancy at customer arrival epochs. Using a spectral decomposition technique, we obtain the steady state probability generating function of the delay of a random customer. We also show that the distribution of the delay of a random customer corresponds to a phase-type distribution. Finally, some numerical examples are given that provide further insight in the impact of asymmetry and variance in the arrival process on the number of customers in the system and the delay of a random customer.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:mathme:v:88:y:2018:i:1:d:10.1007_s00186-017-0627-8
    DOI: 10.1007/s00186-017-0627-8
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    References listed on IDEAS

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    1. Warren B. Powell & Pierre Humblet, 1986. "The Bulk Service Queue with a General Control Strategy: Theoretical Analysis and a New Computational Procedure," Operations Research, INFORMS, vol. 34(2), pages 267-275, April.
    2. 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.
    3. Gabriel R. Bitran & D. Tirupati, 1989. "Approximations for Product Departures from a Single-Server Station with Batch Processing in Multi-Product Queues," Management Science, INFORMS, vol. 35(7), pages 851-878, July.
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    Cited by:

    1. 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.
    2. Srinivas R. Chakravarthy & Shruti & Alexander Rumyantsev, 2021. "Analysis of a Queueing Model with Batch Markovian Arrival Process and General Distribution for Group Clearance," Methodology and Computing in Applied Probability, Springer, vol. 23(4), pages 1551-1579, December.
    3. Fabian Schéele & Darek M. Haftor & Natallia Pashkevich, 2022. "Predicting delays in service operations," Service Business, Springer;Pan-Pacific Business Association, vol. 16(2), pages 211-226, June.

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