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Analysis of a Discrete-time Queue with Modified Batch Service Policy and Batch-size-dependent Service

Author

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  • Gopinath Panda

    (Dhirubhai Ambani Institute of Information and Communication Technology)

  • Veena Goswami

    (Kalinga Institute of Industrial Technology)

Abstract

We consider a discrete-time single server batch service queue, with a modified bulk service rule, where jobs will process in batches with a minimum batch size of L and maximum batch size K. In addition, we let jobs join the service if the server has started the service and has less than K jobs. The service times of the batches depend on the size of the service batch. We find explicit analytical expressions for the joint and marginal probability distribution of the number of jobs in the system, in the queue, and with the server. We also compute several performance measures and illustrate their dependence on various system parameters. Finally, we match the presented results with some results in the literature and establish a link to the continuous-time counterpart.

Suggested Citation

  • Gopinath Panda & Veena Goswami, 2023. "Analysis of a Discrete-time Queue with Modified Batch Service Policy and Batch-size-dependent Service," Methodology and Computing in Applied Probability, Springer, vol. 25(1), pages 1-18, March.
    • Handle: RePEc:spr:metcap:v:25:y:2023:i:1:d:10.1007_s11009-023-09985-2
    DOI: 10.1007/s11009-023-09985-2
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    References listed on IDEAS

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    1. Bar-Lev, Shaul K. & Parlar, Mahmut & Perry, David & Stadje, Wolfgang & Van der Duyn Schouten, Frank A., 2007. "Applications of bulk queues to group testing models with incomplete identification," European Journal of Operational Research, Elsevier, vol. 183(1), pages 226-237, November.
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    5. Claeys, Dieter & Walraevens, Joris & Laevens, Koenraad & Bruneel, Herwig, 2010. "A queueing model for general group screening policies and dynamic item arrivals," European Journal of Operational Research, Elsevier, vol. 207(2), pages 827-835, December.
    6. Bar-Lev, S.K. & Parlar, M. & Perry, D. & Stadje, W. & van der Duyn Schouten, F.A., 2007. "Applications of bulk queues to group testing models with incomplete identification," Other publications TiSEM 0b1bfa5e-c1e6-43ec-9684-1, Tilburg University, School of Economics and Management.
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