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Queue-length distribution of a batch service queue with random capacity and batch size dependent service: M / G r Y / 1 $M/{G^{Y}_{r}}/1$

Author

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  • S. Pradhan

    (Indian Institute of Technology)

  • U.C. Gupta

    (Indian Institute of Technology)

  • S.K. Samanta

    (National Institute of Technology)

Abstract

This paper considers a single-server batch-service queue with random service capacity of the server and service time depends on the size of the batch. Customers arrive according to Poisson process and service times of the batches are generally distributed. We obtain explicit closed-form expression for the steady-state queue-length distribution at departure epoch of a batch based on roots of the associated characteristic equation of the probability generating function. Moreover, we also discuss the case when the characteristic equation has non-zero multiple roots. The queue-length distribution at random epoch is obtained using the classical principle based on ‘rate in = rate out’ approach. Finally, variety of numerical results are presented for a number of service time distributions including gamma distribution.

Suggested Citation

  • S. Pradhan & U.C. Gupta & S.K. Samanta, 2016. "Queue-length distribution of a batch service queue with random capacity and batch size dependent service: M / G r Y / 1 $M/{G^{Y}_{r}}/1$," OPSEARCH, Springer;Operational Research Society of India, vol. 53(2), pages 329-343, June.
    • Handle: RePEc:spr:opsear:v:53:y:2016:i:2:d:10.1007_s12597-015-0231-8
    DOI: 10.1007/s12597-015-0231-8
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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.
    2. Seok Ho Chang & Dae Won Choi, 2006. "Modeling and Performance Analysis of a Finite-Buffer Queue with Batch Arrivals, Batch Services, and Setup Times: The M X /G Y /1/K + B Queue with Setup Times," INFORMS Journal on Computing, INFORMS, vol. 18(2), pages 218-228, May.
    3. 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.
    4. Bruneel, Herwig & Steyaert, Bart & Desmet, Emmanuel & Petit, Guido H., 1994. "Analytic derivation of tail probabilities for queue lengths and waiting times in ATM multiserver queues," European Journal of Operational Research, Elsevier, vol. 76(3), pages 563-572, August.
    5. 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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    Cited by:

    1. 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.
    2. G. K. Tamrakar & A. Banerjee, 2020. "On steady-state joint distribution of an infinite buffer batch service Poisson queue with single and multiple vacation," OPSEARCH, Springer;Operational Research Society of India, vol. 57(4), pages 1337-1373, December.

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