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A Novel Computational Procedure for the Waiting-Time Distribution (In the Queue) for Bulk-Service Finite-Buffer Queues with Poisson Input

Author

Listed:
  • Mohan Chaudhry

    (Department of Mathematics and Computer Science, Royal Military College of Canada, STN Forces, P.O. Box 17000, Kingston, ON K7K 7B4, Canada
    These authors contributed equally to this work.)

  • Abhijit Datta Banik

    (School of Basic Sciences, Indian Institute of Technology Bhubaneswar, Permanent Campus Argul, Jatni, Khurda 752050, India
    These authors contributed equally to this work.)

  • Sitaram Barik

    (School of Basic Sciences, Indian Institute of Technology Bhubaneswar, Permanent Campus Argul, Jatni, Khurda 752050, India
    These authors contributed equally to this work.)

  • Veena Goswami

    (School of Computer Applications, Kalinga Institute of Industrial Technology, Bhubaneswar 751024, India
    These authors contributed equally to this work.)

Abstract

In this paper, we discuss the waiting-time distribution for a finite-space, single-server queueing system, in which customers arrive singly following a Poisson process and the server operates under ( a , b ) -bulk service rule. The queueing system has a finite-buffer capacity ‘ N ’ excluding the batch in service. The service-time distribution of batches follows a general distribution, which is independent of the arrival process. We first develop an alternative approach of obtaining the probability distribution for the queue length at a post-departure epoch of a batch and, subsequently, the probability distribution for the queue length at a random epoch using an embedded Markov chain, Markov renewal theory and the semi-Markov process. The waiting-time distribution (in the queue) of a random customer is derived using the functional relation between the probability generating function (pgf) for the queue-length distribution and the Laplace–Stieltjes transform (LST) of the queueing-time distribution for a random customer. Using LSTs, we discuss the derivation of the probability density function of a random customer’s waiting time and its numerical implementations.

Suggested Citation

  • Mohan Chaudhry & Abhijit Datta Banik & Sitaram Barik & Veena Goswami, 2023. "A Novel Computational Procedure for the Waiting-Time Distribution (In the Queue) for Bulk-Service Finite-Buffer Queues with Poisson Input," Mathematics, MDPI, vol. 11(5), pages 1-26, February.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:5:p:1142-:d:1079841
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    References listed on IDEAS

    as
    1. S. Pradhan & U. C. Gupta, 2019. "Analysis of an infinite-buffer batch-size-dependent service queue with Markovian arrival process," Annals of Operations Research, Springer, vol. 277(2), pages 161-196, June.
    2. Veena Goswami & Sudhansu Shekhar Patra & G. B. Mund, 2012. "Performance Analysis of Cloud Computing Centers for Bulk Services," International Journal of Cloud Applications and Computing (IJCAC), IGI Global, vol. 2(4), pages 53-65, October.
    3. Mohan L. Chaudhry & Carl M. Harris & William G. Marchal, 1990. "Robustness of Rootfinding in Single-Server Queueing Models," INFORMS Journal on Computing, INFORMS, vol. 2(3), pages 273-286, August.
    4. J. Medhi, 1975. "Waiting Time Distribution in a Poisson Queue with a General Bulk Service Rule," Management Science, INFORMS, vol. 21(7), pages 777-782, March.
    Full references (including those not matched with items on IDEAS)

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