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A detailed note on the finite-buffer queueing system with correlated batch-arrivals and batch-size-/phase-dependent bulk-service

Author

Listed:
  • Souvik Ghosh

    (Tel Aviv University)

  • A. D. Banik

    (Indian Institute of Technology Bhubaneswar, Argul Campus)

  • Joris Walraevens

    (Ghent University)

  • Herwig Bruneel

    (Ghent University)

Abstract

This paper analyzes a finite-buffer queueing system, where customers arrive in batches and the accepted customers are served in batches by a single server. The service is assumed to be dependent on the batch-size and follows a general bulk service rule. The inter-arrival times of batches are assumed to be correlated and they are represented through the batch Markovian arrival process (BMAP). Computation procedure of the queue-length distributions at the post-batch-service completion, an arbitrary, and the pre-batch-arrival epochs are discussed. Various performance measures along with the consecutive customer loss probabilities are studied considering batch-size-dependent renewal service time distributions. Further, the above finite-buffer bulk-service queueing model is also investigated considering correlated batch-service times which are presented through the Markovian service process (MSP). The phase-dependent consecutive loss probabilities for the correlated batch-service times are determined. In the form of tables and graphs, a variety of numerical results for different batch-service time distributions are presented in this paper.

Suggested Citation

  • Souvik Ghosh & A. D. Banik & Joris Walraevens & Herwig Bruneel, 2022. "A detailed note on the finite-buffer queueing system with correlated batch-arrivals and batch-size-/phase-dependent bulk-service," 4OR, Springer, vol. 20(2), pages 241-272, June.
    • Handle: RePEc:spr:aqjoor:v:20:y:2022:i:2:d:10.1007_s10288-021-00478-x
    DOI: 10.1007/s10288-021-00478-x
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    References listed on IDEAS

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    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. A. D. Banik & M. L. Chaudhry, 2017. "Efficient Computational Analysis of Stationary Probabilities for the Queueing System BMAP / G /1/ N With or Without Vacation(s)," INFORMS Journal on Computing, INFORMS, vol. 29(1), pages 140-151, February.
    3. António Pacheco & Helena Ribeiro, 2008. "Consecutive customer losses in oscillating GI X /M//n systems with state dependent services rates," Annals of Operations Research, Springer, vol. 162(1), pages 143-158, September.
    4. Warren B. Powell, 1985. "Analysis of Vehicle Holding and Cancellation Strategies in Bulk Arrival, Bulk Service Queues," Transportation Science, INFORMS, vol. 19(4), pages 352-377, November.
    5. Winfried K. Grassmann & Michael I. Taksar & Daniel P. Heyman, 1985. "Regenerative Analysis and Steady State Distributions for Markov Chains," Operations Research, INFORMS, vol. 33(5), pages 1107-1116, October.
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    Cited by:

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