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Detailed Analytical and Computational Studies of D-BMAP/D-BMSP/1 Queueing System

Author

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  • Sujit Kumar Samanta

    (National Institute of Technology Raipur)

  • Kousik Das

    (National Institute of Technology Raipur)

Abstract

This paper studies a discrete-time single server batch arrival and batch service queueing model with unlimited waiting space. The discrete-time batch Markovian arrival process and discrete-time batch Markovian service process, respectively, manage the arrival and service processes. We adopt the UL-type RG-factorization approach based on censoring methodology for variable size batch service queue to calculate the stationary probability vectors of the transition probability matrix with general structure Markov chain at outside observer’s epoch. We reblock the transition probability matrix to its desired M/G/1 structure to find the stationary probability vectors at outside observer’s epoch for fixed size batch service queue using the matrix analytic method. We also develop relationships to determine probability vector expressions for other important time epochs such as pre-arrival, intermediate, post-departure, and random epochs. The most challenging aspect of our study is to obtain the probability mass functions of sojourn time in the system for both the variable and fixed size batch service queues. We use our suggested queueing model to derive the results of several specific well-known queueing models. We also discuss about possible managerial implication of our model to produce fruit juices in manufacturing industry. We present computational experience based on the execution of parametrized experiments with various categories in order to validate the analytical results reported in this study.

Suggested Citation

  • Sujit Kumar Samanta & Kousik Das, 2023. "Detailed Analytical and Computational Studies of D-BMAP/D-BMSP/1 Queueing System," Methodology and Computing in Applied Probability, Springer, vol. 25(1), pages 1-37, March.
    • Handle: RePEc:spr:metcap:v:25:y:2023:i:1:d:10.1007_s11009-023-10012-7
    DOI: 10.1007/s11009-023-10012-7
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    References listed on IDEAS

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    1. Souvik Ghosh & A. D. Banik, 2018. "Computing conditional sojourn time of a randomly chosen tagged customer in a $$\textit{BMAP/MSP/}1$$ BMAP / MSP / 1 queue under random order service discipline," Annals of Operations Research, Springer, vol. 261(1), pages 185-206, February.
    2. Achyutha Krishnamoorthy & Anu Nuthan Joshua & Dmitry Kozyrev, 2021. "Analysis of a Batch Arrival, Batch Service Queuing-Inventory System with Processing of Inventory While on Vacation," Mathematics, MDPI, vol. 9(4), pages 1-29, February.
    3. Yung-Chung Wang & Dong-Liang Cai & Li-Hsin Chiang & Cheng-Wei Hu, 2014. "Elucidating the Short Term Loss Behavior of Markovian-Modulated Batch-Service Queueing Model with Discrete-Time Batch Markovian Arrival Process," Mathematical Problems in Engineering, Hindawi, vol. 2014, pages 1-10, March.
    4. Steven M. Brown & Thomas Hanschke & Ingo Meents & Benjamin R. Wheeler & Horst Zisgen, 2010. "Queueing Model Improves IBM's Semiconductor Capacity and Lead-Time Management," Interfaces, INFORMS, vol. 40(5), pages 397-407, October.
    5. Quan-Lin Li & Yu Ying & Yiqiang Zhao, 2006. "A BMAP/G/1 Retrial Queue with a Server Subject to Breakdowns and Repairs," Annals of Operations Research, Springer, vol. 141(1), pages 233-270, January.
    6. Th. Hanschke & H. Zisgen, 2011. "Queueing networks with batch service," European Journal of Industrial Engineering, Inderscience Enterprises Ltd, vol. 5(3), pages 313-326.
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    Cited by:

    1. Srinivas R. Chakravarthy & Serife Ozkar, 2024. "A Queueing Model with BMAP Arrivals and Heterogeneous Phase Type Group Services," Methodology and Computing in Applied Probability, Springer, vol. 26(4), pages 1-30, December.

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