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Computational analysis of $$GI^{[X]}/D$$ G I [ X ] / D - $$MSP^{(a,b)}/1$$ M S P ( a , b ) / 1 queueing system via RG-factorization

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  • Kousik Das

    (National Institute of Technology Raipur)

  • Sujit Kumar Samanta

    (National Institute of Technology Raipur)

Abstract

This paper investigates a single server batch arrival and batch service queueing model with infinite waiting space. The inter-occurrence time of arrival batches with random size is distributed arbitrarily. Customers are served using the discrete-time Markovian service process in accordance with the general bulk-service rule. We compute the prearrival epoch probability vectors using the UL-type RG-factorization method based on censoring technique. The random epoch probability vectors are then obtained using the Markov renewal theory based on the prearrival epoch probability vectors. We derive analytically simple expressions for the outside observer’s, intermediate, and post-departure epochs probability vectors by evolving the relationships among them. Determining the probability mass functions of the waiting time distribution and the service batch size distribution for an arbitrary customer in an arriving batch is the most challenging aspect of this work. Finally, we discuss computational experience for the purpose of validating the analytical results presented in this paper.

Suggested Citation

  • Kousik Das & Sujit Kumar Samanta, 2023. "Computational analysis of $$GI^{[X]}/D$$ G I [ X ] / D - $$MSP^{(a,b)}/1$$ M S P ( a , b ) / 1 queueing system via RG-factorization," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 98(1), pages 1-39, August.
    • Handle: RePEc:spr:mathme:v:98:y:2023:i:1:d:10.1007_s00186-023-00816-1
    DOI: 10.1007/s00186-023-00816-1
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    References listed on IDEAS

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    1. S. K. Samanta & B. Bank, 2022. "Extended analysis and computationally efficient results for the GI/Ma,b/1 queueing system," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 51(11), pages 3739-3760, June.
    2. Yi, Xeung W. & Kim, Nam K. & Yoon, Bong K. & Chae, Kyung C., 2007. "Analysis of the queue-length distribution for the discrete-time batch-service Geo/Ga,Y/1/K queue," European Journal of Operational Research, Elsevier, vol. 181(2), pages 787-792, September.
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    4. Th. Hanschke & H. Zisgen, 2011. "Queueing networks with batch service," European Journal of Industrial Engineering, Inderscience Enterprises Ltd, vol. 5(3), pages 313-326.
    5. 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.
    6. 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.
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