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Analysis of a finite buffer variable batch service queue with batch Markovian arrival process and server’s vacation

Author

Listed:
  • K. Sikdar

    (BMS Institute of Technology & Management
    Visvesvaraya Technological University (VTU))

  • S. K. Samanta

    (National Institute of Technology)

Abstract

In this article, we study a finite buffer single server variable batch service queue where customers arrive according to a batch Markovian arrival process. The server serves the customers with a variable batch size at the starting point of services. When all the customers are served in the system exhaustively, the server leaves for a vacation. Single as well as multiple vacation policies are analyzed. We derive the queue length distributions at different epochs. Some important performance measures such as blocking probabilities, mean queue lengths, mean waiting time have been obtained. A variety of computational results are presented for practitioners and others who would like to check their results with those of ours.

Suggested Citation

  • K. Sikdar & S. K. Samanta, 2016. "Analysis of a finite buffer variable batch service queue with batch Markovian arrival process and server’s vacation," OPSEARCH, Springer;Operational Research Society of India, vol. 53(3), pages 553-583, September.
    • Handle: RePEc:spr:opsear:v:53:y:2016:i:3:d:10.1007_s12597-015-0244-3
    DOI: 10.1007/s12597-015-0244-3
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    References listed on IDEAS

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    1. Warren B. Powell & Pierre Humblet, 1986. "The Bulk Service Queue with a General Control Strategy: Theoretical Analysis and a New Computational Procedure," Operations Research, INFORMS, vol. 34(2), pages 267-275, April.
    2. Alexander Dudin & Srinivas Chakravarthy, 2002. "Optimal Hysteretic Control for the BMAP/G/ 1 System with Single and Group Service Modes," Annals of Operations Research, Springer, vol. 112(1), pages 153-169, April.
    3. Madhu Jain & Shweta Upadhyaya, 2010. "Optimal repairable M x /G/1 queue with multi-optional services and Bernoulli vacation," International Journal of Operational Research, Inderscience Enterprises Ltd, vol. 7(1), pages 109-132.
    4. Gautam Choudhury & Kailash C. Madan, 2007. "A batch arrival Bernoulli vacation queue with a random setup time under restricted admissibility policy," International Journal of Operational Research, Inderscience Enterprises Ltd, vol. 2(1), pages 81-97.
    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.
    6. K. Sikdar & U.C. Gupta & R.K. Sharma, 2008. "The analysis of a finite-buffer general input queue with batch arrival and exponential multiple vacations," International Journal of Operational Research, Inderscience Enterprises Ltd, vol. 3(1/2), pages 219-234.
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    Cited by:

    1. Yera, Yoel G. & Lillo, Rosa E. & Ramírez-Cobo, Pepa, 2019. "Fitting procedure for the two-state Batch Markov modulated Poisson process," European Journal of Operational Research, Elsevier, vol. 279(1), pages 79-92.
    2. Ramírez-Cobo, Pepa, 2017. "Findings about the two-state BMMPP for modeling point processes in reliability and queueing systems," DES - Working Papers. Statistics and Econometrics. WS 24622, Universidad Carlos III de Madrid. Departamento de Estadística.
    3. 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.
    4. Khamis A. K. ALMaqbali & Varghese C. Joshua & Achyutha Krishnamoorthy, 2023. "Multi-Class, Multi-Server Queueing Inventory System with Batch Service," Mathematics, MDPI, vol. 11(4), pages 1-29, February.
    5. 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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