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Complete Analysis of $$M/G_{r}^{(a,b)}/1/N$$ M / G r ( a , b ) / 1 / N Queue with Second Optional Service

Author

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  • Anuradha Banerjee

    (Indian Institute of Technology (BHU), Varanasi)

  • Priti Lata

    (Indian Institute of Technology (BHU), Varanasi)

Abstract

The current article is about a finite buffer, group size dependent bulk service queue, in which a single server renders two type of services, first essential service (FES) and second optional service (SoS). Customers arrive at the system in the Poisson fashion. Service is rendered by a server in groups following ‘general bulk service’ (GBS) rule on first come first serve (FCFS) basis for FES. In this article, we allowed a part of a group, served in FES, to join SoS in group following binomial law. The service time distribution is considered to be generally distributed and dependent on the group size under service for both the cases, FES and SoS. The mathematical analysis is performed using the supplementary variable technique (SVT) and the embedded Markov chain technique to obtain the steady state, departure epoch and arbitrary epoch joint probabilities of the count of customers in the queue and with the server when the server is in FES as well as in SoS. Finally, various numerical studies are presented to show the behaviour of the key efficiency metrics, which eventually shows the importance of the current study.

Suggested Citation

  • Anuradha Banerjee & Priti Lata, 2024. "Complete Analysis of $$M/G_{r}^{(a,b)}/1/N$$ M / G r ( a , b ) / 1 / N Queue with Second Optional Service," Methodology and Computing in Applied Probability, Springer, vol. 26(4), pages 1-33, December.
    • Handle: RePEc:spr:metcap:v:26:y:2024:i:4:d:10.1007_s11009-024-10116-8
    DOI: 10.1007/s11009-024-10116-8
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    References listed on IDEAS

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    1. Chakravarthy, Srinivas R., 2016. "Queueing models with optional cooperative services," European Journal of Operational Research, Elsevier, vol. 248(3), pages 997-1008.
    2. G. Ayyappan & T. Deepa, 2019. "Analysis of batch arrival bulk service queue with additional optional service multiple vacation and setup time," International Journal of Mathematics in Operational Research, Inderscience Enterprises Ltd, vol. 15(1), pages 1-25.
    3. Charan Jeet Singh & Madhu Jain & Binay Kumar, 2011. "Queueing model with state-dependent bulk arrival and second optional service," International Journal of Mathematics in Operational Research, Inderscience Enterprises Ltd, vol. 3(3), pages 322-340.
    4. Gopinath Panda & Veena Goswami, 2023. "Analysis of a Discrete-time Queue with Modified Batch Service Policy and Batch-size-dependent Service," Methodology and Computing in Applied Probability, Springer, vol. 25(1), pages 1-18, March.
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