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Modelling and Analysis of GI/BMSP/1 Queueing System

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Abstract

This paper investigates a single server queueing system with an infinite waiting space in which customers are arrived according to renewal process and are served in batches of random size under continuous-time batch Markovian service process. We first determine the vector probability generating function of the system-length distribution at pre-arrival epoch. The system-length distribution at pre-arrival epoch is extracted in terms of zeros of the related characteristic polynomial of the vector probability generating function. By the Markov renewal theory argument, we determine the system-length distribution at random epoch. We also derive the system-length distribution at post-departure epoch using the ‘rate in = rate out’ argument. Finally, some numerical results are exhibited for different inter-arrival time distribution to demonstrate the system performance measures and correctness of analytical results.

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Acknowledgements

The authors would like to thank the anonymous reviewers for their valuable comments and suggestions to improve the quality of this paper.

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Authors and Affiliations

  1. Department of Mathematics, National Institute of Technology Raipur, Raipur, Chhattisgarh, 492010, India

    S. K. Samanta & B. Bank

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  1. S. K. Samanta
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  2. B. Bank
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Correspondence to S. K. Samanta.

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Communicated by Rosihan M. Ali.

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Samanta, S.K., Bank, B. Modelling and Analysis of GI/BMSP/1 Queueing System. Bull. Malays. Math. Sci. Soc. 44, 3777–3807 (2021). https://doi.org/10.1007/s40840-021-01120-z

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  • DOI: https://doi.org/10.1007/s40840-021-01120-z

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