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On the optimal control of loss probability and profit in a GI/C-BMSP/1/N queueing system

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Abstract

This paper deals with a single server queueing system where the waiting space is limited. The server serves the customer in batches. The arrival process is considered to be renewal type and the services are considered to be correlated which has been presented by a continuous-time batch Markovian service process (C-BMSP). Distribution of the system length at pre-arrival instant of a customer and at an arbitrary-epoch have been determined for this queueing system. These probability distributions have been used for obtaining the blocking probability of an arbitrary customer, expected system-length, expected waiting time of an arbitrary customer in the system, and several other important performance measures. This model may find application in queueing systems involving inventory where delay in demand may lead to perishing of goods due to long wait in the system. Also, a profit function has been derived for such a queueing model to maximize the profit from the system for certain model parameters. Finally, assuming that the inter-arrival time follows phase-type distribution, a few numerical examples have been presented in the form of graphs and tables.

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Acknowledgements

The third author’s research was supported (in part) by the Department of National Defense CDARP Grant GRC0000B1638.

Funding

Funding was provided by Canadian Network for Research and Innovation in Machining Technology, Natural Sciences and Engineering Research Council of Canada (RGPIN-2014-06604).

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Authors and Affiliations

  1. Indian Institute of Technology Bhubaneswar, Argul Campus, Jatni, Khordha, Odisha, 752050, India

    Abhijit Datta Banik

  2. Department of Mathematics, Amity University, Kolkata, West Bengal, 700135, India

    Souvik Ghosh

  3. Department of Mathematics and Computer Science, Royal Military College of Canada, Kingston, Ontario, Canada

    M. L. Chaudhry

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  1. Abhijit Datta Banik
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  2. Souvik Ghosh
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  3. M. L. Chaudhry
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Correspondence to Abhijit Datta Banik.

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Datta Banik, A., Ghosh, S. & Chaudhry, M.L. On the optimal control of loss probability and profit in a GI/C-BMSP/1/N queueing system. OPSEARCH 57, 144–162 (2020). https://doi.org/10.1007/s12597-019-00409-9

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