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Bayesian Inference and UMVU estimation in the single server \(M|M|1|\infty\) queue

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Abstract

In this paper, by considering an \(M|M|1|\infty\) queueing model, Bayes estimators of traffic intensity and system performance measures are discussed under (i) squared error loss function (SELF) (ii) entropy loss function (ELF) and (iii) LINEX loss function with Beta prior. Further, minimum posterior risk and minimum Bayes risk associated with Bayes estimators of traffic intensity and system performance measures are obtained under SELF. The performance of the Bayes estimators of traffic intensity and system performance measures of the queueing model are compared with the Uniformly Minimum Variance Unbiased Estimators (UMVUEs) through simulation.

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Acknowledgements

The authors thank the referees for their useful comments and suggestions, which have helped in improving the presentation of the paper.

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Authors and Affiliations

  1. Department of Statistics, Pondicherry University, Puducherry, India

    V. S. Vaidyanathan

  2. Department of Mathematical and Statistical Sciences, Marquette University, Milwaukee, WI, USA

    Naveen K. Bansal

  3. Department of Statistics, Loyola College, Chennai, India

    P. Chandrasekhar

Authors
  1. V. S. Vaidyanathan
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  2. Naveen K. Bansal
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  3. P. Chandrasekhar
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Correspondence to V. S. Vaidyanathan.

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Vaidyanathan, V.S., Bansal, N.K. & Chandrasekhar, P. Bayesian Inference and UMVU estimation in the single server \(M|M|1|\infty\) queue. J Indian Soc Probab Stat 23, 211–226 (2022). https://doi.org/10.1007/s41096-022-00121-w

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  • DOI: https://doi.org/10.1007/s41096-022-00121-w

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