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Change point problem for Markovian arrival queueing models: Bayes factor approach

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Abstract

This paper considers two Markovian arrival single server queueing models, namely M/M/1 and \(M/E_r/1\). Under the steady state condition, we observe the number of customer present at different time points for the M/M/1 queue while in case of an \(M/E_r/1\) queue we consider the number of arrivals during the service time of a customer. A Bayesian approach is applied to study the change point problems. Testing of hypothesis for change versus no-change is carried out using predictive distributions. Further, Bayes factors are derived for change versus no-change for both the M/M/1 and \(M/E_r/1\) queueing models under natural conjugate beta prior distribution. At last, numerical results are provided for the illustration.

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Acknowledgements

The author is thankful to the three referees for their detailed comments and suggestions, which led to a much improved manuscript.

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  1. Department of Statistics, Sambalpur University, Jyotivihar, Burla, Odisha, 768019, India

    Saroja Kumar Singh

  2. Department of Statistics, Central University of Odisha, Sunabeda, Koraput, Odisha, 763004, India

    Saroja Kumar Singh

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Singh, S.K. Change point problem for Markovian arrival queueing models: Bayes factor approach. Int J Syst Assur Eng Manag 13, 2847–2854 (2022). https://doi.org/10.1007/s13198-022-01750-x

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  • DOI: https://doi.org/10.1007/s13198-022-01750-x

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