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Change point estimation of service rate in M/M/1/m queues: A Bayesian approach

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  • Singh, Saroja Kumar
  • Cruz, Gabriel M.B.
  • Cruz, Frederico R.B.

Abstract

This article presents a novel approach for detecting a change point in the service rate of an M/M/1/m queue. The change point is identified by detecting a change in the probability distribution of a stochastic process. To achieve this, the article proposes a likelihood function that is constructed based on the observed number of customers left in the system at departures. Bayesian estimators are then derived using this likelihood function. The effectiveness of the proposed methods is evaluated through extensive Monte Carlo simulations. Overall, the results demonstrate the effectiveness of the proposed approach for detecting change points in service rates.

Suggested Citation

  • Singh, Saroja Kumar & Cruz, Gabriel M.B. & Cruz, Frederico R.B., 2024. "Change point estimation of service rate in M/M/1/m queues: A Bayesian approach," Applied Mathematics and Computation, Elsevier, vol. 465(C).
    • Handle: RePEc:eee:apmaco:v:465:y:2024:i:c:s0096300323005921
    DOI: 10.1016/j.amc.2023.128423
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    References listed on IDEAS

    as
    1. Singh, Saroja Kumar & Acharya, Sarat Kumar & Cruz, Frederico R.B. & Quinino, Roberto C., 2021. "Bayesian sample size determination in a single-server deterministic queueing system," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 187(C), pages 17-29.
    2. Saroja Kumar Singh & Sarat Kumar Acharya & Frederico R. B. Cruz & Roberto C. Quinino, 2023. "Bayesian inference and prediction in an M/D/1 queueing system," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 52(24), pages 8844-8864, December.
    3. Saroja Kumar Singh & Sarat Kumar Acharya, 2019. "Equivalence between Bayes and the maximum likelihood estimator in M/M/1 queue," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 48(19), pages 4780-4793, October.
    4. Saroja Kumar Singh & Sarat Kumar Acharya, 2022. "A Bayesian inference to estimate change point for traffic intensity in M/M/1 queueing model," OPSEARCH, Springer;Operational Research Society of India, vol. 59(1), pages 166-206, March.
    5. Sarat Kumar Acharya & César Emilio Villarreal-Rodríguez, 2013. "Change point estimation of service rate in an M/M/1/m queue," International Journal of Mathematics in Operational Research, Inderscience Enterprises Ltd, vol. 5(1), pages 110-120.
    6. Loschi, R. H. & Cruz, F. R. B., 2002. "An analysis of the influence of some prior specifications in the identification of change points via product partition model," Computational Statistics & Data Analysis, Elsevier, vol. 39(4), pages 477-501, June.
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