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Estimating changes in traffic intensity for Markovian finite queueing systems: a Bayesian perspective

Author

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  • Saroja Kumar Singh

    (Ravenshaw University)

  • J. F. R. Aguirre

    (Universidade Federal de Minas Gerais)

  • F. R. B. Cruz

    (Universidade Federal de Minas Gerais)

Abstract

Detecting the change point between different distributions in queueing theory presents a significant challenge, especially when working with observed data. Tra-ditionally, both parametric and non-parametric methods have been employed to address this issue in Markov single-server finite queueing models. While these methods can successfully identify the change point, they often come with the draw-back of high variance in the estimates. This article introduces Bayesian approaches to improve precision in change point detection by utilizing squared error and pre-cautionary loss functions. The study is based on a dataset that records the number of customers present in the system immediately before the arrival of the n-th cus-tomer, which is analyzed through an embedded Markov chain framework. The findings demonstrate that Bayesian methods achieve comparable error rates to traditional approaches but with a significant reduction in variance, particularly when dealing with smaller sample sizes. To showcase the practical benefits of this Bayesian methodology, a comprehensive numerical example is provided, illustrat-ing how these approaches can enhance the accuracy and reliability of change point detection in queueing models.

Suggested Citation

  • Saroja Kumar Singh & J. F. R. Aguirre & F. R. B. Cruz, 2025. "Estimating changes in traffic intensity for Markovian finite queueing systems: a Bayesian perspective," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 16(7), pages 2467-2479, July.
    • Handle: RePEc:spr:ijsaem:v:16:y:2025:i:7:d:10.1007_s13198-025-02791-8
    DOI: 10.1007/s13198-025-02791-8
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    References listed on IDEAS

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    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. Jack Jewson & David Rossell, 2022. "General Bayesian loss function selection and the use of improper models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 84(5), pages 1640-1665, November.
    3. 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.
    4. Kiapour, A. & Nematollahi, N., 2011. "Robust Bayesian prediction and estimation under a squared log error loss function," Statistics & Probability Letters, Elsevier, vol. 81(11), pages 1717-1724, November.
    5. P. Mozgunov & T. Jaki & M. Gasparini, 2019. "Loss functions in restricted parameter spaces and their Bayesian applications," Journal of Applied Statistics, Taylor & Francis Journals, vol. 46(13), pages 2314-2337, October.
    6. Saroja Kumar Singh & Frederico R. B. Cruz & Eriky S. Gomes & Abhijit Datta Banik, 2024. "Classical and Bayesian estimations of performance measures in a single server Markovian queueing system based on arrivals during service times," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 53(10), pages 3517-3546, May.
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