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

Saroja Kumar Singh (), J. F. R. Aguirre () and F. R. B. Cruz ()
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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

International Journal of System Assurance Engineering and Management, 2025, vol. 16, issue 7, No 10, 2467-2479

Abstract: 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.

Keywords: Finite queues; M/M/1/m model; Bayesian estimator; Change point; Loss function; 60K25; 68M20; 90B22 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s13198-025-02791-8

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