Inferential aspects of a M/M/1 queuing system using bivariate prior

Namrata Pareek; Amit Choudhury

doi:https://doi.org/10.59139/stattrans-2026-028

Inferential aspects of a M/M/1 queuing system using bivariate prior

Namrata Pareek Department of Statistics, Gauhati University, Guwahati, Assam-781014, India & Department of Statistics, Handique Girls' College, Guwahati, Assam-781001, India ORCID:https://orcid.org/0009-0002-4217-8328 , Amit Choudhury Department of Statistics, Gauhati University, Guwahati, Assam-781014, India ORCID:https://orcid.org/0000-0001-8777-8883 Statistics in Transition new series, vol. 27, 2026, 3, pages: 69-86 Published online: 9 September 2026 https://doi.org/10.59139/stattrans-2026-028 Citation: Pareek N., Choudhury A., 2026. Inferential aspects of a M/M/1 queuing system using bivariate prior. Statistics in Transition new series, 27 (3), pp. 69-86. https://doi.org/10.59139/stattrans-2026-028

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ABSTRACT

This paper presents a Bayesian framework for estimating the performance measures of a single-server Markovian queue. A bivariate prior is employed to naturally incorporate the system's ergodicity condition along with the traditional likelihood function, which fundamentally differentiates this work from that of the existing literature. The Bayesian estimators of the performance measures are presented in the study, and we investigate standard errors and credible intervals of the Bayesian estimates. In addition, the predictive distributions for waiting times and the number of customers in the system at departure epoch were derived, offering deeper insights into the system dynamics. We also conducted a simulation study to assess the efficacy and reliability of the proposed methodology. Finally, a real-world scenario was presented to demonstrate the practical applicability of the developed algorithms.

KEYWORDS

Bayesian inference, bivariate prior, credible region, Markovian queuing system, performance measures, single server queuing model, standard error, traffic intensity

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