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

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.