A note on Bayesian estimation of traffic intensity in single-server Markovian queues

ABSTRACT

In queuing theory, a major interest of researchers is studying the behavior and formation process and analyzing the performance characteristics of queues, particularly the traffic intensity, which is defined as the ratio between the arrival rate and the service rate. How these parameters can be estimated using some statistical inferential method is the mathematical problem treated here. This article aims to obtain better Bayesian estimates for the traffic intensity of M/M/1 queues, which, in Kendall notation, stand for Markovian single-server infinity queues. The Jeffreys prior is proposed to obtain the posterior and predictive distributions of some parameters of interest. Samples are obtained through simulation and some performance characteristics are analyzed. It is observed from the Bayes factor that Jeffreys prior is competitive, among informative and non-informative prior distributions, and presents the best performance in many of the cases tested.