Bayesian inference and prediction in the single server Markovian queue

Abstract

The use of stochastic models and performance measures for the analysis of real life queuing scenarios are based on the fundamental premise that parameters values are known. This is a rarity since more often than not, parameters are usually unknown and require to be estimated. This paper presents techniques for the same from Bayesian perspective. The queue we intend to deal with is the M/M/1 queuing model. Several closed form expressions on posterior inference and prediction are presented which can be readily implemented using standard spreadsheet tools. Previous work in this direction resulted in non-existence of posterior moments. A way out is suggested. Interval estimates and tests of hypothesis on performance measures are also presented.