Bayesian inference of traffic intensity in <i>M</i>/<i>M</i>/1 queue under symmetric and asymmetric loss functions

Abstract In this article, Bayesian estimators of the traffic intensity (ρ) in single server Markovian ( <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:mi>M</m:mi> <m:mo>/</m:mo> <m:mi>M</m:mi> <m:mo>/</m:mo> <m:mn>1</m:mn> </m:mrow> </m:math> {M/M/1} ) queueing system are derived under the squared error loss function (SELF) and precautionary loss function (PLF). These Bayes estimators are derived using three different priors viz. beta, independent gamma and Jeffrey distribution. The effectiveness of the proposed Bayes estimators are compared in terms of their posterior risks. A suitable prior is chosen for Bayesian analysis using the model comparison criterion based on the Bayes factor.