Bayesian estimation of the expected queue length of a system M/M/1 with certain and uncertain priors

One of characteristics of the traffic intensity in M/M/1 queue is the expected queue length. In this article, the problem of Bayes, E-Bayes, and robust Bayes estimation of the expected length in a M/M/1 queue system under a scale invariant squared error loss function is considered. We find the Bayes, E-Bayes, and robust Bayes estimators of the expected length. Finally, a simulation study is conducted for comparison of the proposed Bayes estimators.