Bayesian Estimation of Traffic Intensity in M/D/1 Queue Relative to Balanced Loss Function

In the Imbedded Markov Chain analysis of M/G/1 queue, X1, X2, …Xn, ... is a sequence of i.i.d random variables. In particular, for the M/D/1 queue, the distribution of common random variable turns out to be well known Poisson distribution with mean ρ, the traffic intensity. In this article, the Bayes estimator of traffic intensity in steady state relative to the Balanced loss function (BLF) has been derived based on observations on X, the number of customer’s arrival during the customer's service period. Admissibility and inadmissibility of the linear estimator under unconstrained optimization are also obtained.