Estimation of Steady State Probability Distribution of System Size in M/M/1 Queue

Abstract

Recently Choudhury and Borthakur (2008) obtained classical and Bayesian estimators of performance measures based on a random sample of size n from a geometric distribution with mean ρ / (1− ρ) , which is the steady state probability distribution of system size. Here weobtain classical estimators, the Maximum Likelihood (ML) and Uniformly Minimum Variance Unbiased (UMVU) estimators, and Bayesian estimators of Pk , k=0,1,2,.... relative to beta prior distribution and Weighted Squared Error Loss (WSEL) function as well as relative to Standard Two-Sided Power (STSP) distribution and squared error loss / WSEL functions. Bayes, ML and UMVU estimates of the probability that the server is idle are also computed. Also Consistent Asymptotic Normality (CAN) for Pk , k=0,1,2,.... are examined.