Best unbiased estimation and CAN property in the stable M/M/1 queue

The Uniform Minimum Variance Unbiased (UMVU) estimators of Ïâ, the probability of having â or more customers, L, the expected system size, Lq, the expected number of customers in the queue, and, the expected number of customers in a non empty queue, are derived based on a random sample of fixed size n on system size at departure points from the geometric distribution on the support 0, 1, 2,. with mean, which is the distribution of system size in M/M/1 queueing system in equilibrium. The derivations are based on application of Lehmann-Scheffe theorem. Also, CAN estimators of performance measures are derived. In addition the probability distribution of UMVU estimators are obtained. © 2014 Copyright Taylor and Francis Group, LLC