Best Unbiased Estimation and CAN Property in the Stable M/M/1 Queue

The Uniform Minimum Variance Unbiased (UMVU) estimators of ρl, the probability of having l or more customers, L, the expected system size, L q , 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.