On estimation in M/G/c/c queues

We derive the minimum variance unbiased estimator and the maximum likelihood estimator of the stationary probability function (pf) of the number of customers in a collection of independent M/G/c/c subsystems. It is assumed that the offered load and number of servers in each subsystem are unknown. We assume that observations of the total number of customers in the system are utilized because it may be impractical or impossible to observe individual server occupancies. Both estimators depend on the R distribution (the distribution of the sum of independent right truncated Poisson random variables) and R numbers.