Estimation of retrial rate in a retrial queue (Q1896698)

Describing the time evolution of a purely exponential retrial queue by a two-dimensional vector (number of call attempts since last departure, number of calls in retrial queue) yields a nonstandard Markovian description of the system's time evolution. The second coordinate of this process determines essentially the retrial rate, but is not accessible to observations. So the estimation of the retrial rate must be done indirectly. It suffices to count the external arrivals (primary calls) and the first coordinate of the new process to obtain a strongly consistent estimator of the arrival rate. The asymptotic variance of the estimator is computed.