Estimation for an M/G/ queue with incomplete information

Abstract

SUMMARY We consider the estimation of the arrival rate and holding distribution of a discrete time queue using only information about the size of the queue. Arrivals are not matched to departures so that direct observations of the holding times are not available. We study two estimators, quickly computed moment estimators and maximum likelihood estimators based on an entropy-motivated geometric approximation. This approximation lends the problem a Markovian structure that permits use of algorithms designed for estimating hidden Markov models. Under the assumed model, the resulting maximum likelihood estimators are efficient, but the difficulty of their calculation increases exponentially with the number of parameters. Simulations show that the root mean squared error of maximum likeilihood estimators is about 25% smaller than that of moment estimators. Simulations also show how the absence of direct observations of holding times reduce the power of tests for detecting deviations from simple models.