AN ASYMPTOTICALLY RISK-EFFICIENT SAMPLE ALLOCATION FOR ESTIMATING THE MEAN WAITING TIME IN THE M/M/1 and M/Ek/1 QUEUES

In this paper, we consider the problem of optimally allocating a sampling budget between the interarrival times and service times for the stationary queue and stationary queue with the goal of minimizing the mean squared error of one of four system performance measures. The natural estimator of the mean waiting time, obtained by substituting estimators for the arrival rate and service rate in the formula for the mean waiting time, has infinite mean squared error and cannot be used. Using an alternative estimator, we propose a two-stage sampling plan and show that this plan is asymptotically risk-efficient in the sense that the mean squared error of the resulting estimator converges to the minimum mean squared error as the sampling budget gets large. Asymptotic normality and other properties of the two-stage estimator are also proved. Simulation results for the system are given to support the theoretical results. **Supported by grant MDA904-00-1-0025 from NSA.