Inference in ergodic queues using occupation cycles

Abstract

We deal with inference problems on traffic intensity and on the mean number of customers in the system in steady state (q). We define the slopping time in terms of occupation cycles and apply the resulting estimators to a large class of stationary queues comparing it with alternative methods and with the integral estimator obtained directly from the sample in the Markovian case. Our method is quite effocient to estimate q. Also the asymptotic problems posed by Schruben and Kulkarni [7] do not appear. We observe that reductions in the sample information do not necessarily give worse estimations. We also give some numerical examples by simulating known models.