On the implementation of a smoothed perturbation analysis estimator for a single-server queue with multiple vacations

We consider applying perturbation analysis (PA) to a single-server queue with multiple server vacations. A major difficulty in the implementation of a PA estimator for such queueing systems is that the introduced perturbations are propagated and accumulated continuously without any resetting. This fact may lead to the divergence of PA estimates even if the limiting distribution exists. We show that it is possible to construct a sequence of points on the observed sample path such that the perturbations are accumulated only between the two adjacent points. The key idea lies in constructing a perturbed path which is not on the same sample as the observed nominal path but is identical in probability law