PERTURBATION ANALYSIS OF THE GI GI 1 QUEUE

We examine a family of GI/GI/1 queueing processes generated by a param etric family of service time distributions, F(x, theta), and we show t hat under suitable conditions the corresponding customer stationary ex pectation of the system time is twice continuously differentiable with respect to theta. Expressions for the derivatives are given which are suitable for single run derivative estimation. These results are exte nded to parameters of the interarrival time distribution and expressio ns for the corresponding second derivatives (as well as partial second derivatives involving both interarrival and service time parameters) are also obtained. Finally, we present perturbation analysis algorithm s based on these expressions along with simulation results demonstrati ng their performance.