Perturbation analysis of theGI/GI/1 queue

We examine a family of GI/GI/1 queueing processes generated by a parametric family of service time distributions, F (x, θ), and we show that under suitable conditions the corresponding customer stationary expectation of the system time is twice continuously differentiable with respect to θ. Expressions for the derivatives are given which are suitable for single run derivative estimation. These results are extended to parameters of the interarrival time distribution and expressions 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 algorithms based on these expressions along with simulation results demonstrating their performance.