Customer-oriented finite perturbation analysis for queueing networks

We consider queueing networks for which the performance measure J(theta) de pends on a parameter theta, which can be a service time parameter or a buff er size, and we are interested in sensitivity analysis of J(theta) with res pect to theta. We introduce a new method, called customer-oriented finite p erturbation analysis (CFPA), which predicts J(theta + Delta) for an arbitra ry, finite perturbation Delta from a simulation experiment at theta. CFPA c an estimate the entire performance function (by using a finite number of ch osen points and fitting a least-squares approximating polynomial to the obs ervation) within one simulation experiment. We obtain CFPA by reformulating finite perturbation analysis (FPA) for customers. The main difference betw een FPA and CFPA is that the former calculates the sensitivities of timing epochs of events, such as external arrivals or service time completions, wh ile the latter yields sensitivities of departure epochs of customers. We gi ve sufficient conditions for unbiasedness of CFPA. Numerical examples show the efficiency of the method. In particular, we address sensitivity analysi s with respect to buffer sizes and thereby give a solution to the problem f or which perturbation analysis was originally built.