Customer-Oriented Finite Perturbation Analysis for Queueing Networks

We consider queueing networks for which the performance measureJ ( θ ) depends on a parameter θ, which can be a service time parameter or a buffer size, and we are interested in sensitivity analysis of J ( θ ) with respect to θ. We introduce a new method, called customer-oriented finite perturbation analysis (CFPA), which predicts J ( θ + Δ ) for an arbitrary, finite perturbation Δ from a simulation experiment at θ. CFPA can estimate the entire performance function (by using a finite number of chosen points and fitting a least-squares approximating polynomial to the observation) within one simulation experiment. We obtain CFPA by reformulating finite perturbation analysis (FPA) for customers. The main difference between FPA and CFPA is that the former calculates the sensitivities of timing epochs of events, such as external arrivals or service time completions, while the latter yields sensitivities of departure epochs of customers. We give sufficient conditions for unbiasedness of CFPA. Numerical examples show the efficiency of the method. In particular, we address sensitivity analysis with respect to buffer sizes and thereby give a solution to the problem for which perturbation analysis was originally built.