A new method of performance sensitivity analysis for non-Markovian queueing networks

The paper develops a new method of calculating and estimating the sensitivities of a class of performance measures with respect to a parameter of the service or interarrival time distributions in queueing networks. The distribution functions may be of a general form. The study is based on perturbation analysis of queueing networks. A new concept, the realization factor of a perturbation, is introduced for the network studied. The properties of realization factors are discussed, and a set of linear differential equations specifying the realization factors are derived. The sensitivity of the steady-state performance with respect to a parameter can be expressed in a simple form using realization factors. Based on this, the sensitivity can be estimated by applying a perturbation analysis algorithm to a sample path of the system. We show that the derivative of the performance measure with respect to a parameter based on a single sample path converges with probability one to the derivative of the steady-state performance as the length of the sample path goes to infinity. The results provide a new analytical method of calculating performance sensitivities and justifies the application of perturbation analysis algorithms to non-Markovian queueing networks.