Sensitivity analysis of performance in queueing systems with phase-type service distributions

The queueing networks with nonexponential service distributions have been widely applied in many areas, such as communication networks and management systems. In this paper, by using the approach of infinitesimal generator perturbation, we study the problems of sensitivity analysis of the steady-state performance for M/PH/1 queueing systems. Sensitivity formulas of performance are given. It is shown that sensitivity of the steady-state performance can be easily calculated by using the potentials of systems. An algorithm to compute potentials and performance derivatives is proposed. This algorithm can be directly used in controlling and optimization problems, because it bases on analysing a single sample path of a queueing system. A numerical example is provided to illustrate the application of the algorithm.