Computation of Derivatives by Means of the Power-Series Algorithm

The power-series algorithm (PSA) is a flexible tool for computing performance measures for moderately-sized queueing systems for which the underlying process has a multidimensional quasi birth-and-death structure. In the present paper the PSA is extended to the computation of derivatives of system performance measures with respect to a general class of system parameters. This extension is useful for analyzing the sensitivity of the system performance with respect to the system parameters and for solving a wide variety of optimization problems in queueing systems.