Some Linear Algebraic Formulas of the Performance Sensitivities of Queueing Networks

Queueing networks have been widely used to model discrete event dynamic systems (DEDSs). The dynamic point of view provides a new approach to the study of DEDSs. This paper continues the effort of investigating the inherent properties of DEDSs by using a system point of view. The main result is, for any single-class closed queueing network with state dependent service rates, the sensitivities of any steady state performance measure can be expressed in a single algebraic form by using a sensitivity matrix. That is, all the performance sensitivities are linear combinations of the entries of the sensitivity matrix. The entries of the sensitivity matrix can be obtained by solving a set of linear equations or by applying some simple algorithms to a single sample path. The similarity between the results and those for continuous variable dynamic system (CVDSs) is discussed.