Performance sensitivity formulas and optimal control of closed queueing networks

For closed exponential queueing networks, the derivatives of performance measures with respect to a service rate can be expressed in terms of a realization factor which satisfies a set of linear equations. In this paper, the derivative of the performance measure is first analytically derived via realization factors for a two-server cyclic network and is then extended to networks with load-dependent servers. In particular, the derivative with respect to a service rate is shown to be a product of a positive term and a quantity whose sign only depends on other service rates of the network. The results have immediate applications to optimal control of queues. Examples from flow control and service rate control of queueing networks are discussed