Sensitivity results in open, closed, and mixed product-form queueing networks

General formulas are proposed to quantify the effects of changing the arrival and service rates in the so-called BCMP network. These formulas relate the derivative of the expectation of any function F of the state of the network with respect to any arrival/service rate in the network, to known functions of the state of the network. As an application, sensitivity results of interest bearing on throughputs and on the moments of queue lengths can be derived by appropriate choices of the function F.