SENSITIVITY RESULTS IN OPEN, CLOSED AND MIXED PRODUCT FORM QUEUING-NETWORKS

General formulas are proposed to quantify the effects of changing the model parameters in the so-called BCMP network [F. Baskett et al.. J. ACM 22 (2) (April 1975) 248-260]. These formulas relate the derivative of the expectation of any function of both the state and the paramaters of the network with respect to any model parameter (i.e., arrival rate, mean service demand, service rate, visit ratio, traffic intensity) to known functions of the state variables. Applications of our results to sensitivity analysis and optimization problems are given.