On perturbation analysis of queueing networks with finitely supported service time distributions

Infinitesimal perturbation analysis (IPA) has emerged as an efficient tool for estimating the gradient of a function defined on the steady state of a queuing network. Differentiability of such functions is often assumed due to difficulties in proving it. It is pointed out that such functions may be nondifferentiable at an infinite set of points, dense in a given interval, for a large class of realistic system models. This phenomenon is largely due to correlation of traffic patterns on the links of a network, and to the presence of atoms in the distributions of their service times. The issue of nondifferentiability goes beyond IPA, to any method for estimating the gradients of functions in steady state