Moment problems and their applications to the stability of queueing models

This paper deals with the following question: "Will the proposed deterministic queueing model yield a satisfactory approximation to the real queueing system under consideration and if so, within which limits?" At first, we analyze the degree of approximation of the random real model by a deterministic one. This is achieved by estimating the Prokhorov distance between the output sequences of both models. The right-hand sides of the obtained estimates depend on the Prokhorov or Ky Fan distances between the inputs of the underlined models. To estimate the latter distances we evaluate the Ky Fan radius of a set of probability measures satisfying basic moment conditions involving linear combinations of {t,t²} or {cos t, sin t}. In particular, the last results lead to quantitative criteria for the weak convergence of probability measures to a point mass.