Performance index functions with integer parameters are important in t
he evaluation and analysis of computer systems, communication networks
and general distributed and parallel processing systems, These functi
ons are often difficult to evaluate for large integers, On the other h
and, most of these performance functions have nice properties such as
monotonicity, convexity, analyticity, as well as obtainable asymptotic
behavior. These properties make it possible to use rational approxima
nts to extrapolate the performance functions. In this paper we present
the rational approximants for several example systems, Our numerical
results suggest that this approach could lead to a promising tool for
many applications.