Rational approximants for some performance analysis problems

Performance index functions with integer parameters are important in the evaluation and analysis of computer systems, communication networks and general distributed and parallel processing systems. These functions are often difficult to evaluate for large integers. On the other hand, 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 approximants 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.