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. This research uses such properties to extrapolate the performance functions based on their values at small integers. The objective of this research is to further establish the theoretical foundation and to develop guidelines, algorithms and their software implementations that will be applicable to a wide array of systems. The results of this research will make it possible to express the performance measure function in terms of the system size of dimension as a low-degree rational function for some general classes of systems. The successful completion of this research will provide a framework in which various difficult modeling, control and optimization issues can be attacked.
