Rational Approximation for Some Computationally Complex Performance Analysis Problems

带整数参数的性能指标函数在计算机系统、通信网络以及一般分布和并行处理系统的评估和分析中具有重要意义。对于大整数，这些函数通常很难求值。另一方面，这些性能函数大多具有单调性、凸性、解析性以及可获得的渐近性等性质。这项研究使用这些性质来根据它们在小整数处的值来外推性能函数。这项研究的目的是进一步建立理论基础，并开发适用于各种系统的指南、算法及其软件实现。本研究的结果将使得将性能度量函数用系统维度的大小来表示为一些一般系统类的低次有理函数成为可能。这项研究的成功完成将提供一个框架，在其中可以解决各种困难的建模、控制和优化问题。

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.