Novel regression approach to estimate the parameters of “Universal Scalability Law”

The Universal Scalability Law (USL) of computational capacity has been proposed by Neil J. Gunther. USL abstracts the coefficients of inter process interactions and other contentions in the area of parallel and distributed computing in a set of constant parameters {σ, λ}. One cannot apply USL for the purpose of predicting performance, unless the values of those constant parameters are known. A computationally light weight and theoretically correct algorithm to estimate those parameters from measured performance data is not available yet. Simple linear-regression or standard least-square-error-approximation is a widely used efficient statistical technique to estimate parameters. A simple linear-regression cannot be applied directly to estimate the coefficients σ, λ of USL, because USL is a rational function. In this work, we propose a novel and elegant algorithm based on standard least-square-error-approximation or linear-regression to estimate the parameters. The explanation of failure of simple linear-regression is discussed by visiting the basic theory of linear-regression. A novel approach, consisting of algebraic manipulations to transform the problem into two linear-regression problems, is presented. The linear-regression is applied successively in a certain order to estimate the constant parameters, σ, λ, of USL. The proposed technique is applied to a set of measured performance data to validate and verify the proposed technique.