Method for determining the acceleration of a parallel specialised computer system based on Amdahl's law

Abstract

The modification of Amdahl's law for the case of increment of processor elements in a computer system is considered. The coefficient $k$ linking accelerations of parallel and parallel specialized computer systems is determined. The limiting values of the coefficient are investigated and its theoretical maximum is calculated. It is proved that $k$ > 1 for any positive increment of processor elements. The obtained formulas are combined into a single method allowing to determine the maximum theoretical acceleration of a parallel specialized computer system in comparison with the acceleration of a minimal parallel computer system. The method is tested on Apriori, k-nearest neighbors, CDF 9/7, fast Fourier transform and naive Bayesian classifier algorithms.