A General Theory of Computational Scalability Based on Rational Functions

The universal scalability law (USL) of computational capacity is a rational function Cp = P (p)/Q(p) with P (p) a linear polynomial and Q(p) a second-degree polynomial in the number of physical processors p, that has been long used for statistical modeling and prediction of computer system performance. We prove that Cp is equivalent to the synchronous throughput bound for a machine-repairman with state-dependent service rate. Simpler rational functions, such as Amdahl’s law and Gustafson speedup, are corollaries of this queue-theoretic bound. Cp is both necessary and sufficient for modeling all practical characteristics of computational scalability.