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arXiv · 0808.1431

A General Theory of Computational Scalability Based on Rational Functions

Neil J. Gunther
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Abstract

The universal scalability law of computational capacity is a rational function C_p = 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 C_p 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. C_p is further shown to be both necessary and sufficient for modeling all practical characteristics of computational scalability.

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Neil J. Gunther. 2008-08-25. A General Theory of Computational Scalability Based on Rational Functions. https://arxiv.org/abs/0808.1431

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