A General Theory of Computational Scalability Based on Rational Functions

Details A General Theory of Computational Scalability Based on Rational Functions A General Theory of Computational Scalability Based on Rational Functions

2008-08-11

arxiv.org/abs/0808.1431v2

Computer Science

Performance

14 pages, 5 figures; several typos corrected, 1 reference updated, page number reduced with 10 pt font

Scientific paper

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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