A General Theory of Computational Scalability Based on Rational Functions

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dc.creatorGunther, Neil J.
dc.date2008-08-11
dc.date2008-08-25
dc.date.accessioned2026-07-07T09:57:53Z
dc.date.available2026-07-07T09:57:53Z
dc.descriptionThe 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.
dc.description14 pages, 5 figures; several typos corrected, 1 reference updated, page number reduced with 10 pt font
dc.identifierhttps://arxiv.org/abs/0808.1431
dc.identifierhttp://arxiv.org/abs/0808.1431
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/167508
dc.subjectPerformance
dc.subjectDistributed, Parallel, and Cluster Computing
dc.subjectB.8; C.4; C.5.5; D.4.8; F.1.2
dc.titleA General Theory of Computational Scalability Based on Rational Functions
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