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Abstract: The universal scalability law of computational capacity is a rationalfunction C p = Pp-Qp with Pp a linear polynomial and Qp a second-degreepolynomial in the number of physical processors p, that has been long used forstatistical modeling and prediction of computer system performance. We provethat C p is equivalent to the synchronous throughput bound for amachine-repairman with state-dependent service rate. Simpler rationalfunctions, such as Amdahl-s law and Gustafson speedup, are corollaries of thisqueue-theoretic bound. C p is further shown to be both necessary and sufficientfor modeling all practical characteristics of computational scalability.



Author: Neil J. Gunther

Source: https://arxiv.org/



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