2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/167508The 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.14 pages, 5 figures; several typos corrected, 1 reference updated, page number reduced with 10 pt fontPerformanceDistributed, Parallel, and Cluster ComputingB.8; C.4; C.5.5; D.4.8; F.1.2text