  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.
