  The multiprocessor effect refers to the loss of computing cycles due to
processing overhead. Amdahl's law and the Multiprocessing Factor (MPF) are two
scaling models used in industry and academia for estimating multiprocessor
capacity in the presence of this multiprocessor effect. Both models express
different laws of diminishing returns. Amdahl's law identifies diminishing
processor capacity with a fixed degree of serialization in the workload, while
the MPF model treats it as a constant geometric ratio. The utility of both
models for performance evaluation stems from the presence of a single parameter
that can be determined easily from a small set of benchmark measurements. This
utility, however, is marred by a dilemma. The two models produce different
results, especially for large processor configurations that are so important
for today's applications. The question naturally arises: Which of these two
models is the correct one to use? Ignoring this question merely reduces
capacity prediction to arbitrary curve-fitting. Removing the dilemma requires a
dynamical interpretation of these scaling models. We present a physical
interpretation based on queueing theory and show that Amdahl's law corresponds
to synchronous queueing in a bus model while the MPF model belongs to a Coxian
server model. The latter exhibits unphysical effects such as sublinear response
times hence, we caution against its use for large multiprocessor
configurations.
