Amdahl's and Gustafson-Barsis laws revisited

TL;DR

This paper revisits the relationship between Amdahl's law and the Gustafson–Barsis law in parallel computing. It shows that the Gustafson–Barsis speedup can be derived directly from Amdahl's law by treating the sequential execution time for a given problem size as constant across processor counts, without normalizing to one. The authors argue that GB's improved speedups with growing problem size are a consequence of problem-size scaling, causing the fractional sequential component to approach zero and the speedup to approach the processor count. In doing so, they unify the two laws and challenge the view that GB refutes Amdahl's law. The findings have implications for how speedup limits are interpreted in scalability analyses of parallel systems.

Abstract

The paper presents a simple derivation of the Gustafson-Barsis law from the Amdahl's law. In the computer literature these two laws describing the speedup limits of parallel applications are derived separately. It is shown, that treating the time of the execution of the sequential part of the application as a constant, in few lines the Gustafson-Barsis law can be obtained from the Amdahl's law and that the popular claim, that Gustafson-Barsis law overthrows Amdahl's law is a mistake.