Gustafson Law
Amdahl law sounds gloomy, but it assumes a fixed problem size. In practice, more processors usually means people solve bigger problems. Gustafson law captures this optimistic view.
Scaling the work
Gustafson fixes the runtime and asks how much more work you can finish. If the parallel portion grows with the processor count while the serial portion stays roughly constant:
- The serial part becomes a smaller share of a larger job.
- The achievable speedup grows almost linearly with processors.
- This is called scaled speedup.
Reconciling with Amdahl
Both laws are correct; they answer different questions. Amdahl uses strong scaling, where the problem stays fixed. Gustafson uses weak scaling, where the work per processor stays fixed. Many real workloads such as simulations and rendering naturally grow with available compute, so Gustafson often describes them better.
Key idea
When the problem grows with the cores, the serial share shrinks in relative terms and speedup scales nearly linearly under weak scaling.