Gustafson's Law

What is this formula?

Gustafson's Law estimates the speedup achievable in a parallel system when the workload grows as additional processors become available.

Unlike Amdahl's Law, which assumes a fixed problem size, Gustafson's Law assumes that larger problems can be solved using the extra computational resources.

This makes it particularly useful for evaluating modern high-performance computing systems.

When to use it

Use this formula when:

- evaluating scalable parallel applications,

- studying supercomputing performance,

- analyzing large scientific simulations,

- estimating benefits of additional processors,

- assessing distributed computing systems.

Example

Suppose:

N = 16 processors

alpha = 0.05

Formula:

Sg = N - alpha(N - 1)

Substitution:

Sg = 16 - 0.05(16 - 1)

Sg = 16 - 0.75

Sg = 15.25

Result:

Scaled speedup = 15.25×

This indicates that most of the additional processing power can be effectively utilized when the workload grows with system size.

Applications

- High-performance computing (HPC)

- Scientific computing

- Parallel algorithm design

- Distributed systems

- Large-scale simulations

- Performance engineering

Note

Gustafson's Law is a scalability model rather than a physical law. It assumes that problem size increases proportionally with available processing resources. Real-world performance may be affected by communication overhead, synchronization delays, memory bandwidth limitations, and workload imbalance. It is commonly viewed as a complement to Amdahl's Law rather than a replacement.