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Amdahl's Law

Why throwing more CPUs at a problem doesn't give you proportional speedup.

Tiny Summary

Amdahl's Law proves that speedup from parallelization is limited by the serial portion. If 10% must run serially, your maximum speedup is 10x—even with infinite CPUs.

The Formula

Speedup = 1 / (s + p/n)

s = serial fraction
p = parallel fraction (1 - s)
n = number of processors

The Bottleneck

  • 10% serial → max 10x speedup
  • 25% serial → max 4x speedup
  • 50% serial → max 2x speedup

100 CPUs won't give you 100x speedup if ANY part is serial.

Real Examples

Database: Parse SQL (serial) + scan partitions (parallel) = limited scaling Video Encoding: Header processing (serial) + encode frames (parallel) = good scaling Web Scraping: Rate limiting (serial) + fetch pages (parallel) = moderate scaling

Key Insight

More CPUs ≠ proportionally faster. Serial portions create hard limits regardless of hardware.

Use the simulation to experiment with different serial/parallel ratios!