Amdahl's Law

Description

In computer architecture, Amdahl’s law (or Amdahl’s argument) is a formula which gives the theoretical speedup in latency of the execution of a task at fixed workload that can be expected of a system whose resources are improved. It is named after computer scientist Gene Amdahl, and was presented at the AFIPS Spring Joint Computer Conference in 1967.

Amdahl’s law is often used in parallel computing to predict the theoretical speedup when using multiple processors. For example, if a program needs 20 hours using a single processor core, and a particular part of the program which takes one hour to execute cannot be parallelized, while the remaining 19 hours (p = 0.95) of execution time can be parallelized, then regardless of how many processors are devoted to a parallelized execution of this program, the minimum execution time cannot be less than that critical one hour. Hence, the theoretical speedup is limited to at most 20 times (1/(1 − p) = 20). For this reason, parallel computing with many processors is useful only for highly parallelizable programs.

Related formulas

Variables

Slatencytheoretical speedup of the execution of the whole task (dimensionless)
pproportion of execution time that the part benefiting from improved resources originally occupied (dimensionless)
sspeedup of the part of the task that benefits from improved system resources (dimensionless)