Briefly explain what Amdahl’s law is used for? In Amdahl’s law formula, what does (f)and (k) represent?

Question

Briefly explain what Amdahl’s law is used for? In Amdahl’s law formula, what does (f)and (k) ﻿represent?

Accepted Answer

⚹ Amdahl's law is used to find the maximum improvement in overall system performance when only part of the system is improved ⚹ ⚹ In Amdahl's law formula, (f) represents the fraction of the operation that can be parallelized, while (k) represents the speedup of the enhanced portion ⚹ ∻Understanding Amdahl's Law∻ ‖ ▪ ⋮ Amdahl's law is a formula used to predict the theoretical maximum 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 often used in parallel computing to predict the theoretical maximum speedup using multiple processors ⚹ ‖ ‖ ▪ ⋮ The law highlights the diminishing returns of adding more parallel execution units ⚹ ‖ ∻Significance of (f) and (k) in Amdahl's Law∻ ‖ ▪ ⋮ (f) is the fraction of the program that can be parallelized, which means that (1-f) is the fraction that must remain serial ⚹ ‖ ‖ ▪ ⋮ (k) is the speedup of the portion of the program that benefits from system improvements ⚹ ‖ ‖ ▪ ⋮ The overall speedup of the program is limited by the serial portion, as per Amdahl's law ⚹ ‖ ⚹ The formula for Amdahl's law is $S = \frac{1}{(1-f) + \frac{f}{k}}$, where $S$ is the overall speedup, $(1-f)$ is the non-parallelizable portion, $f$ is the parallelizable portion, and $k$ is the speedup of the parallelizable portion ⚹

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