README.md

Amdahl's Law

when we speed up one part of a system, the effect on the overall system performance depends on both how significant this part was and how much it sped up.

Consider a system in which executing some application require time $T_{old}$. Suppose some part of the a system requires a fraction $/alpha$ of this time, and that we improve its performance by a factor of $k$. That is, the component originally required time $\alpha T_{old}$, and it now requires time $\frac{\alpha T_{old}}{k}$.

And the overall execution time would thus be: $T_{new} = (1 - \alpha) T_{old} + (\alpha * T_{old}) / k$.

From above, we can compute the speedup $S = \frac{T_{old}}{T_{new}}$ as $S = \frac{1}{(1 - \alpha + \frac{\alpha}{k})}$

And this law tell us: even though we made a substantial improvement to a major part of system, out net speedup was significantly less than speedup for the one part.

Special Case

One interesting special case of Amdahl's law is to consider the effect of setting $k$ to $\infty$, and now we are able to take some part fo the system and speed it up to the point at which it takes a negligible amount of time.

We then get: $S_{\infty} = \frac{1}{1 - \alpha}$.

Summary

Amdahl's law describes a general principle for improving any process. In addition to its application to speeding up computer systems, it can guide a company trying to reduce the cost of manufacturing razor blades, or a student trying to improve his grade point average.

Perhaps it is most meaningful in the world of computers, where we routinely improve performance by factors of 2 or more, Such high factors can only be achieved by optimizing large parts of a system.