I find a formula on my book to estimate cpu utilization under multi-processing.

$ U = 1 - P^n $

U: cpu utilization P: cpu idle

I want to know why or how to proof.


The book is about operating system, not in english.

This may be like https://stackoverflow.com/questions/20328619/calculate-cpu-utilization/20328695?noredirect=1#comment88673153_20328695

I get an answer that is

it's just basic probability theory

  • $\begingroup$ What book? What are these variables? There is no proof afterwards? $\endgroup$ – Evil Jun 13 '18 at 11:03

$P^n$ is the probability that all "cores" are idle simultaneously, hence $1-P^n$ is the probability that at least one core is in use.

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  • $\begingroup$ @Vonfry: This is what can be imagined form the little you provide. $\endgroup$ – Yves Daoust Jun 13 '18 at 15:49
  • $\begingroup$ why using $ P^n $, not $ nP $ or others? Just experienced? $\endgroup$ – Vonfry Jun 14 '18 at 1:09
  • $\begingroup$ @Vonfry: elementary probabilities. $\endgroup$ – Yves Daoust Jun 14 '18 at 7:35

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