Little’s Law, Scalability and Fault Tolerance: The OS is your bottleneck

Re:Little’s Law, Scalability and Fault Tolerance: The OS is ... by DougMerritt on Tuesday February 04, 2014 @04:13PM (#7180287)

> What’s remarkable about this result is that it does not depend on the precise distribution of the requests, the order in which requests are processed or any other variable that might have conceivably affected the result.

It says that (# requests) = (# requests / time) * time

There is nothing else "that might have conceivably affected the result", it's just algebraic cancellation.

Everything else that might have mattered is ruled out by saying "stable system" and saying that all variables are averages.

I'm not saying it's not useful, but that's an awfully "gee whiz" tone to use to comment on r = (r/t) * t

This part is more worthy of an exclamation point, since it makes clear a practical impact:

> Because L is the minimum of all these limits, the OS scheduler suddenly dropped our capacity, L, from the high 100Ks-low millions, to well under 20,000!

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Re:Little’s Law, Scalability and Fault Tolerance: The OS is ... by pron on Tuesday February 04, 2014 @04:21PM (#7180324)

Well, it's not quite as simple as that. We're talking about a stochastic process here, and while a "hand-wavy" proof may satisfy some, there's a Little ;) more to it: http://www.ece.virginia.edu/~mv/edu/715/lectures/littles-law...

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Re:Little’s Law, Scalability and Fault Tolerance: The OS is ... by DougMerritt on Tuesday February 04, 2014 @05:47PM (#7180778)

Fair enough, although even that terse lecture hand-waved (by leaving it to a reference) about ergodic systems.

I think the deeper point is along the lines of Wigner's classic "The Unreasonable Effectiveness of Mathematics in the Natural Sciences"

http://en.wikipedia.org/wiki/The_Unreasonable_Effectiveness_...

It happens to be the case that elementary dimensional analysis is sufficient in the case in hand -- and it often is.

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