[tahoe-dev] Analysis of file reliability, error reduction hack:

Josh Wilcox wilcoxjg at gmail.com
Mon Sep 17 02:37:48 UTC 2007

 For a binomial r.v. "X" where:

 p = The probability of success
 k = The number of successes under consideration
 n = The total number of trials

 P{X = k + 1} = [p/(1-p)]*[(n-k)/(k+1)]*P{X = k}

 Using this relation one can calculate the probability of e.g. an N-K
erasure coded file on a network with servers whose individual reliabilities
(i.e. probability of
availability) are independently "p".
  Interestingly it requires no use of choose functions,
and a single use of floating points that are raised to large
powers, so the error term should be quite small, relative to the naive
calculation.   I wrote an ugly
function that calculates the relevant Cumulative Distribution Function.
 Perhaps I should cut-n-
paste the monster here?

 Would it be pedantic to go through calculating the
prob. and erasure coded file is available?

Tersely:  Start with P{X = 0} and work from there.
Then use 1 -  P{file unavailable}.

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