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Suppose that a file server has an uptime of 80%. How many more replicated servers with same uptime have to be used to give an availability of at least 99.99 percent?

TylerH
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Fabrizio
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  • I’m voting to close this question because it is a math question (or, at best, one about server update) rather than one about programming. – TylerH May 07 '21 at 19:30

2 Answers2

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An easier way to calculate this is to calculate the inverse. You want your servers to be up 99.99% => 0.9999 this means they are allowed to be down for a factor of 0.0001 of the time (0.01%)

The probability that one server fails is 20% (1 - 0.8). The probability that x servers fail at the same time is 0.2^x. So you want to solve the equation:

0.2^x <= 0.0001

now even wolfram alpha didn't want to solve this, but we still can type it into the calculator with different numbers for x:

  • x = 1: 0.2
  • x = 2: 0.04
  • x = 3: 0.008
  • x = 4: 0.0016
  • x = 5: 0.00032
  • x = 6: 0.000064 <- solution
peter
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The logic you require follows this pattern:

Server1 is up 80% of the time.

Server2 is up 80% of the time that Server1 isn't up: in other words, for the 20% of the time that server1 is down, server2 is up.

Server3 is up 80% of the time that Server1 and Server2 aren't up: in other words, for the 20% of the time that server1 (80%) and server2 (80% of 20%) are down, server3 is up.

Server4 is up 80% of the time that Server1, Server2 and Server3 aren't up: in order words, for the 20% of the time that (server1 (80%) and server2 (80% of 20%) and server3 (80% of (80% of 20%)) are down, server4 is up.

Etc., etc., ad nauseam.

Does that give you enough information to figure the answer out?

Paul Hicks
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  • yes,this is clear, but I don't know how to formalize it in relation to availability. sorry for the ignorance. Considering one server, the availability should be 80%, because there is only one server with uptime of 80%. If I add another server, how change the availability? I have to add simply 0,2*0,8 = 0,16? – Fabrizio Feb 25 '14 at 09:16
  • Updated answer with a few more hints. Best of luck figuring it out, I have to go to bed now! – Paul Hicks Feb 25 '14 at 09:25
  • Should be 0,96 + ((1 - 0,96) * 0,8) = 0,96 + 0,032 = 0,992 = 99,2%. Is that right? – Fabrizio Feb 25 '14 at 09:25
  • Your way to compute it is correct but a bit complicated – peter Feb 27 '14 at 08:00
  • I was more looking to explain what was going on, rather than handing an easy answer :) – Paul Hicks Feb 27 '14 at 08:02