Correlation between uptime and availability of file servers

Question

Hi all :) I have a question about availability of a file server. I'm studying something about it but is not yet entirely clear, so I ask this question :

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?

Answer 1

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?

Answer 2

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