I am looking at deploying a bunch of nodes all over the world that each replicate the exact same data.

These are all active-active and let's say the probability of a given node going down in given time period t is p.

How do I figure out then, the minimum number of nodes (n) I need to deploy, to achieve a global availability v, with these parameters t and p?

This may or may not be a math question but I am certain this is something someone has dealt with.

For example, with 99.99% ("four nines") availability, my network only is unavailable for a max of 52.60 minutes a year, which is 4.38 minutes per month, 1.01 minutes per week, or 8.64 seconds per day.

Thanks.