Analyze how long after earning the HSDir flag relays go away
Relays that are running for at least 24 hours get the HSDir flag from the directory authorities. We should find out how long after after earning the HSDir flag relays go away.
In a first analysis we'll look at HSDir sessions, that is, intervals between a relay earning the HSDir flag and going away. The shortest HSDir session would be 0 hours when a relay loses the HSDir flag right after obtaining it. The longest HSDir session might be 1 year, which is the analysis interval, if a relay never goes offline.
Note that the session time resolution is 1 hour, because of the consensus publication interval. If a relay goes away 15 minutes after receiving the HSDir flag, we won't notice until the end of the hour. In that case we assume that the relay disappeared after 0 minutes.
The attached graph shows HSDir session times as an empirical cumulative distribution function plot. It shows what fraction of HSDir session is at least x hours long. For example, all sessions are by definition at least 0 hours long, but only slightly under 90 % of these sessions last for at least 1 hour.
I'm not sure what the exact research question here is and whether this analysis answers this question. Thoughts?