[metrics-bugs] #28305 [Metrics/Statistics]: Include client numbers even if we think we got reports from more than 100% of all relays

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#28305: Include client numbers even if we think we got reports from more than 100%
of all relays
--------------------------------+------------------------------
 Reporter:  karsten             |          Owner:  karsten
     Type:  defect              |         Status:  accepted
 Priority:  High                |      Milestone:
Component:  Metrics/Statistics  |        Version:
 Severity:  Normal              |     Resolution:
 Keywords:                      |  Actual Points:
Parent ID:                      |         Points:
 Reviewer:                      |        Sponsor:  SponsorV-can
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Changes (by karsten):

 * owner:  metrics-team => karsten
 * status:  new => accepted


Comment:

 I think I now know what's going on: some relays report written directory
 byte statistics for times when they were hardly listed in consensuses.

 Here's a graph with all variables going into the `frac` formula, plus
 intermediate products, and finally the `frac` value:

 [[Image(frac-raw-2018-11-28.png, 500px)]]

 Note the red arrow. At this point `n(H)` grows larger than `n(N)`. That's
 an issue. By definition, a relay cannot report written directory bytes
 statistics for a longer time than it's online.

 I also looked at random relay `002B024E24A30F113982FCB17DFE05B6F38C0C79`
 that had a larger `n(H)` value than `n(N)` value on 2018-10-28:

  - This relay was listed in 3 out of 24 consensuses on 2018-10-28 (19:00,
 20:00, and 21:00). As a result, we count this relay with `n(N) = 10800`
 (we're using seconds internally, not hours).
  - The same relay published an extra-info descriptor on 2018-10-31 at
 09:28:04 with the following line: `dirreq-write-history 2018-10-30
 08:04:04 (86400 s) 0,0`. We count this as `n(H) = 57356` on 2018-10-28.

 A possible mitigation (other than the one I suggested above) could be to
 replace `n(H)` with `n(N^H)` in the `frac` formula. This would mean that
 we'd cap the amount of time for which a relay reported written directory
 bytes to the amount of time it was listed in the consensus.

 I'm currently dumping and downloading the database to try this out at
 home. However, I'm afraid that deploying this fix is going to be much more
 expensive than making the simple fix suggested above. I'll report here
 what I find out.

--
Ticket URL: <https://trac.torproject.org/projects/tor/ticket/28305#comment:5>
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