```
Filename: 108-mtbf-based-stability.txt
Title: Base "Stable" Flag on Mean Time Between Failures
Author: Nick Mathewson
Created: 10-Mar-2007
Status: Closed
Implemented-In: 0.2.0.x

Overview:

   This document proposes that we change how directory authorities set the
   stability flag from inspection of a router's declared Uptime to the
   authorities' perceived mean time between failure for the router.

Motivation:

   Clients prefer nodes that the authorities call Stable.  This flag is (as
   of 0.2.0.0-alpha-dev) set entirely based on the node's declared value for
   uptime.  This creates an opportunity for malicious nodes to declare
   falsely high uptimes in order to get more traffic.

Spec changes:

   Replace the current rule for setting the Stable flag with:

   "Stable" -- A router is 'Stable' if it is active and its observed Stability
   for the past month is at or above the median Stability for active routers.
   Routers are never called stable if they are running a version of Tor
   known to drop circuits stupidly. (0.1.1.10-alpha through 0.1.1.16-rc
   are stupid this way.)

   Stability shall be defined as the weighted mean length of the runs
   observed by a given directory authority.  A run begins when an authority
   decides that the server is Running, and ends when the authority decides
   that the server is not Running.  In-progress runs are counted when
   measuring Stability.  When calculating the mean, runs are weighted by
   $\alpha ^ t$, where $t$ is time elapsed since the end of the run, and
   $0 < \alpha < 1$.  Time when an authority is down do not count to the
   length of the run.

Rejected Alternative:

   "A router's Stability shall be defined as the sum of $\alpha ^ d$ for every
   $d$ such that the router was considered reachable for the entire day
   $d$ days ago.

   This allows a simpler implementation: every day, we multiply
   yesterday's Stability by alpha, and if the router was observed to be
   available every time we looked today, we add 1.

   Instead of "day", we could pick an arbitrary time unit.  We should
   pick alpha to be high enough that long-term stability counts, but low
   enough that the distant past is eventually forgotten.  Something
   between .8 and .95 seems right.

   (By requiring that routers be up for an entire day to get their
   stability increased, instead of counting fractions of a day, we
   capture the notion that stability is more like "probability of
   staying up for the next hour" than it is like "probability of being
   up at some randomly chosen time over the next hour."  The former
   notion of stability is far more relevant for long-lived circuits.)

Limitations:

   Authorities can have false positives and false negatives when trying to
   tell whether a router is up or down.  So long as these aren't terribly
   wrong, and so long as they aren't significantly biased, we should be able
   to use them to estimate stability pretty well.

   Probing approaches like the above could miss short incidents of
   downtime.  If we use the router's declared uptime, we could detect
   these: but doing so would penalize routers who reported their uptime
   accurately.

Implementation:

   For now, the easiest way to store this information at authorities
   would probably be in some kind of periodically flushed flat file.
   Later, we could move to Berkeley db or something if we really had to.

   For each router, an authority will need to store:
     The router ID.
     Whether the router is up.
     The time when the current run started, if the router is up.
     The weighted sum length of all previous runs.
     The time at which the weighted sum length was last weighted down.

   Servers should probe at random intervals to test whether servers are
   running.
```