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    SubjectRe: [PATCH 2/5] writeback: dirty position control
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    On Tue, 2011-08-09 at 12:32 +0200, Peter Zijlstra wrote:
    > > origin - dirty
    > > pos_ratio = --------------
    > > origin - goal
    >
    > > which comes from the below [*] control line, so that when (dirty == goal),
    > > pos_ratio == 1.0:
    >
    > OK, so basically you want a linear function for which:
    >
    > f(goal) = 1 and has a root somewhere > goal.
    >
    > (that one line is much more informative than all your graphs put
    > together, one can start from there and derive your function)
    >
    > That does indeed get you the above function, now what does it mean?

    So going by:

    write_bw
    ref_bw = dirty_ratelimit * pos_ratio * --------
    dirty_bw

    pos_ratio seems to be the feedback on the deviation of the dirty pages
    around its setpoint. So we adjust the reference bw (or rather ratelimit)
    to take account of the shift in output vs input capacity as well as the
    shift in dirty pages around its setpoint.

    From that we derive the condition that:

    pos_ratio(setpoint) := 1

    Now in order to create a linear function we need one more condition. We
    get one from the fact that once we hit the limit we should hard throttle
    our writers. We get that by setting the ratelimit to 0, because, after
    all, pause = nr_dirtied / ratelimit would yield inf. in that case. Thus:

    pos_ratio(limit) := 0

    Using these two conditions we can solve the equations and get your:

    limit - dirty
    pos_ratio(dirty) = ----------------
    limit - setpoint

    Now, for some reason you chose not to use limit, but something like
    min(limit, 4*thresh) something to do with the slope affecting the rate
    of adjustment. This wants a comment someplace.


    Now all of the above would seem to suggest:

    dirty_ratelimit := ref_bw

    However for that you use:

    if (pos_bw < dirty_ratelimit && ref_bw < dirty_ratelimit)
    dirty_ratelimit = max(ref_bw, pos_bw);

    if (pos_bw > dirty_ratelimit && ref_bw > dirty_ratelimit)
    dirty_ratelimit = min(ref_bw, pos_bw);

    You have:

    pos_bw = dirty_ratelimit * pos_ratio

    Which is ref_bw without the write_bw/dirty_bw factor, this confuses me..
    why are you ignoring the shift in output vs input rate there?





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