Re: [PATCH 2/5] writeback: dirty position control

[Wu Fengguang]

On Wed, Aug 10, 2011 at 01:20:27AM +0800, Peter Zijlstra wrote:
> 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.

Yes.

> 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.

However the above function should better be interpreted as

                                            write_bw
    ref_bw = task_ratelimit_in_past_200ms * --------
                                            dirty_bw

where
        task_ratelimit_in_past_200ms ~= dirty_ratelimit * pos_ratio

It would be highly confusing if trying to find the direct "logical"
relationships between ref_bw and pos_ratio in the above equation.

> From that we derive the condition that: 
> 
>   pos_ratio(setpoint) := 1

Right.

> 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.

Thanks to your reasoning that lead to the more elegant 

                            setpoint - dirty 3
   pos_ratio(dirty) := 1 + (----------------)
                            limit - setpoint

Thanks,
Fengguang
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