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

[Peter Zijlstra <peterz@infradead.org>]

On Mon, 2011-08-29 at 21:37 +0800, Wu Fengguang wrote:
> > 
> > Ok so this argument makes sense, is there some formalism to describe
> > such systems where such things are more evident?
> 
> I find the most easy and clean way to describe it is,
> 
> (1) the below formula
>                                                           write_bw  
>     bdi->dirty_ratelimit_(i+1) = bdi->dirty_ratelimit_i * --------- * pos_ratio
>                                                           dirty_bw
> is able to yield
> 
>     dirty_ratelimit_(i) ~= (write_bw / N)
> 
> as long as
> 
> - write_bw, dirty_bw and pos_ratio are not changing rapidly
> - dirty pages are not around @freerun or @limit
> 
> Otherwise there will be larger estimation errors.
> 
> (2) based on (1), we get
> 
>     task_ratelimit ~= (write_bw / N) * pos_ratio
> 
> So the pos_ratio feedback is able to drive dirty count to the
> setpoint, where pos_ratio = 1.
> 
> That interpretation based on _real values_ can neatly decouple the two
> feedback loops :) It makes full utilization of the fact "the
> dirty_ratelimit _value_ is independent on pos_ratio except for
> possible impacts on estimation errors". 

OK, so the 'problem' I have with this is that the whole control thing
really doesn't care about N. All it does is measure:

 - dirty rate
 - writeback rate

observe:

 - dirty count; with the independent input of its setpoint

control:

 - ratelimit

so I was looking for a way to describe the interaction between the two
feedback loops without involving the exact details of what they're
controlling, but that might just end up being an oxymoron.