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

[Wu Fengguang]

On Mon, Aug 29, 2011 at 09:12:07PM +0800, Peter Zijlstra wrote:
> On Wed, 2011-08-24 at 14:00 -0400, Vivek Goyal wrote:
> > 
> > Ok, I think I am beginning to see your point. Let me just elaborate on
> > the example you gave.
> > 
> > Assume a system is completely balanced and a task is writing at 100MB/s
> > rate.
> > 
> > write_bw = dirty_rate = 100MB/s, pos_ratio = 1; N=1
> > 
> > bdi->dirty_ratelimit = 100MB/s
> > 
> > Now another tasks starts dirtying the page cache on same bdi. Number of 
> > dirty pages should go up pretty fast and likely position ratio feedback
> > will kick in to reduce the dirtying rate. (rate based feedback does not
> > kick in till next 200ms) and pos_ratio feedback seems to be instantaneous.
> > Assume new pos_ratio is .5
> > 
> > So new throttle rate for both the tasks is 50MB/s.
> > 
> > bdi->dirty_ratelimit = 100MB/s (a feedback has not kicked in yet)
> > task_ratelimit = bdi->dirty_ratelimit * pos_ratio = 100 *.5 = 50MB/s
> > 
> > Now lets say 200ms have passed and rate base feedback is reevaluated.
> > 
> >                                                       write_bw  
> > bdi->dirty_ratelimit_(i+1) = bdi->dirty_ratelimit_i * ---------
> >                                                       dirty_bw
> > 
> > bdi->dirty_ratelimit_(i+1) = 100 * 100/100 = 100MB/s
> > 
> > Ideally bdi->dirty_ratelimit should have now become 50MB/s as N=2 but 
> > that did not happen. And reason being that there are two feedback control
> > loops and pos_ratio loops reacts to imbalances much more quickly. Because
> > previous loop has already reacted to the imbalance and reduced the
> > dirtying rate of task, rate based loop does not try to adjust anything
> > and thinks everything is just fine.
> > 
> > Things are fine in the sense that still dirty_rate == write_bw but
> > system is not balanced in terms of number of dirty pages and pos_ratio=.5
> > 
> > So you are trying to make one feedback loop aware of second loop so that
> > if second loop is unbalanced, first loop reacts to that as well and not
> > just look at dirty_rate and write_bw. So refining new balanced rate by
> > pos_ratio helps.
> >                                                       write_bw  
> > bdi->dirty_ratelimit_(i+1) = bdi->dirty_ratelimit_i * --------- * pos_ratio
> >                                                       dirty_bw
> > 
> > Now if global dirty pages are imbalanced, balanced rate will still go
> > down despite the fact that dirty_bw == write_bw. This will lead to
> > further reduction in task dirty rate. Which in turn will lead to reduced
> > number of dirty rate and should eventually lead to pos_ratio=1.
> 
> 
> 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".

Thanks,
Fengguang
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