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

[Wu Fengguang <fengguang.wu@intel.com>]

On Tue, Aug 23, 2011 at 06:01:00PM +0800, Peter Zijlstra wrote:
> On Tue, 2011-08-23 at 11:40 +0800, Wu Fengguang wrote:
> > - not a factor at all for updating balanced_rate (whether or not we do (2))
> >   well, in this concept: the balanced_rate formula inherently does not
> >   derive the balanced_rate_(i+1) from balanced_rate_i. Rather it's
> >   based on the ratelimit executed for the past 200ms:
> > 
> >           balanced_rate_(i+1) = task_ratelimit_200ms * bw_ratio
> 
> Ok, this is where it all goes funny..
> 
> So if you want completely separated feedback loops I would expect

If call it feedback loops, then it's a series of independent feedback
loops of depth 1.  Because each balanced_rate is a fresh estimation
dependent solely on

- writeout bandwidth
- N, the number of dd tasks

in the past 200ms.

As long as a CONSTANT ratelimit (whatever value it is) is executed in
the past 200ms, we can get the same balanced_rate.

        balanced_rate = CONSTANT_ratelimit * write_bw / dirty_rate

The resulted balanced_rate is independent of how large the CONSTANT
ratelimit is, because if we start with a doubled CONSTANT ratelimit,
we'll see doubled dirty_rate and result in the same balanced_rate. 

In that manner, balance_rate_(i+1) is not really depending on the
value of balance_rate_(i): whatever balance_rate_(i) is, we are going
to get the same balance_rate_(i+1) if not considering estimation
errors. Note that the estimation errors mainly come from the
fluctuations in dirty_rate.

That may well be what's already in your mind, just that we disagree
about the terms ;)

> something like:
> 
> 	balance_rate_(i+1) = balance_rate_(i) * bw_ratio   ; every 200ms
> 
> The former is a complete feedback loop, expressing the new value in the
> old value (*) with bw_ratio as feedback parameter; if we throttled too
> much, the dirty_rate will have dropped and the bw_ratio will be <1
> causing the balance_rate to drop increasing the dirty_rate, and vice
> versa.

In principle, the bw_ratio works that way. However since
balance_rate_(i) is not the exact _executed_ ratelimit in
balance_dirty_pages().

> (*) which is the form I expected and why I thought your primary feedback
> loop looked like: rate_(i+1) = rate_(i) * pos_ratio * bw_ratio
 
Because the executed ratelimit was rate_(i) * pos_ratio.

> With the above balance_rate is an independent variable that tracks the
> write bandwidth. Now possibly you'd want a low-pass filter on that since
> your bw_ratio is a bit funny in the head, but that's another story.

Yeah.

> Then when you use the balance_rate to actually throttle tasks you apply
> your secondary control steering the dirty page count, yielding:
> 
> 	task_rate = balance_rate * pos_ratio

Right. Note the above formula is not a derived one, but an original
one that later leads to pos_ratio showing up in the calculation of
balanced_rate.

> >   and task_ratelimit_200ms happen to can be estimated from
> > 
> >           task_ratelimit_200ms ~= balanced_rate_i * pos_ratio
> 
> >   We may alternatively record every task_ratelimit executed in the
> >   past 200ms and average them all to get task_ratelimit_200ms. In this
> >   way we take the "superfluous" pos_ratio out of sight :) 
> 
> Right, so I'm not at all sure that makes sense, its not immediately
> evident that <task_ratelimit> ~= balance_rate * pos_ratio. Nor is it
> clear to me why your primary feedback loop uses task_ratelimit_200ms at
> all. 

task_ratelimit is used and hence defined to be (balance_rate * pos_ratio)
by balance_dirty_pages(). So this is an original formula:

        task_ratelimit = balance_rate * pos_ratio

task_ratelimit_200ms is also used as an original data source in

        balanced_rate = task_ratelimit_200ms * write_bw / dirty_rate

Then we try to estimate task_ratelimit_200ms by assuming all tasks
have been executing the same CONSTANT ratelimit in
balance_dirty_pages(). Hence we get

        task_ratelimit_200ms ~= prev_balance_rate * pos_ratio

> >   There is fundamentally no dependency between balanced_rate_(i+1) and
> >   balanced_rate_i/task_ratelimit_200ms: the balanced_rate estimation
> >   only asks for _whatever_ CONSTANT task ratelimit to be executed for
> >   200ms, then it get the balanced rate from the dirty_rate feedback.
> 
> How can there not be a relation between balance_rate_(i+1) and
> balance_rate_(i) ? 

In this manner: even though balance_rate_(i) is somehow used for
calculating balance_rate_(i+1), the latter will evaluate to the same
value given whatever balance_rate_(i).

That is, there is two dependencies, the seemingly dependency in the
formula, and the effective dependency in the data values.

Thank,
Fengguang