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

[Wu Fengguang]

> You somehow directly jump to  
> 
> 	balanced_rate = task_ratelimit_200ms * write_bw / dirty_rate
> 
> without explaining why following will not work.
> 
> 	balanced_rate_(i+1) = balance_rate(i) * write_bw / dirty_rate

Thanks for asking that, it's probably the root of confusions, so let
me answer it standalone.

It's actually pretty simple to explain this equation:

                                               write_bw
        balanced_rate = task_ratelimit_200ms * ----------       (1)
                                               dirty_rate

If there are N dd tasks, each task is throttled at task_ratelimit_200ms
for the past 200ms, we are going to measure the overall bdi dirty rate

        dirty_rate = N * task_ratelimit_200ms                   (2)

put (2) into (1) we get

        balanced_rate = write_bw / N                            (3)

So equation (1) is the right estimation to get the desired target (3).


As for

                                                  write_bw
        balanced_rate_(i+1) = balanced_rate_(i) * ----------    (4)
                                                  dirty_rate

Let's compare it with the "expanded" form of (1):

                                                              write_bw
        balanced_rate_(i+1) = balanced_rate_(i) * pos_ratio * ----------      (5)
                                                              dirty_rate

So the difference lies in pos_ratio.

Believe it or not, it's exactly the seemingly use of pos_ratio that
makes (5) independent(*) of the position control.

Why? Look at (4), assume the system is in a state

- dirty rate is already balanced, ie. balanced_rate_(i) = write_bw / N
- dirty position is not balanced, for example pos_ratio = 0.5

balance_dirty_pages() will be rate limiting each tasks at half the
balanced dirty rate, yielding a measured

        dirty_rate = write_bw / 2                               (6)

Put (6) into (4), we get

        balanced_rate_(i+1) = balanced_rate_(i) * 2
                            = (write_bw / N) * 2

That means, any position imbalance will lead to balanced_rate
estimation errors if we follow (4). Whereas if (1)/(5) is used, we
always get the right balanced dirty ratelimit value whether or not
(pos_ratio == 1.0), hence make the rate estimation independent(*) of
dirty position control.

(*) independent as in real values, not the seemingly relations in equation

Thanks,
Fengguang
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