Sum of weights idea for CFS PI

[Joel Fernandes <joel@joelfernandes.org>]

Hi Peter, all,

Just following-up about the idea Peter suggested at LPC22 about sum of weights
to solve the CFS priority inversion issues using priority inheritance. I am not
sure if a straight forward summation of the weights of dependencies in the
chain, is sufficient (or may cause too much unfairness).

I think it will work if all the tasks on CPU are 100% in utilization:

Say if you have 4 tasks (A, B, C, D) running and each one has equal
weight (W) except for A which has twice the weight (2W).
So the CPU bandwidth distribution is (assuming all are running):
A:   2 / 5
B, C. D:  1 / 5

Say out of the 4 tasks, 3 of them are a part of a classical priority
inversion scenario (A, B and C).

Say now A blocks on a lock and that lock's owner C is running, however now
because A has blocked, B gets 1/3 bandwidth, where as it should have been
limited to 1/5. To remedy this, say you give C a weight of 2W. B gets 1/4
bandwidth - still not fair since B is eating away CPU bandwidth causing the
priority inversion we want to remedy.

The correct bandwidth distribution should be (B and D should be unchanged):
B = 1/5
D = 1/5

C = 3/5

This means that C's weight should be 3W , and B and D should be W each
as before. So indeed, C's new weight is its original weight PLUS the
weight of the A - that's needed to keep the CPU usage of the other
tasks (B, D) in check so that C makes forward progress on behalf of A and the
other tasks don't eat into the CPU utilization.

However, I think this will kinda fall apart if A is asleep 50% of the time
(assume the sleep is because of I/O and unrelated to the PI chain).

Because now if all were running (and assume no PI dependencies), with A being
50%, the bandwidth of B, C and D each would be divided into 2 components:

a.  when A is running, it would be as above.
b.  but if A was sleeping, B, C, and D would get 1/3.

So on average, B, C and D get:  (1/3 + 1/5) / 2 = 8/30. This gives A about 6/30
or 1/5 bandwidth.

But now say A happen to block on a lock that C is holding. You would boost C to
weight 3W which gives it 3/5 (or 18/30) as we saw above, which is more than what
C should actually get.

C should get (8/30 + 6/30 = 14/30) AFAICS.

Hopefully one can see that a straight summation of weights is not enough. It
needs to be something like:

C's new weight = C's original weight + (A's weight) * (A's utilization)

Or something, otherwise the inherited weight may be too much to properly solve it.

Any thoughts on this? You mentioned you had some notes on this and/or proxy
execution, could you share it?

Thanks,

 - Joel