Re: [patch] CFS scheduler, -v8

Ting Yang
2007-05-02T03:07:08Z

Hi, Ingo

My name is Ting Yang, a graduate student from UMASS. I am currently
studying the linux scheduler and virtual memory manager to solve some
page swapping problems. I am very excited with the new scheduler CFS.
After I read through your code, I think that you might be interested in
reading this paper:

"A Proportional Share REsource Allocation Algorithm for Real-Time,
Time-Shared Systems", by Ion Stoica. You can find the paper here:
http://citeseer.ist.psu.edu/37752.html

Authors of this paper proposed a scheduler: Earlist Eligible Virtual
Deadline First (EEVDF). EEVDF uses exactly the same method as CFS to
track the execution of each running task. The only difference between
EEVDF and CFS is that EEVDF tries to _deadline_ fair while CFS is
_start-time_ fair. Scheduling based on deadline gives better reponse
time bound and seems to more fair.

In the following part of this email, I will try to explain the
similarities and differences between EEVDF and CFS. Hopefully, this
might provide you with some useful information w.r.t your current work
on CFS.

Similarities:
1. both EEVDF and CFS use virtual time to track the system's progress.

CFS maintains rq->fair_clock for each cpu, which is updated every
tick by:
SCALE/sum(p_i->loadweight)
where p_i->loadweight is the weight of each task mapped from its nice
value in prio_to_load_shift[], given that the default weight is SCALE (1024)

EEVDF maintains a virtual time, which is advanced every tick by:
1/sum(w_i)
where w_i is the weight of each task, given that the default weight is 1.

Therefore, EEVDF and CFS monitors system progress in the same way,
except normalized to different scale.

2. EEVDF and CFS monitors the progress in the same way.

CFS maintains a p->fair_key which indicating the amount of work done
by this task. When p executes for a period t, then p->fair_key
incremented by:
t * SCALE/p->loadweight //the default weight is SCALE
(based on solving equations in your code :-))

EEVDF does the same thing with assumption that the default weight is
1, it uses the same equation to calculate deadlines for running tasks.

Differences:
The main difference between CFS and EEVDF lies in the scheduling
policy, although they follow the same model for tracking tasks.

*** CFS: When a task starts, it gets p->fair_key from the current
virtual time rq->fair_clock. It will not be scheduled for execution
until all other running tasks' fair_key go beyond p->fair_key by certain
virtual ticks (which is 5 ticks for the current setting of CFS).

(I wish I could show examples with graphs, instead of my not-so-good
english, but I am not sure if it appropriate to attach figures on this
maillist)

EXAMPLE: assume the system runs at 1000 tick/second, i.e. 1ms a tick,
and the granularity of pre-exemption for CFS is 5 virtual ticks (the
current setting). If, at time t=0, we start 2 tasks: p1 and p2, both
have nice value 0 (weight 1024), and rq->fair_clock is initialized to 0.
Now we have:
p1->fair_key = p2->fair_key = rq->fair_clock = 0.
CFS breaks the tie arbitrarily, say it executes p1. After 1 system tick
(1ms later) t=1, we have:
rq->fair_clock = 1/2, p1->fair_key = 1, p2->fair_key = 0.
Suppose, a new task p3 starts with nice value -10 at this moment, that
is p3->fair_key=1/2. In this case, CFS will not schedule p3 for
execution until the fair_keys of p1 and p2 go beyond 5+1/2 (which
translates to about 10ms later in this setting), _regardless_ the
priority (weight) of p3. Further imagine, if we starts n tasks at time
t=0 and then start a task p_(n+1) at time t = 1, the delay of task
p_(n+1) actually is proportional to the number of running tasks n.

Formally speaking, CFS can has a *O(n)* lag w.r.t the ideal
proportional shared fluid-flow system, which can be arbitrarily fine
granularity. The cause of this problem is that p->fair_key only reflects
a fair point that a task should be started, but does not has any
information about how urgent the task is (i.e. the priority or weight of
the task).

*** In EEVDF, each task p_i is specified by 2 parameters: weight w_i
and timeslice length l_i. EEVDF tries to schedule tasks based on the
virtual deadline vd_i where a timeslice l_i should be finished.
EEVDF keeps a virtual start (ve_i) and virtual deadline (vd_i) for
each tasks. When a tasks starts, its ve_i is initialized to be the
current virtual time, and calculates its virtual deadline as:
vd_i = ve_i + l_i/w_i //the same method as CFS updates fair_key.
When l_i amount of work is done, the just finished vd_i becomes the new
ve_i. That is the virtual start time of next l_i amount work is the
deadline of previous finished timeslice. The virtual deadline vd_i is
then updated using the above equation.

EEVDF schedule policy: always executes the task with the _earliest_
virtual deadline.

EXAMPLE: Assume the system has 1000 ticks per second. At time t = 0,
we start 2 tasks: p1 and p2, such that w_1 = w_2 = 1 and l_1 = l_2 = 5
ticks, i.e 5ms (which reflects the similar setting in CFS case).
Furthermore, the system virtual time vt is initialized to be 0. Now at
time t = 0, we have
vt = 0,
ve_1 = 0, vd_1 = ve_1 + l_1/w_1 = 5
ve_2 = 0, vd_2 = vd_2 + l_2/w_2 = 5
As p1 and p2 have the same virtual deadline, EEVDF breaks the tie
arbitrarily, say it executes p1. After 1 system tick (1ms later), we have:
vt = 0 + 1 / (w_1 + w_2) = 1/2 //just as CFS updates rq->fair_clock
ve_1 = 0, vd_1 = 5 //not changed
ve_2 = 0, vd_1 = 5 //not changed
Suppose, we starts a new task p2 at this moment, with weight w_3 = 2 and
timeslice l_3 = 5 ticks (5ms), Then
ve_3 = vt = 1/2
vd_3 = ve_3 + l_3/w_2 = 1/2 + 5/2 = 3
hmmm, the scheduler now will execute task p3 first since it has the
earliest deadline. The deadline implicitly contains some very important
information that the CFS fair_key does not have: how urgent this amount of
work has to be done, which comes from the weight of a task.

Formally speaking, EEVDF has a constant O(1) lag w.r.t the ideal
proportional shared fluid-flow system. (Please look at the paper for
detail proofs.) Under normal cases, for a task p_i, EEVDF ensures that
it does not fall behind the ideal system by more than l_i time.
Occasionally, the delay can be max(l_i), the maximum timeslice used by
all active tasks, due to the dynamic entering and leaving of tasks.
(Again, the paper give more detailed explanation on this).

We can see that here the timeslice l_i used by a task p_i actually
controls accuracy of scheduling p_i. The smaller l_i, the closer to the
ideal system during p_i's execution. For example, in above case, if p3
has w_3 = 1 (the same as p1 and p2) and l_3 = 3 (3ms). Since vd_3 = 1/2
+ l_3/w_3 = 7/2, the scheduler still executes p3 first, even though
p1,p2 and p3 have the same weight. Smaller l_i leads the scheduler to
handle p_i in finer granularity. Intuitively, it makes scheduler checks
the deadline of p_i more frequently
and ensures each small piece of work is done on time, while larger l_i
does the reverse.

The decouple of weight w_i and timeslice l_i is important. Generally
speaking, weight determines throughput and timeslice determines the
responsiveness of a task. In normal situation, high priority tasks
usually need more cpu capacity within short period of time (bursty, such
as keyboard, mouse move, X updates, daemons, etc), and need to be
processed as quick as possible (responsiveness and interactiveness).
Follow the analysis above, we know that for higher priority tasks we
should give _higher weight_ to ensure its CPU throughput, and at the
same time give _smaller timeslice_ to ensure better responsiveness.
This is a bit counter-intuitive against the current linux
implementation: smaller nice value leads to higher weight and larger
timeslice.

Now let's see what happens in the Real-Time world. Usually a real-time
application is specified with (C_i, T_i), where C_i is the amount of
work and T_i is the period of time that the work has to be finished.
For example, (20ms, 50ms) says the scheduler has to do 20ms work within
a window of 50ms for this task. Smaller T_i gives tighter response
constraints. Note that Bi = Ci/Ti is really the CPU proportion for the
task during its execution. In our proportional time share world, weight
w_i decides the cpu proportion which maps to Bi, and timeslice l_i gives
the amount works should be done each time, which maps Ci. Then using w_i
and l_i, we can get a window size, which actually maps Ti. Therefore
smaller l_i leads to smaller Ti which means tighter response
constraints. It seems to me all these make a lot sense in both
proportional time share and real-time world.

Based on my understanding, adopting something like EEVDF in CFS should
not be very difficult given their similarities, although I do not have
any idea on how this impacts the load balancing for SMP. Does this worth
a try?

Sorry for such a long email :-)

Ting