On Fri, 2009-07-10 at 23:50 +0200, Henrik Austad wrote:
Hi all!
This is a proposal for a global [1], deadline driven scheduler for
real-time tasks in the Linux kernel. I thought I should send out an RFC to
gather some feedback instead of wildy hack away at it.
This proposed scheduler is a modified MLLF (modified Least Laxity First)
called Earliest Failure First (EFF) as it orders tasks according to when
they will miss their deadlines, not when the actual deadline is.
<snip>
Everybody agrees we want a deadline scheduler, we'll probably put a user
interface into -rt shortly which should work for all the involved
research groups so that we can share tests and have better comparisons.
The only thing (aside from an utter lack of time to work on things
recently) that has been holding us back is a proper solution to the
priority inversion issue.
I haven't fully read through the proposed algorithm below, and left it
in place for the new people on CC.
As already mentioned on IRC, the fact that you push the work to the last
possible moment indicates that this algorithm will utterly fall apart on
overload and would thus be unsuited for soft-rt loads, but I guess we
could implement things like EDF-fm and keep this as a hard-rt class.
=== Notation ===
- Take a set of tasks with corresponding attributes. This set and their
attributes are called the schedule, 'S' and contains *all* tasks for
the given scheduling class (i.e. all EFF-tasks).
- Consider a multi-core system with 'm' processors.
- Let the i'th task in the schedule be denoted tau_i. [3]
- Each task will run in intervals, each 'round' is called a job. A task
consists of an infinite sequence of jobs. The k'th job of tau_i is
called tau_{i,k}
- Each task has a set of (relative) attributes supplied when the task is
inserted into the scheduler (passed via syscall)
* Period T_i
* Deadline D_i
* WCET C_i
- Each job (tau_{i,k}) has absolute attributes (computed from the relative
tasks-attributes coupled with physical time).
* Release-time r_{i,k}
* Deadline d_{i,k}
* Allocated time so for a job, C_a(t, tau_{i,k})
When C_a equals WCET, the jobs budget is exhausted and it should
start a new cycle. This is tested (see below) by the scheduler.
* Remaining time for the job, C_r(t, tau_{i,nk})
- The acceptance function for EFF screens new tasks on their expected
utilization. Depending on the mode and implementation, it can be based
on the period, or on the deadline. The latter will cause firmer
restraints, but may lead to wasted resources.
U = C_i / T_i For SRT (bounded deadline tardiness)
U = C_i / D_i For HRT
- A relative measure, time to failure, ttf, indicates how much time is
left before a job must be scheduled to run in order to avoid a
deadline-miss. This will decrease as time progresses and the job is
not granted CPU time. For tasks currently running on a CPU, this value
will be constant.
Take a job with a WCET of 10ms, it has been allowed to run for 4
ms so far. The deadline is 8 ms away. Then the job must be
scheduled to run within the next 4 ms, otherwise it will not be
able to finish in time.
- An absolute value, time of failure (tof) can also be computed in a
static manner. For tasks not running on a CPU, the allocated time is
static. That means you can take the absolute deadline, subtract the
allocated time and you have the absolute point in time when a given
job will fail to meet its deadline.
=== Outline of scheduler ===
Store tasks in 2 queues. One of size m, containing all the tasks
currently running on the CPUs (queue R). The other will hold all
currently active tasks waiting to execute (queue W).
queue R is sorted based on ttf (time to failure, the relative time left
until a task will miss it's deadline). As the tasks approaches the
absolute time of failure at the same rate C_a increases, ttf is
constant. R is only a 'map' of tasks to the CPUs. Position 0 in R
(i.e. smallest ttf) does not result in CPU#0, as the position->CPU will
be quite fluent.
queue W is sorted based on absolute time of failure (tof). Since this is
a fixed point in time, and the tasks in W are not running (C_a is
unchanged), this value is constant.
When a task is scheduled to run, a timer is set at the point in time
where it has exhausted it's budget (t_now + WCET - C_a). This is to
ensure that a runaway task does not grab the CPU.
When a new task arrives, it is handled according the following rules:
- The system has one or more CPUs not running EFF-tasks. Pick any of the
free CPUs and assign the new job there. Set a timer to
- All CPUs are busy, the new task has greater time to failure than the
head of W. The task is inserted into W at the appropriate place.
- All CPUs are busy and the new task has smaller time to failure than
the head of W. The new task is compared to the last task in Q. If time
to failure is larger than the task at the tail, it is added to the
head of W.
- If all CPUs are busy, and time to failure is smaller than the tail of
Q, the new task is a candidate for insertion. At this point the tasks
must be compared to see if picking one or the other will cause a
deadline-miss. If both will miss the deadline if the other is
scheduled, keep the existing running and place the new at the head of
W (as you will have a deadline-miss anyway unless the the task is
picked up by another CPU soon).
- A task running on a CPU with ttf=0 should *never* be preempted with
another task. If all tasks in R have ttf=0, and a newly arrived task
has ttf=0, a deadline-miss is inevitable and switching tasks will only
waste resources.
When a task in R finish (or is stopped due to the timer-limit), it is
removed from R, and the head of W is added to R, inserted at the
appropriate place.
It has been some discussion lately (in particular on #linux-rt) about
the bandwidth inheritance (BWI) and proxy execution protocol (PEP). It
should be possible to extend EFF to handle both. As a side note, if
anyone has some good information about PEP, I'd like a copy :)
Based on this, I think the utilization can be set as high as M
(i.e. full utilization of all CPUs), but the jitter can probably be
quite bad, so for jitter-sensitive tasks, a short period/deadline should
be used.
There are still some issues left to solve, for instance how to best
handle sporadic tasks, and whether or not deadline-miss should be allow,
or just 'bounded deadline tardiness'. Either way, EFF should be able to
handle it. Then, there are problems concerning blocking of tasks. One
solution would be BWI or PEP, but I have not had the time to read
properly through those, but from what I've gathered a combination of BWI
and PEP looks promising (anyone with good info about BWI and PEP - feel
free to share! (-: ).
Our SSSUP friends have a BWI paper here:
http://retis.sssup.it/~tommaso/publications/OSPERT-2008.pdf
The thing we call PEP was christened so by Douglas Niehaus (on CC), I'm
not sure if he has any papers on it.
Also, when talking about it at OSPERT last week Ted Baker (also on CC)
said it reminded him of something else of which I seem to have forgotten
the name.
Thing is, both BWI and PEP seems to work brilliantly on Uni-Processor
but SMP leaves things to be desired. Dhaval is currently working on a
PEP implementation that will migrate all the blocked tasks to the
owner's cpu, basically reducing it to the UP problem.
1) Before you freeze at 'global' and get all caught up on "This won't
ever scale to X", or "He will be haunted by Y" - I do not want to
extend a global algorithm to 2000 cores. I would like to scale to a
single *chip* and then we can worry about 2-way and 4-way systems
later. For the record, I've donned my asbestos suit anyway.
My preferred approach here is to find a distributed algorithm that
converges to the global one.
2) http://austad.us/kernel/thesis_henrikau.pdf
3) Anyone want to include LaTeX-notation into an email-rfc?
Not unheard of ;-)
