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Subject[ANNOUNCE] RSDL completely fair starvation free interactive cpu scheduler
This message is to announce the first general public release of the "Rotating 
Staircase DeadLine" cpu scheduler.

Based on previous work from the staircase cpu scheduler I set out to design,
from scratch, a new scheduling policy design which satisfies every
requirement for SCHED_NORMAL (otherwise known as SCHED_OTHER) task management.

Available for download are:

A full rollup of the patch for 2.6.20:

Split patches for 2.6.20(which will follow this email):

The readme (which will also constitute the rest of this email):

The following readme is also included as documentation in

Rotating Staircase Deadline cpu scheduler policy

Design summary

A novel design which incorporates a foreground-background descending priority
system (the staircase) with runqueue managed minor and major epochs (rotation
and deadline).


A starvation free, strict fairness O(1) scalable design with interactivity
as good as the above restrictions can provide. There is no interactivity
estimator, no sleep/run measurements and only simple fixed accounting.
The design has strict enough a design and accounting that task behaviour
can be modelled and maximum scheduling latencies can be predicted by
the virtual deadline mechanism that manages runqueues. The prime concern
in this design is to maintain fairness at all costs determined by nice level,
yet to maintain as good interactivity as can be allowed within the
constraints of strict fairness.

Design description

RSDL works off the principle of providing each task a quota of runtime that
it is allowed to run at each priority level equal to its static priority
(ie. its nice level) and every priority below that. When each task is queued,
the cpu that it is queued onto also keeps a record of that quota. If the
task uses up its quota it is decremented one priority level. Also, if the cpu
notices a quota full has been used for that priority level, it pushes
everything remaining at that priority level to the next lowest priority
level. Once every runtime quota has been consumed of every priority level,
a task is queued on the "expired" array. When no other tasks exist with
quota, the expired array is activated and fresh quotas are handed out. This
is all done in O(1).

Design details

Each cpu has its own runqueue which micromanages its own epochs, and each
task keeps a record of its own entitlement of cpu time. Most of the rest
of these details apply to non-realtime tasks as rt task management is
straight forward.

Each runqueue keeps a record of what major epoch it is up to in the
rq->prio_rotation field which is incremented on each major epoch. It also
keeps a record of quota available to each priority value valid for that
major epoch in rq->prio_quota[].

Each task keeps a record of what major runqueue epoch it was last running
on in p->rotation. It also keeps a record of what priority levels it has
already been allocated quota from during this epoch in a bitmap p->bitmap.

The only tunable that determines all other details is the RR_INTERVAL. This
is set to 6ms (minimum on 1000HZ, higher at different HZ values).

All tasks are initially given a quota based on RR_INTERVAL. This is equal to
RR_INTERVAL between nice values of 0 and 19, and progressively larger for
nice values from -1 to -20. This is assigned to p->quota and only changes
with changes in nice level.

As a task is first queued, it checks in recalc_task_prio to see if it has
run at this runqueue's current priority rotation. If it has not, it will
have its p->prio level set to equal its p->static_prio (nice level) and will
be given a p->time_slice equal to the p->quota, and has its allocation
bitmap bit set in p->bitmap for its static priority (nice value). This
quota is then also added to the current runqueue's rq->prio_quota[p->prio].
It is then queued on the current active priority array.

If a task has already been running during this major epoch, if it has
p->time_slice left and the rq->prio_quota for the task's p->prio still
has quota, it will be placed back on the active array, but no more quota
will be added to either the task or the runqueue quota.

If a task has been running during this major epoch, but does not have
p->time_slice left or the runqueue's prio_quota for this task's p->prio
does not have quota, it will find the next lowest priority in its bitmap
that it has not been allocated quota from. It then gets the a full quota
in p->time_slice and adds that to the quota value for the relevant priority
rq->prio_quota. It is then queued on the current active priority array at
the newly determined lower priority.

If a task has been running during this major epoch, and does not have
any entitlement left in p->bitmap and no time_slice left, it will have its
bitmap cleared, and be queued at its p->static_prio again, but on the expired
priority array. No quota will be allocated until this task is scheduled.

When a task is queued, it has its static_prio bit set in the current
runqueue's rq->static_bitmap, and the relevant bit in the rq->dyn_bitmap.
In order to minimise the number of bitmap lookups, the bitmap of queued
tasks on the expired array is at the end of the same bitmap as the active
array. The number of tasks queued at the current static_prio is kept in

During a scheduler_tick where a task is running, the p->time_slice is
decremented, and if it reaches zero then the recalc_task_prio is readjusted
and the task rescheduled.

During a task running tick, the runqueue prio_quota is also decremented. If
it empties then a priority rotation occurs (a major or minor epoch). If the
current runqueue's priority level is better than that of nice 19 tasks, a
minor rotation is performed, otherwise a major rotation will occur.

A minor rotation takes the remaining tasks at this priority level queue and
merges them with a list_splice_tail with the queue from the next lowest
priority level. At this time, any tasks that have been merged will now
have invalid values in p->prio so this must be considered when dequeueing
the task, and for testing for preemption.

A major rotation takes the remaining tasks at this priority level queue and
merges them with a list_splice_tail with the best priority task running on
the expired array, and swaps the priority arrays. The priority quotas are
reset at this time. Any tasks that have been merged will now have invalid
values in p->array and possibly p->prio so this must be considered. The
rq->prio_rotation is incremented at this time.

When a task is dequeued, the dyn_bitmap bit is unset only after testing
that the relevant queue is actually empty since p->prio may be inaccurate
and no hard accounting of the number of tasks at that level is possible.

When selecting a new task for scheduling, after the first dynamic bit is
found on the dyn_bitmap, it is checked to see that a task is really queued
at that priority or if it is a false positive due to the task being
dequeued at a time when its p->prio does not match which queue it is on
after some form of priority rotation. This is a rare occurrence as it tends
to only occur if a task that is already waiting on a runqueue gets dequeued.
If the bitmap value is in the expired array range, a major priority rotation
is performed. If the chosen task has not been running during this major or
minor rotation it has new quota allocated at this time, and added to the
runqueue's quota.

Modelling deadline behaviour

As the accounting in this design is hard and not modified by sleep average
calculations or interactivity modifiers, it is possible to accurately
predict the maximum latency that a task may experience under different
conditions. This is a virtual deadline mechanism enforced by mandatory
runqueue epochs, and not by trying to keep complicated accounting of each

The maximum duration a task can run during one major epoch is determined
by its nice value. Nice 0 tasks can run at 19 different priority levels
for RR_INTERVAL duration during each epoch (the equivalent of nice 0 to nice
19). Nice 10 tasks can run at 9 priority levels for each epoch, and so on.

Therefore the maximum duration a runqueue epoch can take is determined by
the number of tasks running, and their nice level. After that, the maximum
duration it can take before a task can wait before it get scheduled is
determined by the difference between its nice value and the nice value of
the highest priority task queued.

In the following examples, these are _worst case scenarios_ and would rarely
occur, but can be modelled nonetheless to determine the maximum possible

So for example, if two nice 0 tasks are running, and one has just expired as
another is activated for the first time receiving a full quota for this
runqueue rotation, the first task will wait:

nr_tasks * max_duration + nice_difference * rr_interval
1 * 19 * RR_INTERVAL + 0 = 114ms

In the presence of a nice 10 task, a nice 0 task would wait a maximum of
1 * 10 * RR_INTERVAL + 0 = 60ms

In the presence of a nice 0 task, a nice 10 task would wait a maximum of
1 * 19 * RR_INTERVAL + 9 * RR_INTERVAL = 168ms

Using a more complicated example, if there are 4 tasks running fully cpu
bound, one each at nice -20, nice 0, nice 10 and nice 19, we can calculate
the maximum latency possible for the nice 10 task. Note that -20 tasks are
heavily biased for so this will be a long time, but can be modelled.

The nice -20 task has quota = RR_INTERVAL + 20*RR_INTERVAL = 21*RR_INTERVAL.
It can run at 39 priority levels so its maximum duration =
39 * 21 * RR_INTERVAL.
The nice 0 task works out to
The nice 19 task works out to

So major epoch can take up a maximum of

Then before the nice 10 task will run, the nice -20 and nice 0 task will
run for 28 * 21 * RR_INTERVAL and 9 * RR_INTERVAL respectively for a total
of 597 * RR_INTERVAL.

This means the maximum duration a nice 10 task can wait in the presence of
these other tasks is 1826*RR_INTERVAL. This is a long time of course and is
heavily penalised by the presence of nice -20 tasks which would not be part
of a normal environment.

While this section describes the maximum latency a task can have, this size
latencies will only be seen by fully cpu bound tasks.

Achieving interactivity

A requirement of this scheduler design was to achieve good interactivity
despite being a completely fair deadline based design. The disadvantage of
designs that try to achieve interactivity is that they usually do so at
the expense of maintaining fairness. As cpu speeds increase, the requirement
for some sort of metered unfairness towards interactive tasks becomes a less
desirable phenomenon, but low latency and fairness remains mandatory to
good interactive performance.

This design relies on the fact that interactive tasks, by their nature,
sleep often. Most fair scheduling designs end up penalising such tasks
indirectly giving them less than their fair possible share because of the
sleep, and have to use a mechanism of bonusing their priority to offset
this based on the duration they sleep. This becomes increasingly inaccurate
as the number of running tasks rises and more tasks spend time waiting on
runqueues rather than sleeping, and it is impossible to tell whether the
task that's waiting on a runqueue only intends to run for a short period and
then sleep again after than runqueue wait. Furthermore, all such designs rely
on a period of time to pass to accumulate some form of statistic on the task
before deciding on how much to give them preference. The shorter this period,
the more rapidly bursts of cpu ruin the interactive tasks behaviour. The
longer this period, the longer it takes for interactive tasks to get low
scheduling latencies and fair cpu.

This design does not measure sleep time at all. Interactive tasks that sleep
often will wake up having consumed very little if any of their quota for
the current major priority rotation. The longer they have slept, the less
likely they are to even be on the current major priority rotation. Once
woken up, though, they get to use up a their full quota for that epoch,
whether part of a quota remains or a full quota. Overall, however, they
can still only run as much cpu time for that epoch as any other task of the
same nice level. This means that two tasks behaving completely differently
from fully cpu bound to waking/sleeping extremely frequently will still
get the same quota of cpu, but the latter will be using its quota for that
epoch in bursts rather than continuously. This guarantees that interactive
tasks get the same amount of cpu as cpu bound ones.

The other requirement of interactive tasks is also to obtain low latencies
for when they are scheduled. Unlike fully cpu bound tasks and the maximum
latencies possible described in the modelling deadline behaviour section
above, tasks that sleep will wake up with quota available usually at the
current runqueue's priority_level or better. This means that the most latency
they are likely to see is one RR_INTERVAL, and often they will preempt the
current task if it is not of a sleeping nature. This then guarantees very
low latency for interactive tasks, and the lowest latencies for the least
cpu bound tasks.

Sunday, 4th March 2007
Con Kolivas

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