RSDL

=Rotating Staircase Deadline cpu scheduler policy=

http://ck.kolivas.org/patches/staircase-deadline/

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).

Features
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 rq->prio_queued[].

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 task.

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 latency.

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 19 * RR_INTERVAL The nice 19 task works out to RR_INTERVAL.

So major epoch can take up a maximum of 39 * 21 * RR_INTERVAL + 19 * RR_INTERVAL + RR_INTERVAL = 1229 * RR_INTERVAL;

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.