The Case for Multiprocessor Fair Scheduling

1
The Case for Multiprocessor Fair Scheduling

• James H. Anderson
• University of North Carolina at Chapel Hill

2
Real-time Adaptivity on Multiprocessors

• Motivating Application Whisper acoustic tracker
  for virtual environments.

Microphones on ceiling
Speakers on hands and feet
User
TrackingComputer
3
Whisper Characteristics

• Workload requires a multiprocessor.
• Predictive techniques used in tracking.
• Time to compute next prediction depends on
  accuracy of previous prediction.
• ? computational costs will vary.
• Lots of microphones/speakers ? lots of tasks!
• Not practical to provision all tasks assuming max
  costs.
• Question How to ensure adaptive real-time
  execution on a multiprocessor?

4
Multiprocessor SchedulingPartitioning
Partition tasks so that each task always runs on
the same processor.

• Steps
• Assign tasks to processors (bin packing).
• Schedule tasks on each processor using
  uniprocessor algorithms.

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Problems with Partitioning

• Variations in computation costs may necessitate a
  re-partitioning.
• Problematic because
• Partitioning bin packing
• an intractable problem.
• Re-partitionings may cause task migrations
• the very thing partitioning is designed to
  avoid.

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Global SchedulingAn Alternative to Partitioning
A single scheduling algorithm is used
that schedules all tasks.

• Important Difference
• Tasks may migrate among the processors.
• Probably appropriate only on
• tightly-coupled systems.

Rest of the Talk Global scheduling
algorithms that facilitate real-time adaptivity.
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Deadline SchedulingOur Focus

• We consider deadline scheduling algorithms
  wherein
• tasks repeatedly submit pieces of work to the
  system to schedule
• these pieces of work have deadlines
• the system schedules work on an
  earliest-deadline-first basis.

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The Periodic Task ModelThe Simplest Form of
Recurrent Execution

• Periodic Tasks
• Task T (T.e, T.p) releases a job with execution
  cost T.e every T.p time units.
• Ts weight (or utilization or processor share) is
  T.wt T.e/T.p.
• Each job of T has a deadline at the next job
  release of T.

2
5
T (2,5)
U (9,15)
0
10
20
30
5
15
25
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Job-based Scheduling Doesnt Work

• Cant consider jobs as the pieces of work to
  schedule because deadlines can be missed.
• Example Scheduling three (2,3) tasks on two
  processors.

Processor 1
Job 1 of Task 1
Job 1 of Task 3
Processor 2
Job 1 of Task 2
0
2
1
3
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Alternative Pfair Scheduling

• Basic Ideas
• Processor time is allocated in multiples of some
  basic quantum.
• Break jobs into quantum-length subtasks.
• Assign deadlines to subtasks.

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Some DetailsSubtasks and Windows

• Each subtask must execute within a certain time
  window.
• End of window deadline.
• Window layout determined by tasks weight.
• Several optimal Pfair scheduling algorithms are
  known.
• Optimal capable of ensuring all subtask (and
  job) deadlines as long as ?T T.wt ? M (the no. of
  processors)

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Windowing Example
Deadline of T3
T6
Subtasks
T5
First 6 windows of a task T with weight 6/10
T4
T3
T2
T1
8
9
10
6
7
3
4
5
0
1
2
Windows may be of two different lengths, and
successive windows may overlap by one quantum.
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Example Pfair Schedule
TIME 5
10 15
A 1/2
B 1/3
C 1/3
D 2/9
E 2/9
TASKS
On Processor 1
On Processor 2
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Question Can Non-periodic Recurrent Tasks be
Supported?

• Yes!
• Developed the early-release (ER) model.
• Enables work-conserving behavior.
• Developed the intra-sporadic (IS) model.
• Generalizes the sporadic model.
• ER IS rate-based.

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ER and IS Models
ERfairness (Early Release)
Idea Allow a subtask to execute early, i.e.,
before its window.
Early Release
TIME 0 5 10
15 20
ISfairness (Intra-Sporadic)
Idea Allow delays between subtask windows.
IS Delay
TIME 0 5 10
15 20
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Question Can Dynamic Tasks be Supported?
(Dynamic Tasks can Leave and Join)

• Yes!
• Results
• Devised rules under which tasks can leave and
  join a running system.
• These rules can be applied to adaptively reweight
  tasks.
• Leave with old weight, join with new.
• However, a significant delay may be incurred.

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Question Can Quick Adaptations be Supported?

• Yes!
• Two approaches
• Reactive Increase task shares when there is
  idleness (available capacity).
• Resulting scheme Quick-release fair (QRfair).
• Proactive Allow tasks to register weight-change
  requests with the scheduler.
• Resulting scheme Proactive fair (PROfair).

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Proactive vs. Reactive
(Figure depicts the window layout of one task)
No adaptivity
QRfair (reactive)
idle processor encountered ? shift next
window left
PROfair (proactive)
increase weight to consume available capacity
spare capacity becomes available
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QRfair ExperimentFrom RTSS 2003
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Other Research

• Devised efficient synchronization techniques for
  Pfair-scheduled systems.
• Devised techniques for discouraging task
  migrations.
• Devised techniques for minimizing bus contention
  in such systems.
• Developed a prototype threads package.
• New Project Use this threads package to
  re-implement Whisper.

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Conclusions

• Partitioning seems ill-suited for highly adaptive
  multiprocessor systems.
• Moreover, partitioning has been studied for over
  20 years and isnt likely to improve.
• The case for Global Scheduling (Pfair, in
  particular) is likely to improve with further
  research.
• More research needed (for example) on
• support for device I/O,
• coupling feedback control mechanisms with
  adaptive reweighting schemes,
• better techniques for discouraging migrations,
  particularly in soft real-time systems,
• etc. etc. etc.

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References
J. Anderson, A. Block, and A. Srinivasan,
Quick-release fair scheduling, Proceedings of the
24th IEEE Real-time Systems Symposium, pp.
130-141, December 2003. J. Anderson, P. Holman,
and A. Srinivasan, Fair multiprocessor
scheduling, in Handbook on Scheduling
Algorithms, Models, and Performance Analysis,
Joseph Y. Leung (ed.), Chapman and Hall/CRC, pp.
30.1-30.19, 2004. J. Anderson and A.
Srinivasan, Early-release fair scheduling,
Proceedings of the 12th Euromicro Conference on
Real-time Systems, pp. 35-43, June 2000. J.
Anderson and A. Srinivasan, Mixed Pfair/ERfair
scheduling of asynchronous periodic tasks,
Journal of Computer and System Sciences,
68(1)157-204, February, 2004. Preliminary
version appeared in Proceedings of the 13th
Euromicro Conference on Real-time Systems, pp.
76-85, June 2001. S. Baruah, N. Cohen, C.G.
Plaxton, and D. Varvel, Proportionate progress A
notion of fairness in resource allocation,
Algorithmica, 15600-625, 1996. S. Baruah, J.
Gehrke, and C.G. Plaxton, Fast scheduling of
periodic tasks on multiple resources, Proceedings
of the 9th International Parallel Processing
Symposium, pp. 280-288, April 1995.
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References (Continued)
U. Devi and J. Anderson, Fair integrated
scheduling of soft real-time tardiness class on
multiprocessor platforms, Proceedings of the 10th
IEEE Real-time and Embedded Technology and
Applications Symposium, pp. 554-561, May 2004.
U. Devi and J. Anderson, Improved conditions
for bounded tardiness under EPDF fair
multiprocessor scheduling, Proceedings of 12th
International Workshop on Parallel and
Distributed Real-Time Systems, April 2004 (on CD
ROM). U. Devi and J. Anderson, Schedulable
utilization bounds for EPDF fair multiprocessor
scheduling, Proceedings of the 10th International
Conference on Real-time and Embedded Computing
Systems and Applications, August 2004, to appear.
P. Holman, On the Implementation of
Pfair-scheduled Multiprocessor Systems, Ph.D.
Dissertation, University of North Carolina at
Chapel Hill, August 2004. P. Holman and J.
Anderson, Guaranteeing Pfair supertasks by
reweighting, Proceedings of the 22nd IEEE
Real-time Systems Symposium, pp. 203-212,
December 2001. P. Holman and J. Anderson,
Locking in Pfair-scheduled multiprocessor
systems, Proceedings of the 23rd IEEE Real-time
Systems Symposium, pp. 149-158, December 2002.
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References (Continued)
P. Holman and J. Anderson, Object sharing in
Pfair-scheduled multiprocessor systems,
Proceedings of the 14th Euromicro Conference on
Real-time Systems, pp. 111-120, June 2002. P.
Holman and J. Anderson, Using hierarchal
scheduling to improve resource utilization in
multiprocessor real-time systems, Proceedings of
the 15th Euromicro Conference on Real-time
Systems, pp. 41-50, July 2003. P. Holman and J.
Anderson, Implementing Pfairness on a symmetric
multiprocessor, Proceedings of the 10th IEEE
Real-time and Embedded Technology and
Applications Symposium, pp. 544-553, May 2004.
M. Moir and S. Ramamurthy, Pfair scheduling of
fixed and migrating periodic tasks on multiple
resources, Proceedings of the Twentieth IEEE
Real-time Systems Symposium, pp. 294-303,
December 1999. A. Srinivasan, Efficient and
Flexible Fair Scheduling of Real-time Tasks on
Multiprocessors, Ph.D. Dissertation, University
of North Carolina at Chapel Hill, December 2003.
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References (Continued)
A. Srinivasan and J. Anderson, Optimal rate-based
scheduling on multiprocessors, Proceedings of the
34th ACM Symposium on Theory of Computing, pp.
189-198, May 2002. A. Srinivasan and J.
Anderson, Efficient scheduling of soft real-time
applications on multiprocessors, Journal of
Embedded Computing (to appear), special issue of
best papers from the 15th Euromicro Conference on
Real-time Systems, 2003. Preliminary version
appeared in Proceedings of the 15th Euromicro
Conference on Real-time Systems, pp. 51-59, July
2003. A. Srinivasan and J. Anderson, Fair
scheduling of dynamic task systems on
multiprocessors, Journal of Systems and Software
(to appear), special issue of best papers from
the 11th International Workshop on Parallel and
Distributed Real-time Systems, 2004. A.
Srinivasan, P. Holman, and J. Anderson,
Integrating aperiodic and recurrent tasks on
fair-scheduled multiprocessors, Proceedings of
the 14th Euromicro Conference on Real-time
Systems, pp. 19-28, June 2002. A. Srinivasan,
P. Holman, J. Anderson, and S. Baruah, The case
for fair multiprocessor scheduling, Proceedings
of the 11th International Workshop on Parallel
and Distributed Real-time Systems, April 2003 (on
CD ROM).