New Schedulability Tests for RealTime task sets scheduled by Deadline Monotonic on Multiprocessors

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New Schedulability Tests for Real-Time task sets
scheduled by Deadline Monotonic on Multiprocessors

• Marko Bertogna, Michele Cirinei, Giuseppe Lipari
• Scuola S.Anna, Pisa, Italy

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Overview

• Real-time multiprocessing
• Deadline-Monotonic (DM) for multiprocessors
• Existing schedulability tests for RM/DM
• An improved test for DM
• Existing schedulability bounds
• Improving the bound for fixed priority global
  scheduling

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Real-time scheduling for multiprocessor platforms

• Platform identical, uniform or heterogeneous
• Migration and priorities

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Multiprocessor DM
CPU1
t1
Global queue (ordered by relative deadline)
CPU2
t2
t2
t1
t3
t4
t5
CPU3
t3
The first m tasks are scheduled upon the m CPUs
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Multiprocessor DM
CPU1
t1
Global queue (ordered by relative deadline)
CPU2
t2
t2
t1
t3
t4
t5
CPU3
t3
t4
When a task finishes its execution, the next one
in the queue is scheduled on the available CPU
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Multiprocessor DM
CPU1
t1
Global queue (ordered by relative deadline)
CPU2
t2
t3
t3
CPU3
t4
t3
When a higher priority task arrives, it preempts
the task with highest deadline among the
executing tasks
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Multiprocessor DM
CPU1
t1
t4
Global queue (ordered by relative deadline)
CPU2
t2
t2
t1
t3
t4
t5
t3
t4
Task t4 migrated from CPU3 to CPU1
CPU3
t4
t3
When another task ends its execution, the
preempted task can resume its execution
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Why fixed priority global scheduling?

• Advantages
• Load balancing
• Number of preemptions
• Simple implementation
• Easy rescheduling
• Reclaiming
• Disadvantages
• Cache affinity HW mitigates migration cost
• Utilization bound lower than pfair algorithms

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RM for uniprocessor systems

• Optimality among fixed priority systems

• Bounded number of preemptions

• Efficient implementations

• Easy sufficient schedulability test

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RM uniprocessor necessary and sufficient test

• Response Time Analysis
• Repeat
• Until
• Pseudopolynomial complexity

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RM on multiprocessors

• Low utilization bound (Dhalls effect)

• Bounded number of preemptions/migrations

• Efficient implementations

• Good performances on average

• Schedulability tests (sufficient conditions)
• Andersson, Baruah, Jonsson (2002) ? ABJ test
• Baker (2003) ? BAK test

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Dhalls effect
Example m processors, nm1 tasks, Di Ti t1
,, tm (1,T-1) tm1 (T,T)
DEADLINE MISS
RM can fail at very low utilizations
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The ABJ test

• For implicit deadline systems (Di Ti) using RM
• Linear complexity

• A task set is schedulable with RM on a platform
  with m identical processors if

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The BAK test

• For constrained deadline systems (Di Ti)
• Quadratic complexity

A task set is schedulable with EDF on a platform
with m identical processors if
bi f(ti ,tk)
lk Ck /Dk
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Toward a better schedulability test for RM/DM

• Improve BAK when heavy tasks are considered
• Extend the ABJ test
• for arbitrary task utilizations
• for constrained deadline systems

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Can BAK be improved?
Ik Total interference suffered by task tk
Ii,k Interference of task ti on task tk
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The BCL test
for all i,k Ii,k Ik
IDEA It is sufficient to consider at most the
portion Dk-Ck of each term Ii,k in the sum
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The BCL test for DM
A task set is schedulable with DM on m processors
if and only if, for every task tk

• Computing each Ii,k requires exponential time
• To reduce the complexity
• bound the interference with the load
• give an upper bound on the load
• Derive a sufficient condition to be checked for
  every task

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The BCL test for DM
A task set is schedulable with DM on m processors
if, for every task tk
Complexity is O(n2)
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Can ABJ be improved?

• New analysis for constrained deadline systems and
  priorities according to DM
• Improvement over ABJ
• Preperiod deadline systems
• Arbitrary individual task utilization
• Higher global utilization
• Introduce to a better schedulability bound for
  the fixed priority global scheduling class of
  algorithms

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Density and utilization based test for RM/DM
A task set with constrained deadlines is
schedulable with DM on m 2 identical processors
if
A task set with implicit deadlines is schedulable
with RM on m 2 identical processors if
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Improvement over existing bounds

• Bound more general than ABJ
• taking we have
• as ABJ.
• Corrected (and extended) Bakers bound RTSS03

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Existing schedulability bounds for SMPs

• Mnumber of processors
• Uworst-case total utilization

Carpenter, Funk, Holman, Srinivasan, Anderson,
Baruah
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Hybrid algorithms

• Treat differently heavy and light tasks
• Allow to overcome Dhalls effect

• ALGORITHM RM-USUth
• if (UigtUth) ? task has maximum priority
• else task has priority according to RM

• ALGORITHM DM-DS?th
• if (?igt?th) ? task has maximum priority
• else task has priority according to DM

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RM-US1/3 and DM-DS1/3
A task set with implicit deadlines is schedulable
with RM-US1/3 on m 2 identical processors if
A task set with constrained deadlines is
schedulable with DM-DS1/3 on m 2 identical
processors if
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Existing schedulability bounds for SMPs

• Mnumber of processors
• Uworst-case total utilization

Carpenter, Funk, Holman, Srinivasan, Anderson,
Baruah
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Conclusions

• Extended BAK test for DM
• BCL test that better behaves with heavy tasks
• Improved ABJ test
• generalized to constrained deadline systems
• extended to arbitrary task utilizations/densities
• increased the schedulability bound for RM/DM
• Proposed hybrid algorithms (RM-US, DM-DS)
• improved the schedulability bound of the fixed
  priority global scheduling class of algorithms

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THE END

• Marko marko_at_sssup.it
• Michele cirnei_at_gandalf.sssup.it
• Peppe lipari_at_sssup.it