New Schedulability Tests for Real- Time task sets scheduled by Deadline Monotonic on Multiprocessors...
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Transcript of New Schedulability Tests for Real- Time task sets scheduled by Deadline Monotonic on Multiprocessors...
![Page 1: New Schedulability Tests for Real- Time task sets scheduled by Deadline Monotonic on Multiprocessors Marko Bertogna, Michele Cirinei, Giuseppe Lipari Scuola.](https://reader035.fdocuments.in/reader035/viewer/2022062516/56649e0d5503460f94af6b83/html5/thumbnails/1.jpg)
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
![Page 2: New Schedulability Tests for Real- Time task sets scheduled by Deadline Monotonic on Multiprocessors Marko Bertogna, Michele Cirinei, Giuseppe Lipari Scuola.](https://reader035.fdocuments.in/reader035/viewer/2022062516/56649e0d5503460f94af6b83/html5/thumbnails/2.jpg)
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
![Page 3: New Schedulability Tests for Real- Time task sets scheduled by Deadline Monotonic on Multiprocessors Marko Bertogna, Michele Cirinei, Giuseppe Lipari Scuola.](https://reader035.fdocuments.in/reader035/viewer/2022062516/56649e0d5503460f94af6b83/html5/thumbnails/3.jpg)
Real-time scheduling for multiprocessor platforms Platform: identical, uniform or
heterogeneous Migration and priorities:
MIGRATIONPRIORITY
Full At job boundaries
Not allowed (partitioning)
Static RM-global, DM-global, …
RM-global, DM-global, …
RM-FFDU, DM-WFIU, …
Job-level dynamic
EDF-global, fpEDF, …
EDF, fpEDF, … EDF-FFDU, EDF-WFIU…
Unrestricted dynamic
pfair algorithms, LLF, …
not useful not useful
![Page 4: New Schedulability Tests for Real- Time task sets scheduled by Deadline Monotonic on Multiprocessors Marko Bertogna, Michele Cirinei, Giuseppe Lipari Scuola.](https://reader035.fdocuments.in/reader035/viewer/2022062516/56649e0d5503460f94af6b83/html5/thumbnails/4.jpg)
Multiprocessor DM
CPU1
CPU2
CPU3
Global queue(ordered by relative deadline)
The first m tasks are scheduled upon the m CPUs
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Multiprocessor DM
CPU1
CPU2
CPU3
Global queue(ordered by relative deadline)
When a task finishes its execution, the next one in the queue is scheduled on the available CPU
![Page 6: New Schedulability Tests for Real- Time task sets scheduled by Deadline Monotonic on Multiprocessors Marko Bertogna, Michele Cirinei, Giuseppe Lipari Scuola.](https://reader035.fdocuments.in/reader035/viewer/2022062516/56649e0d5503460f94af6b83/html5/thumbnails/6.jpg)
Multiprocessor DM
CPU1
CPU2
CPU3
Global queue(ordered by relative deadline)
When a higher priority task arrives, it preempts the task with highest deadline among the executing tasks
![Page 7: New Schedulability Tests for Real- Time task sets scheduled by Deadline Monotonic on Multiprocessors Marko Bertogna, Michele Cirinei, Giuseppe Lipari Scuola.](https://reader035.fdocuments.in/reader035/viewer/2022062516/56649e0d5503460f94af6b83/html5/thumbnails/7.jpg)
Multiprocessor DM
CPU1
CPU2
CPU3
Global queue(ordered by relative deadline)
When another task ends its execution, the preempted task can resume its execution
Task “migrated” from
CPU3 to CPU1
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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 (Dhall’s effect) Bounded number of preemptions/migrations
Good performances on average Schedulability tests (sufficient conditions):
Andersson, Baruah, Jonsson (2002) ABJ test
Baker (2003) BAK test
Efficient implementations
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T
Dhall’s effect
Example: m processors, n=m+1 tasks, Di = Ti
1 ,…, m = (1,T-1) m+1 = (T,T)
RM can fail at very low utilizations
DEADLINEMISS
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The ABJ test
For implicit deadline systems (Di = Ti) using RM
Linear complexityA task set is schedulable with RM on a platform with m identical processors if:
1.
2.
Total utilization
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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:
i = f(i ,k) k = 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 > (Dk-Ck)
k
k
k
DEADLINEMISS
CPU1CPU2CPU3
rkrk+Dk
Ik = Total interference suffered by task k
I2,k
I1,kI2,k
I3,kI4,k
I5,k
I6,k
I8,k
I5,k
I3,k
I7,k
I3,k
Ii,k = Interference of task i on task k
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The BCL test
Ii,k > m(Dk-Ck)
k
k
k
DEADLINEMISS
CPU1CPU2CPU3
rkrk+Dk
I2,k
I1,kI2,k
I3,kI4,k
I5,k
I6,k
I8,k
I5,k
I3,k
I7,k
I3,k
IDEA: It is sufficient to consider at most the portion Dk-Ck of each term Ii,k in the sum
for all i,k: Ii,k ≤ Ik
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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 k :
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
i = f(i ,Dk) k = Ck /Dk
Complexity is O(n2)
A task set is schedulable with DM on m processors if, for every task k :
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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) Baker’s bound [RTSS’03]
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Existing schedulability bounds for SMPs
M=number of processorsU=worst-case total utilization
[Carpenter, Funk, Holman, Srinivasan, Anderson, Baruah]
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Hybrid algorithms
Treat differently heavy and light tasks Allow to overcome Dhall’s effect
ALGORITHM RM-US[Uth]- if (Ui>Uth) task has maximum priority- else task has priority according to RM
ALGORITHM DM-DS[λth]- if (λi>λth) task has maximum priority- else task has priority according to DM
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RM-US[1/3] and DM-DS[1/3]
A task set with constrained deadlines is schedulable with DM-DS[1/3] on m ≥ 2 identical processors if:
A task set with implicit deadlines is schedulable with RM-US[1/3] on m ≥ 2 identical processors if:
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Existing schedulability bounds for SMPs
M=number of processorsU=worst-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