hasso-plattner-institut für softwaresystemtechnik gmbh an der universität potsdam multiprocessor...
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![Page 1: HASSO-PLATTNER-INSTITUT für Softwaresystemtechnik GmbH an der Universität Potsdam Multiprocessor Scheduling “Global Multiprocessor Scheduling of Aperiodic](https://reader036.vdocuments.site/reader036/viewer/2022062320/56649d385503460f94a118dd/html5/thumbnails/1.jpg)
HASSO-PLATTNER-INSTITUTfür Softwaresystemtechnik GmbH an der Universität Potsdam
Multiprocessor Scheduling
“Global Multiprocessor Scheduling of Aperiodic Tasks using Time-
Independent Priorities”
Alexander Küchler
![Page 2: HASSO-PLATTNER-INSTITUT für Softwaresystemtechnik GmbH an der Universität Potsdam Multiprocessor Scheduling “Global Multiprocessor Scheduling of Aperiodic](https://reader036.vdocuments.site/reader036/viewer/2022062320/56649d385503460f94a118dd/html5/thumbnails/2.jpg)
Multiprocessor SchedulingProf. Dr. Lars Lundberg, Prof. Dr. Andreas Polze
2
H ASSO -PLATTN ER -IN STITU Tfür Softwaresystem technik G m bH an der Universität Potsdam
Alexander Küchler715659
Agenda
Definitions
Previous work
Problems, assumptions and goals
Results
‘Calculating’ Uthreshold
Strategy for using the bound
References
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Multiprocessor SchedulingProf. Dr. Lars Lundberg, Prof. Dr. Andreas Polze
3
H ASSO -PLATTN ER -IN STITU Tfür Softwaresystem technik G m bH an der Universität Potsdam
Alexander Küchler715659
Definitions I
Global/dynamic scheduling = a process can be migrate from one processor to another at run-time (assumption: no penalty for migration)
Aperiodic tasks = subgroup of periodic tasks, where no statements for arrival can be made
Time-independent priorities = assigned priority does not depend of its absolute arrival time
Preemptive scheduling = a task can be interrupted and continued later
![Page 4: HASSO-PLATTNER-INSTITUT für Softwaresystemtechnik GmbH an der Universität Potsdam Multiprocessor Scheduling “Global Multiprocessor Scheduling of Aperiodic](https://reader036.vdocuments.site/reader036/viewer/2022062320/56649d385503460f94a118dd/html5/thumbnails/4.jpg)
Multiprocessor SchedulingProf. Dr. Lars Lundberg, Prof. Dr. Andreas Polze
4
H ASSO -PLATTN ER -IN STITU Tfür Softwaresystem technik G m bH an der Universität Potsdam
Alexander Küchler715659
Definitions II Multiprocessor with m processors and a set of n
independent tasks Each task Tn has
an arrival time An a worst-case execution time Cn
a deadline Dn, a synthetic utilization Un=Cn/Dn
a priority Pn
Total utilization U is the sum of all Un of tasks that
have arrived but not yet reached their deadline
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Multiprocessor SchedulingProf. Dr. Lars Lundberg, Prof. Dr. Andreas Polze
5
H ASSO -PLATTN ER -IN STITU Tfür Softwaresystem technik G m bH an der Universität Potsdam
Alexander Küchler715659
Definitions III
V(t) is a task set with Ai≤t<Ai+Di
Synthetic utilization is
/i
iT V t
US t U m
![Page 6: HASSO-PLATTNER-INSTITUT für Softwaresystemtechnik GmbH an der Universität Potsdam Multiprocessor Scheduling “Global Multiprocessor Scheduling of Aperiodic](https://reader036.vdocuments.site/reader036/viewer/2022062320/56649d385503460f94a118dd/html5/thumbnails/6.jpg)
Multiprocessor SchedulingProf. Dr. Lars Lundberg, Prof. Dr. Andreas Polze
6
H ASSO -PLATTN ER -IN STITU Tfür Softwaresystem technik G m bH an der Universität Potsdam
Alexander Küchler715659
Previous work I
(1) shows categorization of time-independent and non-time-independent scheduling policies for aperiodic tasks
(2) shows optimal utilization bound of
for liquid tasks (Ci0 and Ci/Di0) on
multiprocessor machines
(3) shows avoidance of Dhall’s effect for periodic tasks
by dividing tasks into two categories (UiUthreshold(m) = heavy; Ui Uthreshold (m) = light)
1
11
2
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Multiprocessor SchedulingProf. Dr. Lars Lundberg, Prof. Dr. Andreas Polze
7
H ASSO -PLATTN ER -IN STITU Tfür Softwaresystem technik G m bH an der Universität Potsdam
Alexander Küchler715659
Previous work I – Dhall’s effect
![Page 8: HASSO-PLATTNER-INSTITUT für Softwaresystemtechnik GmbH an der Universität Potsdam Multiprocessor Scheduling “Global Multiprocessor Scheduling of Aperiodic](https://reader036.vdocuments.site/reader036/viewer/2022062320/56649d385503460f94a118dd/html5/thumbnails/8.jpg)
Multiprocessor SchedulingProf. Dr. Lars Lundberg, Prof. Dr. Andreas Polze
8
H ASSO -PLATTN ER -IN STITU Tfür Softwaresystem technik G m bH an der Universität Potsdam
Alexander Küchler715659
Previous work II
(4) shows similar problem for periodic tasks with a result of ln(1+y)=(1-y)/(1+y) which is approx. 37,482% for m
![Page 9: HASSO-PLATTNER-INSTITUT für Softwaresystemtechnik GmbH an der Universität Potsdam Multiprocessor Scheduling “Global Multiprocessor Scheduling of Aperiodic](https://reader036.vdocuments.site/reader036/viewer/2022062320/56649d385503460f94a118dd/html5/thumbnails/9.jpg)
Multiprocessor SchedulingProf. Dr. Lars Lundberg, Prof. Dr. Andreas Polze
9
H ASSO -PLATTN ER -IN STITU Tfür Softwaresystem technik G m bH an der Universität Potsdam
Alexander Küchler715659
Problems, assumptions and goals
Problems: Dhall’s effect shows that deadline monotonic priority
assignment may lead to missed deadlines even if U is very low
Assumptions: Preemptive scheduling is possible Time-independent priorities for each task (depending
on C and D, not A!)
Goals: All tasks in the task set meet their deadlines
![Page 10: HASSO-PLATTNER-INSTITUT für Softwaresystemtechnik GmbH an der Universität Potsdam Multiprocessor Scheduling “Global Multiprocessor Scheduling of Aperiodic](https://reader036.vdocuments.site/reader036/viewer/2022062320/56649d385503460f94a118dd/html5/thumbnails/10.jpg)
Multiprocessor SchedulingProf. Dr. Lars Lundberg, Prof. Dr. Andreas Polze
10
H ASSO -PLATTN ER -IN STITU Tfür Softwaresystem technik G m bH an der Universität Potsdam
Alexander Küchler715659
Results I
Optimal utilization is a function of the number of processors m:
with
Uthreshold has two meanings: threshold for synthetic utilization in the admission
control of incoming tasks: accept or reject threshold for categorization of light and heavy tasks
2
2
3 2 7 8 2 for 1
1threshold
m m mU m m m
m
3 7 35.425% for thresholdU m m
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Multiprocessor SchedulingProf. Dr. Lars Lundberg, Prof. Dr. Andreas Polze
11
H ASSO -PLATTN ER -IN STITU Tfür Softwaresystem technik G m bH an der Universität Potsdam
Alexander Küchler715659
Results II
Uthreshold is an always valid bound (but not always
optimal for all multiprocessors)
Generalize previous single-processor results [1] to multiprocessors
Extend previous multiprocessor results by considering not only liquid tasks [2] which are a special case of the generalized formulas
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Multiprocessor SchedulingProf. Dr. Lars Lundberg, Prof. Dr. Andreas Polze
12
H ASSO -PLATTN ER -IN STITU Tfür Softwaresystem technik G m bH an der Universität Potsdam
Alexander Küchler715659
‘Calculating’ Uthreshold I
The idea behind the calculation is that one: compute US(t) for a worst-case critically schedulable
task pattern this depends on the number of processors and is a
function of x=Un=Cn/Dn
The calculation based upon one lemma and two theorem’s …
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Multiprocessor SchedulingProf. Dr. Lars Lundberg, Prof. Dr. Andreas Polze
13
H ASSO -PLATTN ER -IN STITU Tfür Softwaresystem technik G m bH an der Universität Potsdam
Alexander Küchler715659
‘Calculating’ Uthreshold II
Lemma 1: A task Tx and a task pattern where each Ti that has higher priority than Tx has Ai≥Ax can be modified to a task pattern with same US(t) and block interference on Tx
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Multiprocessor SchedulingProf. Dr. Lars Lundberg, Prof. Dr. Andreas Polze
14
H ASSO -PLATTN ER -IN STITU Tfür Softwaresystem technik G m bH an der Universität Potsdam
Alexander Küchler715659
‘Calculating’ Uthreshold II (Lemma 1)
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Multiprocessor SchedulingProf. Dr. Lars Lundberg, Prof. Dr. Andreas Polze
15
H ASSO -PLATTN ER -IN STITU Tfür Softwaresystem technik G m bH an der Universität Potsdam
Alexander Küchler715659
‘Calculating’ Uthreshold II (Theorem 1)
Theorem 1: There is a worst-case critically schedulable task pattern, such that no task Ti in this task pattern has an arrival time Ai<An: that means that we can disregard all tasks with an early arrival, because they do not influence the block interference
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Multiprocessor SchedulingProf. Dr. Lars Lundberg, Prof. Dr. Andreas Polze
16
H ASSO -PLATTN ER -IN STITU Tfür Softwaresystem technik G m bH an der Universität Potsdam
Alexander Küchler715659
‘Calculating’ Uthreshold II (Theorem 1)
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Multiprocessor SchedulingProf. Dr. Lars Lundberg, Prof. Dr. Andreas Polze
17
H ASSO -PLATTN ER -IN STITU Tfür Softwaresystem technik G m bH an der Universität Potsdam
Alexander Küchler715659
‘Calculating’ Uthreshold II (Theorem 1)
![Page 18: HASSO-PLATTNER-INSTITUT für Softwaresystemtechnik GmbH an der Universität Potsdam Multiprocessor Scheduling “Global Multiprocessor Scheduling of Aperiodic](https://reader036.vdocuments.site/reader036/viewer/2022062320/56649d385503460f94a118dd/html5/thumbnails/18.jpg)
Multiprocessor SchedulingProf. Dr. Lars Lundberg, Prof. Dr. Andreas Polze
18
H ASSO -PLATTN ER -IN STITU Tfür Softwaresystem technik G m bH an der Universität Potsdam
Alexander Küchler715659
‘Calculating’ Uthreshold II (Theorem 1)
![Page 19: HASSO-PLATTNER-INSTITUT für Softwaresystemtechnik GmbH an der Universität Potsdam Multiprocessor Scheduling “Global Multiprocessor Scheduling of Aperiodic](https://reader036.vdocuments.site/reader036/viewer/2022062320/56649d385503460f94a118dd/html5/thumbnails/19.jpg)
Multiprocessor SchedulingProf. Dr. Lars Lundberg, Prof. Dr. Andreas Polze
19
H ASSO -PLATTN ER -IN STITU Tfür Softwaresystem technik G m bH an der Universität Potsdam
Alexander Küchler715659
‘Calculating’ Uthreshold II (Theorem 2)
Theorem 2: Create m copies of each task disregarding Tn, the load on each processor is identical reduce of the problem to a single-processor case
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Multiprocessor SchedulingProf. Dr. Lars Lundberg, Prof. Dr. Andreas Polze
20
H ASSO -PLATTN ER -IN STITU Tfür Softwaresystem technik G m bH an der Universität Potsdam
Alexander Küchler715659
‘Calculating’ Uthreshold III
Important: by splitting each task into m new tasks block interference from high priority tasks occurs
[1] shows the worst-case how to handle the problem An quadratic equation will be solved to get an optimal
utilization bound for the single-processor case from [1] Regard for the problem of heavy tasks: m heavy tasks
with large D may lead to missed deadlines priority assignment strategy to avoid Dhall’s effect:
1. consider high utilization 2. consider short deadline
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Multiprocessor SchedulingProf. Dr. Lars Lundberg, Prof. Dr. Andreas Polze
21
H ASSO -PLATTN ER -IN STITU Tfür Softwaresystem technik G m bH an der Universität Potsdam
Alexander Küchler715659
Strategy for using the bound I
Accept incoming tasks when current
An accepted task Ti is light if
Use m: accept incoming tasks when current
An accepted task Ti is light if
35,425%thresholdUS t U
i thresholdU U
thresholdUS t U m
i thresholdU U m
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Multiprocessor SchedulingProf. Dr. Lars Lundberg, Prof. Dr. Andreas Polze
22
H ASSO -PLATTN ER -IN STITU Tfür Softwaresystem technik G m bH an der Universität Potsdam
Alexander Küchler715659
Strategy for using the bound II
Keep track of among current tasks: accept incoming tasks if for liquid tasks: accept for [2]
In admission test: for very hard tasks with
increase US(t) with
only in the interval Ai≤t≤Ai+Di, so you reduce
synthetic utilization and can accept more tasks
max max iU U maxmUS t u U
1/ 1 1/ 2US t
2 thresholdU m /thresholdU m m
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Multiprocessor SchedulingProf. Dr. Lars Lundberg, Prof. Dr. Andreas Polze
23
H ASSO -PLATTN ER -IN STITU Tfür Softwaresystem technik G m bH an der Universität Potsdam
Alexander Küchler715659
References(1) “Schedulability Analysis and Utilization Bounds for Highly Scalable Real-
Time Services”; Abdelzaher/Lu
(2) “The Aperiodic Multiprocessor Utilization Bounds for Liquid Tasks”; Abdelzaher et.al
(3) “Static-priority scheduling on multiprocessors”; Andersson/Baruah/Jonsson
(4) “Analyzing Fixed-Priority Multiprocessor Scheduling”; Lundberg
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Multiprocessor SchedulingProf. Dr. Lars Lundberg, Prof. Dr. Andreas Polze
24
H ASSO -PLATTN ER -IN STITU Tfür Softwaresystem technik G m bH an der Universität Potsdam
Alexander Küchler715659
Questions?
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