Energy-aware scheduling under reliability and makespan constraints - - PowerPoint PPT Presentation

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Energy-aware scheduling under reliability and makespan constraints - - PowerPoint PPT Presentation

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Energy-aware scheduling under reliability and makespan constraints Guillaume Aupy A. Benoit & Y. Robert December 20, 2012 Energy, Reliability, Makespan G. Aupy Introduction Models 4 Heuristics Makespan 1 Introduction Reliability

slide-1
SLIDE 1

Energy-aware scheduling under reliability and makespan constraints

Guillaume Aupy

  • A. Benoit & Y. Robert

December 20, 2012

slide-2
SLIDE 2

Energy, Reliability, Makespan

  • G. Aupy

Introduction Models

Makespan Reliability Energy

Theoretical results

Intractability

Heuristics

Energy reducing heuristics (ERH) More theory B.SUS-Crit- Slow A.SUS-Crit Results

Conclusion

1.0

1 Introduction 2 Models

Makespan Reliability Energy

3 Theoretical results

Intractability

4 Heuristics

Energy reducing heuristics (ERH) More theory B.SUS-Crit-Slow A.SUS-Crit Results

5 Conclusion

slide-3
SLIDE 3

Energy, Reliability, Makespan

  • G. Aupy

Introduction Models

Makespan Reliability Energy

Theoretical results

Intractability

Heuristics

Energy reducing heuristics (ERH) More theory B.SUS-Crit- Slow A.SUS-Crit Results

Conclusion

2.0

Motivation

  • Scheduling = Makespan minimization

Difficulty of scheduling: choosing the right processor to assign the task to.

  • General mapping

If deadline not tight, why not take our time?

  • Pros: Economy + environment: ց Energy.
  • Cons: Fault-tolerance: ց Reliability.

Goal: “efficiently” use speed scaling (DVFS)

slide-4
SLIDE 4

Energy, Reliability, Makespan

  • G. Aupy

Introduction Models

Makespan Reliability Energy

Theoretical results

Intractability

Heuristics

Energy reducing heuristics (ERH) More theory B.SUS-Crit- Slow A.SUS-Crit Results

Conclusion

2.0

Motivation

  • Scheduling = Makespan minimization

Difficulty of scheduling: choosing the right processor to assign the task to.

  • General mapping

If deadline not tight, why not take our time?

  • Pros: Economy + environment: ց Energy.
  • Cons: Fault-tolerance: ց Reliability.

Goal: “efficiently” use speed scaling (DVFS)

slide-5
SLIDE 5

Energy, Reliability, Makespan

  • G. Aupy

Introduction Models

Makespan Reliability Energy

Theoretical results

Intractability

Heuristics

Energy reducing heuristics (ERH) More theory B.SUS-Crit- Slow A.SUS-Crit Results

Conclusion

2.0

Motivation

  • Scheduling = Makespan minimization

Difficulty of scheduling: choosing the right processor to assign the task to.

  • General mapping

If deadline not tight, why not take our time?

  • Pros: Economy + environment: ց Energy.
  • Cons: Fault-tolerance: ց Reliability.

Goal: “efficiently” use speed scaling (DVFS)

D

slide-6
SLIDE 6

Energy, Reliability, Makespan

  • G. Aupy

Introduction Models

Makespan Reliability Energy

Theoretical results

Intractability

Heuristics

Energy reducing heuristics (ERH) More theory B.SUS-Crit- Slow A.SUS-Crit Results

Conclusion

2.0

Motivation

  • Scheduling = Makespan minimization

Difficulty of scheduling: choosing the right processor to assign the task to.

  • General mapping

If deadline not tight, why not take our time?

  • Pros: Economy + environment: ց Energy.
  • Cons: Fault-tolerance: ց Reliability.

Goal: “efficiently” use speed scaling (DVFS)

D D

slide-7
SLIDE 7

Energy, Reliability, Makespan

  • G. Aupy

Introduction Models

Makespan Reliability Energy

Theoretical results

Intractability

Heuristics

Energy reducing heuristics (ERH) More theory B.SUS-Crit- Slow A.SUS-Crit Results

Conclusion

3.0

1 Introduction 2 Models

Makespan Reliability Energy

3 Theoretical results

Intractability

4 Heuristics

Energy reducing heuristics (ERH) More theory B.SUS-Crit-Slow A.SUS-Crit Results

5 Conclusion

slide-8
SLIDE 8

Energy, Reliability, Makespan

  • G. Aupy

Introduction Models

Makespan Reliability Energy

Theoretical results

Intractability

Heuristics

Energy reducing heuristics (ERH) More theory B.SUS-Crit- Slow A.SUS-Crit Results

Conclusion

4.0

Application Graph and Architecture Model

DAG: G = (V , E). n = |V | tasks Ti of weight wi. p identical processors fully-connected. DVFS: Interval of available speeds [fmin, fmax]. One speed per task.

slide-9
SLIDE 9

Energy, Reliability, Makespan

  • G. Aupy

Introduction Models

Makespan Reliability Energy

Theoretical results

Intractability

Heuristics

Energy reducing heuristics (ERH) More theory B.SUS-Crit- Slow A.SUS-Crit Results

Conclusion

5.0

Makespan

Execution time of Ti at speed fi: Exe(wi, fi) = wi fi If Ti is executed twice on the same processor at speeds fi and f ′

i :

di = wi fi + wi f ′

i

Constraints on makespan: End of execution before deadline D.

slide-10
SLIDE 10

Energy, Reliability, Makespan

  • G. Aupy

Introduction Models

Makespan Reliability Energy

Theoretical results

Intractability

Heuristics

Energy reducing heuristics (ERH) More theory B.SUS-Crit- Slow A.SUS-Crit Results

Conclusion

6.0

Reliability

Transient fault = local failure. No impact on the rest of the system. Reliability Ri of task Ti as a function of speed f : f Ri(f ) 1 fmin fmax

slide-11
SLIDE 11

Energy, Reliability, Makespan

  • G. Aupy

Introduction Models

Makespan Reliability Energy

Theoretical results

Intractability

Heuristics

Energy reducing heuristics (ERH) More theory B.SUS-Crit- Slow A.SUS-Crit Results

Conclusion

6.0

Reliability

Transient fault = local failure. No impact on the rest of the system. Reliability Ri of task Ti as a function of speed f : f Ri(f ) 1 fmin fmax frel Ri(frel)

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SLIDE 12

Energy, Reliability, Makespan

  • G. Aupy

Introduction Models

Makespan Reliability Energy

Theoretical results

Intractability

Heuristics

Energy reducing heuristics (ERH) More theory B.SUS-Crit- Slow A.SUS-Crit Results

Conclusion

6.0

Reliability

Transient fault = local failure. No impact on the rest of the system. Reliability Ri of task Ti as a function of speed f : f Ri(f ) 1 fmin fmax frel Ri(frel)

slide-13
SLIDE 13

Energy, Reliability, Makespan

  • G. Aupy

Introduction Models

Makespan Reliability Energy

Theoretical results

Intractability

Heuristics

Energy reducing heuristics (ERH) More theory B.SUS-Crit- Slow A.SUS-Crit Results

Conclusion

7.0

Re-execution is a solution where a task is re-executed on the same processor, right after the first execution. With two executions, reliability Ri of task Ti is: Ri = 1 − (1 − Ri(fi))(1 − Ri(f ′

i ))

Constraints on reliability: Reliability: Ri ≥ Ri(frel), and at most one re-execution.

slide-14
SLIDE 14

Energy, Reliability, Makespan

  • G. Aupy

Introduction Models

Makespan Reliability Energy

Theoretical results

Intractability

Heuristics

Energy reducing heuristics (ERH) More theory B.SUS-Crit- Slow A.SUS-Crit Results

Conclusion

7.0

Re-execution is a solution where a task is re-executed on the same processor, right after the first execution. With two executions, reliability Ri of task Ti is: Ri = 1 − (1 − Ri(fi))(1 − Ri(f ′

i ))

Constraints on reliability: Reliability: Ri ≥ Ri(frel), and at most one re-execution.

slide-15
SLIDE 15

Energy, Reliability, Makespan

  • G. Aupy

Introduction Models

Makespan Reliability Energy

Theoretical results

Intractability

Heuristics

Energy reducing heuristics (ERH) More theory B.SUS-Crit- Slow A.SUS-Crit Results

Conclusion

8.0

Energy

Energy to execute task Ti once at speed fi: Ei(fi) = Exe(wi, fi)f 3

i = wif 2 i .

→ Dynamic part of classical energy models. With re-executions, it is natural to take the worst-case scenario: Energy: Ei = wi

  • f 2

i + f

′2

i

slide-16
SLIDE 16

Energy, Reliability, Makespan

  • G. Aupy

Introduction Models

Makespan Reliability Energy

Theoretical results

Intractability

Heuristics

Energy reducing heuristics (ERH) More theory B.SUS-Crit- Slow A.SUS-Crit Results

Conclusion

8.0

Energy

Energy to execute task Ti once at speed fi: Ei(fi) = Exe(wi, fi)f 3

i = wif 2 i .

→ Dynamic part of classical energy models. With re-executions, it is natural to take the worst-case scenario: Energy: Ei = wi

  • f 2

i + f

′2

i

slide-17
SLIDE 17

Energy, Reliability, Makespan

  • G. Aupy

Introduction Models

Makespan Reliability Energy

Theoretical results

Intractability

Heuristics

Energy reducing heuristics (ERH) More theory B.SUS-Crit- Slow A.SUS-Crit Results

Conclusion

9.0

1 Introduction 2 Models

Makespan Reliability Energy

3 Theoretical results

Intractability

4 Heuristics

Energy reducing heuristics (ERH) More theory B.SUS-Crit-Slow A.SUS-Crit Results

5 Conclusion

slide-18
SLIDE 18

Energy, Reliability, Makespan

  • G. Aupy

Introduction Models

Makespan Reliability Energy

Theoretical results

Intractability

Heuristics

Energy reducing heuristics (ERH) More theory B.SUS-Crit- Slow A.SUS-Crit Results

Conclusion

10.0

Tri-Crit-Cont

G = (V , E). Find

  • A schedule of the tasks
  • I = {i | Ti is executed twice}
  • ∀i ∈ I, fi, f ′

i ; ∀i /

∈ I, fi such that

  • i∈I

wi(f 2

i + f ′2 i ) +

  • i /

∈I

wif 2

i

is minimized, while matching reliability and deadline.

slide-19
SLIDE 19

Energy, Reliability, Makespan

  • G. Aupy

Introduction Models

Makespan Reliability Energy

Theoretical results

Intractability

Heuristics

Energy reducing heuristics (ERH) More theory B.SUS-Crit- Slow A.SUS-Crit Results

Conclusion

11.0

Lemma

For any solution of Tri-Crit-Cont, either

  • ∀i ∈ I, fi = f ′

i , or

  • there is a better solution computable in linear time.

Theorem

With one processor Tri-Crit-Cont is NP-hard.

slide-20
SLIDE 20

Energy, Reliability, Makespan

  • G. Aupy

Introduction Models

Makespan Reliability Energy

Theoretical results

Intractability

Heuristics

Energy reducing heuristics (ERH) More theory B.SUS-Crit- Slow A.SUS-Crit Results

Conclusion

11.0

Lemma

For any solution of Tri-Crit-Cont, either

  • ∀i ∈ I, fi = f ′

i , or

  • there is a better solution computable in linear time.

Theorem

With one processor Tri-Crit-Cont is NP-hard.

slide-21
SLIDE 21

Energy, Reliability, Makespan

  • G. Aupy

Introduction Models

Makespan Reliability Energy

Theoretical results

Intractability

Heuristics

Energy reducing heuristics (ERH) More theory B.SUS-Crit- Slow A.SUS-Crit Results

Conclusion

12.0

1 Introduction 2 Models

Makespan Reliability Energy

3 Theoretical results

Intractability

4 Heuristics

Energy reducing heuristics (ERH) More theory B.SUS-Crit-Slow A.SUS-Crit Results

5 Conclusion

slide-22
SLIDE 22

Energy, Reliability, Makespan

  • G. Aupy

Introduction Models

Makespan Reliability Energy

Theoretical results

Intractability

Heuristics

Energy reducing heuristics (ERH) More theory B.SUS-Crit- Slow A.SUS-Crit Results

Conclusion

13.0

Energy reducing heuristics (ERH)

Two-steps:

  • Mapping (NP-hard) → List-Scheduling
  • Speed Scaling + Re-execution (NP-hard) → ERH
slide-23
SLIDE 23

Energy, Reliability, Makespan

  • G. Aupy

Introduction Models

Makespan Reliability Energy

Theoretical results

Intractability

Heuristics

Energy reducing heuristics (ERH) More theory B.SUS-Crit- Slow A.SUS-Crit Results

Conclusion

13.0

Energy reducing heuristics (ERH)

Two-steps:

  • Mapping (NP-hard) → List-Scheduling
  • Speed Scaling + Re-execution (NP-hard) → ERH

The List-Scheduling heuristic maps tasks onto processors at speed fmax. We chose not to change this mapping with ERH.

slide-24
SLIDE 24

Energy, Reliability, Makespan

  • G. Aupy

Introduction Models

Makespan Reliability Energy

Theoretical results

Intractability

Heuristics

Energy reducing heuristics (ERH) More theory B.SUS-Crit- Slow A.SUS-Crit Results

Conclusion

13.0

Energy reducing heuristics (ERH)

Two-steps:

  • Mapping (NP-hard) → List-Scheduling
  • Speed Scaling + Re-execution (NP-hard) → ERH

The List-Scheduling heuristic maps tasks onto processors at speed fmax. We chose not to change this mapping with ERH.

slide-25
SLIDE 25

Energy, Reliability, Makespan

  • G. Aupy

Introduction Models

Makespan Reliability Energy

Theoretical results

Intractability

Heuristics

Energy reducing heuristics (ERH) More theory B.SUS-Crit- Slow A.SUS-Crit Results

Conclusion

14.0

More Theory

time speed

p1

Figure : Linear chain

slide-26
SLIDE 26

Energy, Reliability, Makespan

  • G. Aupy

Introduction Models

Makespan Reliability Energy

Theoretical results

Intractability

Heuristics

Energy reducing heuristics (ERH) More theory B.SUS-Crit- Slow A.SUS-Crit Results

Conclusion

14.0

More Theory

Proposition

Linear chain, one processor. Suppose frel < fmax, then the

  • ptimal solution can be computed in two rounds:

(i) Optimal deceleration; (ii) For all tasks at minimum speed frel, solve the re-execution issue.

slide-27
SLIDE 27

Energy, Reliability, Makespan

  • G. Aupy

Introduction Models

Makespan Reliability Energy

Theoretical results

Intractability

Heuristics

Energy reducing heuristics (ERH) More theory B.SUS-Crit- Slow A.SUS-Crit Results

Conclusion

14.0

More Theory

Proposition

Linear chain, one processor. Suppose frel < fmax, then the

  • ptimal solution can be computed in two rounds:

(i) Optimal deceleration; (ii) For all tasks at minimum speed frel, solve the re-execution issue.

slide-28
SLIDE 28

Energy, Reliability, Makespan

  • G. Aupy

Introduction Models

Makespan Reliability Energy

Theoretical results

Intractability

Heuristics

Energy reducing heuristics (ERH) More theory B.SUS-Crit- Slow A.SUS-Crit Results

Conclusion

14.0

More Theory

Proposition

Linear chain, one processor. Suppose frel < fmax, then the

  • ptimal solution can be computed in two rounds:

(i) Optimal deceleration; (ii) For all tasks at minimum speed frel, solve the re-execution issue.

slide-29
SLIDE 29

Energy, Reliability, Makespan

  • G. Aupy

Introduction Models

Makespan Reliability Energy

Theoretical results

Intractability

Heuristics

Energy reducing heuristics (ERH) More theory B.SUS-Crit- Slow A.SUS-Crit Results

Conclusion

15.0

time D

p1

slide-30
SLIDE 30

Energy, Reliability, Makespan

  • G. Aupy

Introduction Models

Makespan Reliability Energy

Theoretical results

Intractability

Heuristics

Energy reducing heuristics (ERH) More theory B.SUS-Crit- Slow A.SUS-Crit Results

Conclusion

15.0

time D

p1

slide-31
SLIDE 31

Energy, Reliability, Makespan

  • G. Aupy

Introduction Models

Makespan Reliability Energy

Theoretical results

Intractability

Heuristics

Energy reducing heuristics (ERH) More theory B.SUS-Crit- Slow A.SUS-Crit Results

Conclusion

15.0

time D

p1

slide-32
SLIDE 32

Energy, Reliability, Makespan

  • G. Aupy

Introduction Models

Makespan Reliability Energy

Theoretical results

Intractability

Heuristics

Energy reducing heuristics (ERH) More theory B.SUS-Crit- Slow A.SUS-Crit Results

Conclusion

15.0

time D

p1

slide-33
SLIDE 33

Energy, Reliability, Makespan

  • G. Aupy

Introduction Models

Makespan Reliability Energy

Theoretical results

Intractability

Heuristics

Energy reducing heuristics (ERH) More theory B.SUS-Crit- Slow A.SUS-Crit Results

Conclusion

15.0

time D

p1

slide-34
SLIDE 34

Energy, Reliability, Makespan

  • G. Aupy

Introduction Models

Makespan Reliability Energy

Theoretical results

Intractability

Heuristics

Energy reducing heuristics (ERH) More theory B.SUS-Crit- Slow A.SUS-Crit Results

Conclusion

15.0

time D

p1

slide-35
SLIDE 35

Energy, Reliability, Makespan

  • G. Aupy

Introduction Models

Makespan Reliability Energy

Theoretical results

Intractability

Heuristics

Energy reducing heuristics (ERH) More theory B.SUS-Crit- Slow A.SUS-Crit Results

Conclusion

15.0

time D

p1

slide-36
SLIDE 36

Energy, Reliability, Makespan

  • G. Aupy

Introduction Models

Makespan Reliability Energy

Theoretical results

Intractability

Heuristics

Energy reducing heuristics (ERH) More theory B.SUS-Crit- Slow A.SUS-Crit Results

Conclusion

15.0

time D

p1

slide-37
SLIDE 37

Energy, Reliability, Makespan

  • G. Aupy

Introduction Models

Makespan Reliability Energy

Theoretical results

Intractability

Heuristics

Energy reducing heuristics (ERH) More theory B.SUS-Crit- Slow A.SUS-Crit Results

Conclusion

16.0

BUT

slide-38
SLIDE 38

Energy, Reliability, Makespan

  • G. Aupy

Introduction Models

Makespan Reliability Energy

Theoretical results

Intractability

Heuristics

Energy reducing heuristics (ERH) More theory B.SUS-Crit- Slow A.SUS-Crit Results

Conclusion

16.0

time D

p1 p2 p3

slide-39
SLIDE 39

Energy, Reliability, Makespan

  • G. Aupy

Introduction Models

Makespan Reliability Energy

Theoretical results

Intractability

Heuristics

Energy reducing heuristics (ERH) More theory B.SUS-Crit- Slow A.SUS-Crit Results

Conclusion

16.0

time D

p1 p2 p3

slide-40
SLIDE 40

Energy, Reliability, Makespan

  • G. Aupy

Introduction Models

Makespan Reliability Energy

Theoretical results

Intractability

Heuristics

Energy reducing heuristics (ERH) More theory B.SUS-Crit- Slow A.SUS-Crit Results

Conclusion

16.0

time D

p1 p2 p3

slide-41
SLIDE 41

Energy, Reliability, Makespan

  • G. Aupy

Introduction Models

Makespan Reliability Energy

Theoretical results

Intractability

Heuristics

Energy reducing heuristics (ERH) More theory B.SUS-Crit- Slow A.SUS-Crit Results

Conclusion

16.0

time D

p1 p2 p3

slide-42
SLIDE 42

Energy, Reliability, Makespan

  • G. Aupy

Introduction Models

Makespan Reliability Energy

Theoretical results

Intractability

Heuristics

Energy reducing heuristics (ERH) More theory B.SUS-Crit- Slow A.SUS-Crit Results

Conclusion

16.0

time D

p1 p2 p3

slide-43
SLIDE 43

Energy, Reliability, Makespan

  • G. Aupy

Introduction Models

Makespan Reliability Energy

Theoretical results

Intractability

Heuristics

Energy reducing heuristics (ERH) More theory B.SUS-Crit- Slow A.SUS-Crit Results

Conclusion

16.0

time D

p1 p2 p3

slide-44
SLIDE 44

Energy, Reliability, Makespan

  • G. Aupy

Introduction Models

Makespan Reliability Energy

Theoretical results

Intractability

Heuristics

Energy reducing heuristics (ERH) More theory B.SUS-Crit- Slow A.SUS-Crit Results

Conclusion

17.0

D

p1

D

p1

D

p1 p2 p3

D

p1 p2 p3

slide-45
SLIDE 45

Energy, Reliability, Makespan

  • G. Aupy

Introduction Models

Makespan Reliability Energy

Theoretical results

Intractability

Heuristics

Energy reducing heuristics (ERH) More theory B.SUS-Crit- Slow A.SUS-Crit Results

Conclusion

18.0

Back to ERH

We define the Super-Weight (SW) of a task: time D

p1 p2 p3 p4

slide-46
SLIDE 46

Energy, Reliability, Makespan

  • G. Aupy

Introduction Models

Makespan Reliability Energy

Theoretical results

Intractability

Heuristics

Energy reducing heuristics (ERH) More theory B.SUS-Crit- Slow A.SUS-Crit Results

Conclusion

18.0

Back to ERH

We define the Super-Weight (SW) of a task: time D

p1 p2 p3 p4

s e

slide-47
SLIDE 47

Energy, Reliability, Makespan

  • G. Aupy

Introduction Models

Makespan Reliability Energy

Theoretical results

Intractability

Heuristics

Energy reducing heuristics (ERH) More theory B.SUS-Crit- Slow A.SUS-Crit Results

Conclusion

18.0

Back to ERH

We define the Super-Weight (SW) of a task: time D

p1 p2 p3 p4

s e

slide-48
SLIDE 48

Energy, Reliability, Makespan

  • G. Aupy

Introduction Models

Makespan Reliability Energy

Theoretical results

Intractability

Heuristics

Energy reducing heuristics (ERH) More theory B.SUS-Crit- Slow A.SUS-Crit Results

Conclusion

19.0

B.SUS-Crit-Slow

  • Sort the tasks of every critical path according to their

SW and try to re-execute them. If it is not possible, then try to slow them down.

  • Sort all tasks according to their weight and try to

re-execute them. If it is not possible, then try to slow them down.

slide-49
SLIDE 49

Energy, Reliability, Makespan

  • G. Aupy

Introduction Models

Makespan Reliability Energy

Theoretical results

Intractability

Heuristics

Energy reducing heuristics (ERH) More theory B.SUS-Crit- Slow A.SUS-Crit Results

Conclusion

20.0

time D

p1 p2 p3 p4

slide-50
SLIDE 50

Energy, Reliability, Makespan

  • G. Aupy

Introduction Models

Makespan Reliability Energy

Theoretical results

Intractability

Heuristics

Energy reducing heuristics (ERH) More theory B.SUS-Crit- Slow A.SUS-Crit Results

Conclusion

20.0

time D

p1 p2 p3 p4

slide-51
SLIDE 51

Energy, Reliability, Makespan

  • G. Aupy

Introduction Models

Makespan Reliability Energy

Theoretical results

Intractability

Heuristics

Energy reducing heuristics (ERH) More theory B.SUS-Crit- Slow A.SUS-Crit Results

Conclusion

20.0

time D

p1 p2 p3 p4

slide-52
SLIDE 52

Energy, Reliability, Makespan

  • G. Aupy

Introduction Models

Makespan Reliability Energy

Theoretical results

Intractability

Heuristics

Energy reducing heuristics (ERH) More theory B.SUS-Crit- Slow A.SUS-Crit Results

Conclusion

20.0

time D

p1 p2 p3 p4

slide-53
SLIDE 53

Energy, Reliability, Makespan

  • G. Aupy

Introduction Models

Makespan Reliability Energy

Theoretical results

Intractability

Heuristics

Energy reducing heuristics (ERH) More theory B.SUS-Crit- Slow A.SUS-Crit Results

Conclusion

20.0

time D

p1 p2 p3 p4

slide-54
SLIDE 54

Energy, Reliability, Makespan

  • G. Aupy

Introduction Models

Makespan Reliability Energy

Theoretical results

Intractability

Heuristics

Energy reducing heuristics (ERH) More theory B.SUS-Crit- Slow A.SUS-Crit Results

Conclusion

21.0

A.SUS-Crit

  • Set the speed of every task to max(frel, maxi=1..n di

D

fmax).

  • Sort the tasks of every critical path according to their

SW and try to re-execute them.

  • Sort all the tasks according to their weight and try to

re-execute them.

slide-55
SLIDE 55

Energy, Reliability, Makespan

  • G. Aupy

Introduction Models

Makespan Reliability Energy

Theoretical results

Intractability

Heuristics

Energy reducing heuristics (ERH) More theory B.SUS-Crit- Slow A.SUS-Crit Results

Conclusion

22.0

time D

p1 p2 p3 p4

slide-56
SLIDE 56

Energy, Reliability, Makespan

  • G. Aupy

Introduction Models

Makespan Reliability Energy

Theoretical results

Intractability

Heuristics

Energy reducing heuristics (ERH) More theory B.SUS-Crit- Slow A.SUS-Crit Results

Conclusion

22.0

time D

p1 p2 p3 p4

slide-57
SLIDE 57

Energy, Reliability, Makespan

  • G. Aupy

Introduction Models

Makespan Reliability Energy

Theoretical results

Intractability

Heuristics

Energy reducing heuristics (ERH) More theory B.SUS-Crit- Slow A.SUS-Crit Results

Conclusion

22.0

time D

p1 p2 p3 p4

slide-58
SLIDE 58

Energy, Reliability, Makespan

  • G. Aupy

Introduction Models

Makespan Reliability Energy

Theoretical results

Intractability

Heuristics

Energy reducing heuristics (ERH) More theory B.SUS-Crit- Slow A.SUS-Crit Results

Conclusion

23.0

B.SUS-Crit-Slow

p1 p2 p3 p4

A.SUS-Crit

p1 p2 p3 p4

slide-59
SLIDE 59

Energy, Reliability, Makespan

  • G. Aupy

Introduction Models

Makespan Reliability Energy

Theoretical results

Intractability

Heuristics

Energy reducing heuristics (ERH) More theory B.SUS-Crit- Slow A.SUS-Crit Results

Conclusion

24.0

We compared the impact of:

  • the number of processors p
  • the ratio of the deadline over the minimum deadline Dmin

(given by the list-scheduling at speed fmax)

  • n the output of each heuristic.
slide-60
SLIDE 60

Energy, Reliability, Makespan

  • G. Aupy

Introduction Models

Makespan Reliability Energy

Theoretical results

Intractability

Heuristics

Energy reducing heuristics (ERH) More theory B.SUS-Crit- Slow A.SUS-Crit Results

Conclusion

24.0

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 10 20 30 40 50 60 70 80 90 100 Eg / Eg_fmax Number of processors A.SUS-Crit B.SUS-Crit-Slow 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 10 20 30 40 50 60 70 80 90 100 Eg / Eg_fmax Number of processors A.SUS-Crit B.SUS-Crit-Slow

Figure : φ(p), D = 1.2 (left), D = 2.4 (right)

slide-61
SLIDE 61

Energy, Reliability, Makespan

  • G. Aupy

Introduction Models

Makespan Reliability Energy

Theoretical results

Intractability

Heuristics

Energy reducing heuristics (ERH) More theory B.SUS-Crit- Slow A.SUS-Crit Results

Conclusion

24.0

0.2 0.4 0.6 0.8 1 1 2 3 4 5 6 7 8 9 10 Eg / Eg_fmax Deadline / Deadline_Min A.SUS-Crit B.SUS-Crit-Slow 0.2 0.4 0.6 0.8 1 1 2 3 4 5 6 7 8 9 10 Eg / Eg_fmax Deadline / Deadline_Min A.SUS-Crit B.SUS-Crit-Slow

Figure : φ(D), 1 processor (left), 50 processors (right)

slide-62
SLIDE 62

Energy, Reliability, Makespan

  • G. Aupy

Introduction Models

Makespan Reliability Energy

Theoretical results

Intractability

Heuristics

Energy reducing heuristics (ERH) More theory B.SUS-Crit- Slow A.SUS-Crit Results

Conclusion

25.0

1 Introduction 2 Models

Makespan Reliability Energy

3 Theoretical results

Intractability

4 Heuristics

Energy reducing heuristics (ERH) More theory B.SUS-Crit-Slow A.SUS-Crit Results

5 Conclusion

slide-63
SLIDE 63

Energy, Reliability, Makespan

  • G. Aupy

Introduction Models

Makespan Reliability Energy

Theoretical results

Intractability

Heuristics

Energy reducing heuristics (ERH) More theory B.SUS-Crit- Slow A.SUS-Crit Results

Conclusion

26.0

  • Tri-criteria energy/makespan/reliability optimization

problem

  • Various theoretical results
  • Two-step approach for polynomial-time heuristics:
  • List-Scheduling Heuristic
  • Energy-Reducing Heuristics
  • Two complementary ERH for Tri-Crit-Cont
slide-64
SLIDE 64

Energy, Reliability, Makespan

  • G. Aupy

Introduction Models

Makespan Reliability Energy

Theoretical results

Intractability

Heuristics

Energy reducing heuristics (ERH) More theory B.SUS-Crit- Slow A.SUS-Crit Results

Conclusion

Thank you for your attention, feel free to ask any questions. If you are interested, additional material on my webpage http://gaupy.org: Approximation algorithms for energy, reliability and makespan optimization problems. I am also available by email: guillaume.aupy@ens-lyon.fr