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

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 Energy reducing Energy 2 Models heuristics (ERH) Theoretical results Makespan More theory Intractability Reliability B.SUS-Crit-Slow Heuristics Energy reducing Energy A.SUS-Crit heuristics (ERH) More theory Results 3 Theoretical results B.SUS-Crit- Slow Intractability 5 Conclusion A.SUS-Crit Results Conclusion 1.0

Energy, Motivation Reliability, Makespan G. Aupy • Scheduling = Makespan minimization Introduction Difficulty of scheduling: choosing the right processor to Models assign the task to. Makespan Reliability Energy Theoretical • General mapping results Intractability If deadline not tight, why not take our time? Heuristics • Pros: Economy + environment: ց Energy. Energy reducing heuristics (ERH) • Cons: Fault-tolerance: ց Reliability. More theory B.SUS-Crit- Slow A.SUS-Crit Goal: “efficiently” use speed scaling (DVFS) Results Conclusion 2.0

Energy, Motivation Reliability, Makespan G. Aupy • Scheduling = Makespan minimization Introduction Difficulty of scheduling: choosing the right processor to Models assign the task to. Makespan Reliability Energy Theoretical • General mapping results Intractability If deadline not tight, why not take our time? Heuristics • Pros: Economy + environment: ց Energy. Energy reducing heuristics (ERH) • Cons: Fault-tolerance: ց Reliability. More theory B.SUS-Crit- Slow A.SUS-Crit Goal: “efficiently” use speed scaling (DVFS) Results Conclusion 2.0

Energy, Motivation Reliability, Makespan G. Aupy • Scheduling = Makespan minimization Introduction Difficulty of scheduling: choosing the right processor to Models assign the task to. Makespan Reliability Energy Theoretical • General mapping results Intractability If deadline not tight, why not take our time? Heuristics • Pros: Economy + environment: ց Energy. Energy reducing heuristics (ERH) • Cons: Fault-tolerance: ց Reliability. More theory B.SUS-Crit- Slow A.SUS-Crit Goal: “efficiently” use speed scaling (DVFS) Results Conclusion D 2.0

Energy, Motivation Reliability, Makespan G. Aupy • Scheduling = Makespan minimization Introduction Difficulty of scheduling: choosing the right processor to Models assign the task to. Makespan Reliability Energy Theoretical • General mapping results Intractability If deadline not tight, why not take our time? Heuristics • Pros: Economy + environment: ց Energy. Energy reducing heuristics (ERH) • Cons: Fault-tolerance: ց Reliability. More theory B.SUS-Crit- Slow A.SUS-Crit Goal: “efficiently” use speed scaling (DVFS) Results Conclusion D D 2.0

Energy, Reliability, Makespan G. Aupy Introduction Models 4 Heuristics Makespan 1 Introduction Reliability Energy reducing Energy 2 Models heuristics (ERH) Theoretical results Makespan More theory Intractability Reliability B.SUS-Crit-Slow Heuristics Energy reducing Energy A.SUS-Crit heuristics (ERH) More theory Results 3 Theoretical results B.SUS-Crit- Slow Intractability 5 Conclusion A.SUS-Crit Results Conclusion 3.0

Energy, Application Graph and Architecture Model Reliability, Makespan G. Aupy Introduction Models Makespan Reliability Energy DAG: G = ( V , E ). Theoretical n = | V | tasks T i of weight w i . results Intractability Heuristics Energy reducing heuristics (ERH) p identical processors fully-connected. More theory B.SUS-Crit- DVFS: Interval of available speeds [ f min , f max ]. One speed per Slow A.SUS-Crit task. Results Conclusion 4.0

Energy, Makespan Reliability, Makespan G. Aupy Introduction Execution time of T i at speed f i : Models Makespan Reliability E xe ( w i , f i ) = w i Energy f i Theoretical results Intractability Heuristics If T i is executed twice on the same processor at speeds f i and Energy reducing heuristics (ERH) f ′ i : More theory d i = w i + w i B.SUS-Crit- Slow A.SUS-Crit f i f ′ Results i Conclusion Constraints on makespan: End of execution before deadline D . 5.0

Energy, Reliability Reliability, Makespan G. Aupy Introduction Transient fault = local failure. No impact on the rest of the Models system. Makespan Reliability Reliability R i of task T i as a function of speed f : Energy Theoretical R i ( f ) results Intractability Heuristics 1 Energy reducing heuristics (ERH) More theory B.SUS-Crit- Slow A.SUS-Crit Results Conclusion f f min f max 6.0

Energy, Reliability Reliability, Makespan G. Aupy Introduction Transient fault = local failure. No impact on the rest of the Models system. Makespan Reliability Reliability R i of task T i as a function of speed f : Energy Theoretical R i ( f ) results Intractability Heuristics 1 R i ( f rel ) Energy reducing heuristics (ERH) More theory B.SUS-Crit- Slow A.SUS-Crit Results Conclusion f f min f rel f max 6.0

Energy, Reliability Reliability, Makespan G. Aupy Introduction Transient fault = local failure. No impact on the rest of the Models system. Makespan Reliability Reliability R i of task T i as a function of speed f : Energy Theoretical R i ( f ) results Intractability Heuristics 1 R i ( f rel ) Energy reducing heuristics (ERH) More theory B.SUS-Crit- Slow A.SUS-Crit Results Conclusion f f min f rel f max 6.0

Energy, Reliability, Makespan G. Aupy Introduction Re-execution is a solution where a task is re-executed on the Models same processor, right after the first execution. Makespan Reliability Energy Theoretical With two executions, reliability R i of task T i is: results Intractability Heuristics R i = 1 − (1 − R i ( f i ))(1 − R i ( f ′ i )) Energy reducing heuristics (ERH) More theory Constraints on reliability: B.SUS-Crit- Slow Reliability : R i ≥ R i ( f rel ), and at most one re-execution. A.SUS-Crit Results Conclusion 7.0

Energy, Reliability, Makespan G. Aupy Introduction Re-execution is a solution where a task is re-executed on the Models same processor, right after the first execution. Makespan Reliability Energy Theoretical With two executions, reliability R i of task T i is: results Intractability Heuristics R i = 1 − (1 − R i ( f i ))(1 − R i ( f ′ i )) Energy reducing heuristics (ERH) More theory Constraints on reliability: B.SUS-Crit- Slow Reliability : R i ≥ R i ( f rel ), and at most one re-execution. A.SUS-Crit Results Conclusion 7.0

Energy, Energy Reliability, Makespan G. Aupy Introduction Models Energy to execute task T i once at speed f i : Makespan Reliability Energy E i ( f i ) = E xe ( w i , f i ) f 3 i = w i f 2 Theoretical i . results Intractability → Dynamic part of classical energy models. Heuristics Energy reducing heuristics (ERH) More theory With re-executions, it is natural to take the worst-case scenario: B.SUS-Crit- Slow � � A.SUS-Crit f 2 ′ 2 Energy : E i = w i i + f Results i Conclusion 8.0

Energy, Energy Reliability, Makespan G. Aupy Introduction Models Energy to execute task T i once at speed f i : Makespan Reliability Energy E i ( f i ) = E xe ( w i , f i ) f 3 i = w i f 2 Theoretical i . results Intractability → Dynamic part of classical energy models. Heuristics Energy reducing heuristics (ERH) More theory With re-executions, it is natural to take the worst-case scenario: B.SUS-Crit- Slow � � A.SUS-Crit f 2 ′ 2 Energy : E i = w i i + f Results i Conclusion 8.0

Energy, Reliability, Makespan G. Aupy Introduction Models 4 Heuristics Makespan 1 Introduction Reliability Energy reducing Energy 2 Models heuristics (ERH) Theoretical results Makespan More theory Intractability Reliability B.SUS-Crit-Slow Heuristics Energy reducing Energy A.SUS-Crit heuristics (ERH) More theory Results 3 Theoretical results B.SUS-Crit- Slow Intractability 5 Conclusion A.SUS-Crit Results Conclusion 9.0

Energy, Tri-Crit-Cont Reliability, Makespan G. Aupy Introduction Models G = ( V , E ). Makespan Reliability Find Energy Theoretical • A schedule of the tasks results Intractability • I = { i | T i is executed twice } Heuristics Energy reducing • ∀ i ∈ I , f i , f ′ i ; ∀ i / ∈ I , f i heuristics (ERH) More theory such that B.SUS-Crit- Slow � � w i ( f 2 i + f ′ 2 w i f 2 i ) + A.SUS-Crit i Results i ∈ I i / ∈ I Conclusion is minimized, while matching reliability and deadline. 10.0

Energy, Reliability, Makespan G. Aupy Introduction Models Lemma Makespan Reliability For any solution of Tri-Crit-Cont , either Energy Theoretical • ∀ i ∈ I, f i = f ′ i , or results Intractability • there is a better solution computable in linear time. Heuristics Energy reducing heuristics (ERH) Theorem More theory B.SUS-Crit- With one processor Tri-Crit-Cont is NP-hard. Slow A.SUS-Crit Results Conclusion 11.0

Energy, Reliability, Makespan G. Aupy Introduction Models Lemma Makespan Reliability For any solution of Tri-Crit-Cont , either Energy Theoretical • ∀ i ∈ I, f i = f ′ i , or results Intractability • there is a better solution computable in linear time. Heuristics Energy reducing heuristics (ERH) Theorem More theory B.SUS-Crit- With one processor Tri-Crit-Cont is NP-hard. Slow A.SUS-Crit Results Conclusion 11.0