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0 Dec. 2013 Santiago Pagani and Jian-Jia ChenEnergy Efficient Task Partitioning based on the Single Frequency Approximation Scheme
KIT
KARLSRUHE INSTITUTE OF TECHNOLOGY (KIT)
Energy Efficient Task Partitioning based on the SingleFrequency Approximation Scheme
Santiago Pagani and Jian-Jia Chen
2013 IEEE 34th Real-Time Systems Symposium (RTSS)December 3-6 2013, Vancouver, Canada
KIT – University of the State of Baden-Wuerttemberg andNational Research Center of the Helmholtz Association www.kit.edu
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Outline
1 Dec. 2013 Santiago Pagani and Jian-Jia ChenEnergy Efficient Task Partitioning based on the Single Frequency Approximation Scheme
KIT
Introduction
Motivation and Problem Definition
Task Partitioning Scheme: Double-Largest-Task-First (DLTF)
Approximation Factor Analysis (energy consumption): DLTF and SFANegligible Leakage Power Consumption
Non-negligible Leakage Power Consumption
Non-negligible Sleeping Overhead
Simulations
Conclusions
![Page 3: Energy Efficient Task Partitioning based on the Single ...cesdownloads.itec.kit.edu/pdf/pagani/Pagani-RTSS... · 2 Dec. 2013 Santiago Pagani and Jian-Jia Chen Energy Efficient Task](https://reader034.vdocuments.us/reader034/viewer/2022052009/601e4ca0e754601a697c6af1/html5/thumbnails/3.jpg)
Outline
2 Dec. 2013 Santiago Pagani and Jian-Jia ChenEnergy Efficient Task Partitioning based on the Single Frequency Approximation Scheme
KIT
Introduction
Motivation and Problem Definition
Task Partitioning Scheme: Double-Largest-Task-First (DLTF)
Approximation Factor Analysis (energy consumption): DLTF and SFANegligible Leakage Power Consumption
Non-negligible Leakage Power Consumption
Non-negligible Sleeping Overhead
Simulations
Conclusions
![Page 4: Energy Efficient Task Partitioning based on the Single ...cesdownloads.itec.kit.edu/pdf/pagani/Pagani-RTSS... · 2 Dec. 2013 Santiago Pagani and Jian-Jia Chen Energy Efficient Task](https://reader034.vdocuments.us/reader034/viewer/2022052009/601e4ca0e754601a697c6af1/html5/thumbnails/4.jpg)
Introduction
3 Dec. 2013 Santiago Pagani and Jian-Jia ChenEnergy Efficient Task Partitioning based on the Single Frequency Approximation Scheme
KIT
Importance of Energy Efficiency:
Slow increases of battery capacity.Less Energy Consumption⇒ Prolong Battery Lifetime of EmbeddedSystems.
Increasing costs of energy.Less Energy Consumption⇒ Lower Power Bills for Servers.
Outcome for Computing Systems:
Motivated to move from single-core to multi-core.
Techniques for power management.
![Page 5: Energy Efficient Task Partitioning based on the Single ...cesdownloads.itec.kit.edu/pdf/pagani/Pagani-RTSS... · 2 Dec. 2013 Santiago Pagani and Jian-Jia Chen Energy Efficient Task](https://reader034.vdocuments.us/reader034/viewer/2022052009/601e4ca0e754601a697c6af1/html5/thumbnails/5.jpg)
Introduction
3 Dec. 2013 Santiago Pagani and Jian-Jia ChenEnergy Efficient Task Partitioning based on the Single Frequency Approximation Scheme
KIT
Importance of Energy Efficiency:
Slow increases of battery capacity.Less Energy Consumption⇒ Prolong Battery Lifetime of EmbeddedSystems.
Increasing costs of energy.Less Energy Consumption⇒ Lower Power Bills for Servers.
Outcome for Computing Systems:
Motivated to move from single-core to multi-core.
Techniques for power management.
![Page 6: Energy Efficient Task Partitioning based on the Single ...cesdownloads.itec.kit.edu/pdf/pagani/Pagani-RTSS... · 2 Dec. 2013 Santiago Pagani and Jian-Jia Chen Energy Efficient Task](https://reader034.vdocuments.us/reader034/viewer/2022052009/601e4ca0e754601a697c6af1/html5/thumbnails/6.jpg)
Introduction
4 Dec. 2013 Santiago Pagani and Jian-Jia ChenEnergy Efficient Task Partitioning based on the Single Frequency Approximation Scheme
KIT
Dynamic Power Management (DPM):
Technique for putting cores in a low-power mode: idle, sleep, off, etc.
Dynamic Voltage and Frequency Scaling (DVFS):
Technique for scaling the voltage and frequency of cores.
Per-core DVFS:Individual voltage and frequency for cores.
Optimal, but too expensive to manufacture.
Global DVFS:All cores share the same voltage.
Energy inefficient.
![Page 7: Energy Efficient Task Partitioning based on the Single ...cesdownloads.itec.kit.edu/pdf/pagani/Pagani-RTSS... · 2 Dec. 2013 Santiago Pagani and Jian-Jia Chen Energy Efficient Task](https://reader034.vdocuments.us/reader034/viewer/2022052009/601e4ca0e754601a697c6af1/html5/thumbnails/7.jpg)
Introduction
4 Dec. 2013 Santiago Pagani and Jian-Jia ChenEnergy Efficient Task Partitioning based on the Single Frequency Approximation Scheme
KIT
Dynamic Power Management (DPM):
Technique for putting cores in a low-power mode: idle, sleep, off, etc.
Dynamic Voltage and Frequency Scaling (DVFS):
Technique for scaling the voltage and frequency of cores.
Per-core DVFS:Individual voltage and frequency for cores.
Optimal, but too expensive to manufacture.
Global DVFS:All cores share the same voltage.
Energy inefficient.
![Page 8: Energy Efficient Task Partitioning based on the Single ...cesdownloads.itec.kit.edu/pdf/pagani/Pagani-RTSS... · 2 Dec. 2013 Santiago Pagani and Jian-Jia Chen Energy Efficient Task](https://reader034.vdocuments.us/reader034/viewer/2022052009/601e4ca0e754601a697c6af1/html5/thumbnails/8.jpg)
Introduction
4 Dec. 2013 Santiago Pagani and Jian-Jia ChenEnergy Efficient Task Partitioning based on the Single Frequency Approximation Scheme
KIT
Dynamic Power Management (DPM):
Technique for putting cores in a low-power mode: idle, sleep, off, etc.
Dynamic Voltage and Frequency Scaling (DVFS):
Technique for scaling the voltage and frequency of cores.
Per-core DVFS:Individual voltage and frequency for cores.
Optimal, but too expensive to manufacture.
Global DVFS:All cores share the same voltage.
Energy inefficient.
![Page 9: Energy Efficient Task Partitioning based on the Single ...cesdownloads.itec.kit.edu/pdf/pagani/Pagani-RTSS... · 2 Dec. 2013 Santiago Pagani and Jian-Jia Chen Energy Efficient Task](https://reader034.vdocuments.us/reader034/viewer/2022052009/601e4ca0e754601a697c6af1/html5/thumbnails/9.jpg)
Introduction
4 Dec. 2013 Santiago Pagani and Jian-Jia ChenEnergy Efficient Task Partitioning based on the Single Frequency Approximation Scheme
KIT
Dynamic Power Management (DPM):
Technique for putting cores in a low-power mode: idle, sleep, off, etc.
Dynamic Voltage and Frequency Scaling (DVFS):
Technique for scaling the voltage and frequency of cores.
Per-core DVFS:Individual voltage and frequency for cores.
Optimal, but too expensive to manufacture.
Global DVFS:All cores share the same voltage.
Energy inefficient.
![Page 10: Energy Efficient Task Partitioning based on the Single ...cesdownloads.itec.kit.edu/pdf/pagani/Pagani-RTSS... · 2 Dec. 2013 Santiago Pagani and Jian-Jia Chen Energy Efficient Task](https://reader034.vdocuments.us/reader034/viewer/2022052009/601e4ca0e754601a697c6af1/html5/thumbnails/10.jpg)
Introduction
5 Dec. 2013 Santiago Pagani and Jian-Jia ChenEnergy Efficient Task Partitioning based on the Single Frequency Approximation Scheme
KIT
Dynamic Voltage and Frequency Scaling (DVFS):
Multiple Voltage Islands:Compromise between Per-core DVFS and Global DVFS.
Cores are grouped into Voltage Islands.
Islands can have different voltages.
Figure: Intel’s SCC snapshot
Intel Corporation. Single-chip Cloud Computer (SCC). URL:http://www.intel.com/content/www/us/en/research/intel-labs-single-chip-cloud-computer.html
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Introduction
6 Dec. 2013 Santiago Pagani and Jian-Jia ChenEnergy Efficient Task Partitioning based on the Single Frequency Approximation Scheme
KIT
CMOS-core Power Model
P (s) = Pdynamic (s) + Pstatic
Considering that:
Pdynamic (s) = CeffV2dds
s ∝(Vdd − Vt )
2
Vdd
We can approximate to:
P (s) = αsγ + β
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Introduction
6 Dec. 2013 Santiago Pagani and Jian-Jia ChenEnergy Efficient Task Partitioning based on the Single Frequency Approximation Scheme
KIT
CMOS-core Power Model
P (s) = Pdynamic (s) + Pstatic
Considering that:
Pdynamic (s) = CeffV2dds
s ∝(Vdd − Vt )
2
Vdd
We can approximate to:
P (s) = αsγ + β
![Page 13: Energy Efficient Task Partitioning based on the Single ...cesdownloads.itec.kit.edu/pdf/pagani/Pagani-RTSS... · 2 Dec. 2013 Santiago Pagani and Jian-Jia Chen Energy Efficient Task](https://reader034.vdocuments.us/reader034/viewer/2022052009/601e4ca0e754601a697c6af1/html5/thumbnails/13.jpg)
Introduction
6 Dec. 2013 Santiago Pagani and Jian-Jia ChenEnergy Efficient Task Partitioning based on the Single Frequency Approximation Scheme
KIT
CMOS-core Power Model
P (s) = Pdynamic (s) + Pstatic
Considering that:
Pdynamic (s) = CeffV2dds
s ∝(Vdd − Vt )
2
Vdd
We can approximate to:
P (s) = αsγ + β
![Page 14: Energy Efficient Task Partitioning based on the Single ...cesdownloads.itec.kit.edu/pdf/pagani/Pagani-RTSS... · 2 Dec. 2013 Santiago Pagani and Jian-Jia Chen Energy Efficient Task](https://reader034.vdocuments.us/reader034/viewer/2022052009/601e4ca0e754601a697c6af1/html5/thumbnails/14.jpg)
Introduction
6 Dec. 2013 Santiago Pagani and Jian-Jia ChenEnergy Efficient Task Partitioning based on the Single Frequency Approximation Scheme
KIT
CMOS-core Power Model
P (s) = Pdynamic (s) + Pstatic
Considering that:
Pdynamic (s) = CeffV2dds
s ∝(Vdd − Vt )
2
Vdd
We can approximate to:
P (s) = αsγ + β
0 0.5 1 1.5 20
5
10
15
1.40
7.71
Frequency [GHz]
Pow
er [W
atts
]
Figure: α = 1.76 WattsGHz3 , γ = 3 and β = 0.5 Watts
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Introduction
7 Dec. 2013 Santiago Pagani and Jian-Jia ChenEnergy Efficient Task Partitioning based on the Single Frequency Approximation Scheme
KIT
Energy Consumption
E (s) = (αsγ + β)∆cs
Critical Frequency:
scrit =γ
√β
(γ− 1) α
0 0.5 1 1.5 20
2
4
6
8
10
Frequency [GHz]
Ene
rgy
[Jou
le]
Figure: α = 1.76 WattsGHz3 , γ = 3, β = 0.5 Watts and
∆c = 109 cycles
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Outline
8 Dec. 2013 Santiago Pagani and Jian-Jia ChenEnergy Efficient Task Partitioning based on the Single Frequency Approximation Scheme
KIT
Introduction
Motivation and Problem Definition
Task Partitioning Scheme: Double-Largest-Task-First (DLTF)
Approximation Factor Analysis (energy consumption): DLTF and SFANegligible Leakage Power Consumption
Non-negligible Leakage Power Consumption
Non-negligible Sleeping Overhead
Simulations
Conclusions
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Motivation
9 Dec. 2013 Santiago Pagani and Jian-Jia ChenEnergy Efficient Task Partitioning based on the Single Frequency Approximation Scheme
KIT
In each voltage island (or Global DVFS), for energy minimization:
Task partitioning and DVFS schedule:Play a major role in energy minimization.
Task Partitioning:
Convexity of E (s): For the same workload⇒ 2 · E (s) ≤ E (2 · s).
In general, load balancing reduces the dynamic energy consumption.
Balanced solution: with high complexity and not always feasible.
Good option: polynomial time algorithm based on load balancing, e.g.,Largest-Task-First (LTF)1 strategy.
1Chuan-Yue Yang, Jian-Jia Chen, and Tei-Wei Kuo. “An Approximation Algorithm for Energy-Efficient Scheduling on A Chip
Multiprocessor”. In: Conference on Design, Automation, and Test in Europe (DATE). 2005, pp. 468–473
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Motivation
9 Dec. 2013 Santiago Pagani and Jian-Jia ChenEnergy Efficient Task Partitioning based on the Single Frequency Approximation Scheme
KIT
In each voltage island (or Global DVFS), for energy minimization:
Task partitioning and DVFS schedule:Play a major role in energy minimization.
Task Partitioning:
Convexity of E (s): For the same workload⇒ 2 · E (s) ≤ E (2 · s).
In general, load balancing reduces the dynamic energy consumption.
Balanced solution: with high complexity and not always feasible.
Good option: polynomial time algorithm based on load balancing, e.g.,Largest-Task-First (LTF)1 strategy.
1Chuan-Yue Yang, Jian-Jia Chen, and Tei-Wei Kuo. “An Approximation Algorithm for Energy-Efficient Scheduling on A Chip
Multiprocessor”. In: Conference on Design, Automation, and Test in Europe (DATE). 2005, pp. 468–473
![Page 19: Energy Efficient Task Partitioning based on the Single ...cesdownloads.itec.kit.edu/pdf/pagani/Pagani-RTSS... · 2 Dec. 2013 Santiago Pagani and Jian-Jia Chen Energy Efficient Task](https://reader034.vdocuments.us/reader034/viewer/2022052009/601e4ca0e754601a697c6af1/html5/thumbnails/19.jpg)
Motivation
10 Dec. 2013 Santiago Pagani and Jian-Jia ChenEnergy Efficient Task Partitioning based on the Single Frequency Approximation Scheme
KIT
Largest-Task-First (LTF) Strategy Example:
8 tasks: {τ1, τ2, . . . , τ8}
Partitioned into 3 task sets: {T1,T2,T3}
τ1 τ2 τ3 τ4 τ5 τ6 τ7 τ8
T1 T2 T3
τ1 τ2 τ3
τ4τ5
τ6
τ7τ8
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Motivation
10 Dec. 2013 Santiago Pagani and Jian-Jia ChenEnergy Efficient Task Partitioning based on the Single Frequency Approximation Scheme
KIT
Largest-Task-First (LTF) Strategy Example:
8 tasks: {τ1, τ2, . . . , τ8}
Partitioned into 3 task sets: {T1,T2,T3}
τ1 τ2 τ3 τ4 τ5 τ6 τ7 τ8
T1 T2 T3
τ1
τ2 τ3
τ4τ5
τ6
τ7τ8
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Motivation
10 Dec. 2013 Santiago Pagani and Jian-Jia ChenEnergy Efficient Task Partitioning based on the Single Frequency Approximation Scheme
KIT
Largest-Task-First (LTF) Strategy Example:
8 tasks: {τ1, τ2, . . . , τ8}
Partitioned into 3 task sets: {T1,T2,T3}
τ1 τ2 τ3 τ4 τ5 τ6 τ7 τ8
T1 T2 T3
τ1 τ2
τ3
τ4τ5
τ6
τ7τ8
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Motivation
10 Dec. 2013 Santiago Pagani and Jian-Jia ChenEnergy Efficient Task Partitioning based on the Single Frequency Approximation Scheme
KIT
Largest-Task-First (LTF) Strategy Example:
8 tasks: {τ1, τ2, . . . , τ8}
Partitioned into 3 task sets: {T1,T2,T3}
τ1 τ2 τ3 τ4 τ5 τ6 τ7 τ8
T1 T2 T3
τ1 τ2 τ3
τ4τ5
τ6
τ7τ8
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Motivation
10 Dec. 2013 Santiago Pagani and Jian-Jia ChenEnergy Efficient Task Partitioning based on the Single Frequency Approximation Scheme
KIT
Largest-Task-First (LTF) Strategy Example:
8 tasks: {τ1, τ2, . . . , τ8}
Partitioned into 3 task sets: {T1,T2,T3}
τ1 τ2 τ3 τ4 τ5 τ6 τ7 τ8
T1 T2 T3
τ1 τ2 τ3
τ4
τ5τ6
τ7τ8
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Motivation
10 Dec. 2013 Santiago Pagani and Jian-Jia ChenEnergy Efficient Task Partitioning based on the Single Frequency Approximation Scheme
KIT
Largest-Task-First (LTF) Strategy Example:
8 tasks: {τ1, τ2, . . . , τ8}
Partitioned into 3 task sets: {T1,T2,T3}
τ1 τ2 τ3 τ4 τ5 τ6 τ7 τ8
T1 T2 T3
τ1 τ2 τ3
τ4τ5
τ6
τ7τ8
![Page 25: Energy Efficient Task Partitioning based on the Single ...cesdownloads.itec.kit.edu/pdf/pagani/Pagani-RTSS... · 2 Dec. 2013 Santiago Pagani and Jian-Jia Chen Energy Efficient Task](https://reader034.vdocuments.us/reader034/viewer/2022052009/601e4ca0e754601a697c6af1/html5/thumbnails/25.jpg)
Motivation
10 Dec. 2013 Santiago Pagani and Jian-Jia ChenEnergy Efficient Task Partitioning based on the Single Frequency Approximation Scheme
KIT
Largest-Task-First (LTF) Strategy Example:
8 tasks: {τ1, τ2, . . . , τ8}
Partitioned into 3 task sets: {T1,T2,T3}
τ1 τ2 τ3 τ4 τ5 τ6 τ7 τ8
T1 T2 T3
τ1 τ2 τ3
τ4τ5
τ6
τ7τ8
![Page 26: Energy Efficient Task Partitioning based on the Single ...cesdownloads.itec.kit.edu/pdf/pagani/Pagani-RTSS... · 2 Dec. 2013 Santiago Pagani and Jian-Jia Chen Energy Efficient Task](https://reader034.vdocuments.us/reader034/viewer/2022052009/601e4ca0e754601a697c6af1/html5/thumbnails/26.jpg)
Motivation
10 Dec. 2013 Santiago Pagani and Jian-Jia ChenEnergy Efficient Task Partitioning based on the Single Frequency Approximation Scheme
KIT
Largest-Task-First (LTF) Strategy Example:
8 tasks: {τ1, τ2, . . . , τ8}
Partitioned into 3 task sets: {T1,T2,T3}
τ1 τ2 τ3 τ4 τ5 τ6 τ7 τ8
T1 T2 T3
τ1 τ2 τ3
τ4τ5
τ6
τ7
τ8
![Page 27: Energy Efficient Task Partitioning based on the Single ...cesdownloads.itec.kit.edu/pdf/pagani/Pagani-RTSS... · 2 Dec. 2013 Santiago Pagani and Jian-Jia Chen Energy Efficient Task](https://reader034.vdocuments.us/reader034/viewer/2022052009/601e4ca0e754601a697c6af1/html5/thumbnails/27.jpg)
Motivation
10 Dec. 2013 Santiago Pagani and Jian-Jia ChenEnergy Efficient Task Partitioning based on the Single Frequency Approximation Scheme
KIT
Largest-Task-First (LTF) Strategy Example:
8 tasks: {τ1, τ2, . . . , τ8}
Partitioned into 3 task sets: {T1,T2,T3}
τ1 τ2 τ3 τ4 τ5 τ6 τ7 τ8
T1 T2 T3
τ1 τ2 τ3
τ4τ5
τ6
τ7τ8
![Page 28: Energy Efficient Task Partitioning based on the Single ...cesdownloads.itec.kit.edu/pdf/pagani/Pagani-RTSS... · 2 Dec. 2013 Santiago Pagani and Jian-Jia Chen Energy Efficient Task](https://reader034.vdocuments.us/reader034/viewer/2022052009/601e4ca0e754601a697c6af1/html5/thumbnails/28.jpg)
Motivation
10 Dec. 2013 Santiago Pagani and Jian-Jia ChenEnergy Efficient Task Partitioning based on the Single Frequency Approximation Scheme
KIT
Largest-Task-First (LTF) Strategy Example:
8 tasks: {τ1, τ2, . . . , τ8}
Partitioned into 3 task sets: {T1,T2,T3}
τ1 τ2 τ3 τ4 τ5 τ6 τ7 τ8
T1 T2 T3
τ1 τ2 τ3
τ4τ5
τ6
τ7τ8
![Page 29: Energy Efficient Task Partitioning based on the Single ...cesdownloads.itec.kit.edu/pdf/pagani/Pagani-RTSS... · 2 Dec. 2013 Santiago Pagani and Jian-Jia Chen Energy Efficient Task](https://reader034.vdocuments.us/reader034/viewer/2022052009/601e4ca0e754601a697c6af1/html5/thumbnails/29.jpg)
Motivation
11 Dec. 2013 Santiago Pagani and Jian-Jia ChenEnergy Efficient Task Partitioning based on the Single Frequency Approximation Scheme
KIT
DVFS Schedule→ Single Frequency Approximation (SFA)2 Scheme:
Use the lowest voltage/frequency, satisfying the timing constraints.
Linear time complexity. Is the simplest and most intuitive strategy.
Not optimal, but significantly reduces the management overhead.
No frequency alignment between cores =⇒ Any uni-core DPMtechnique can be adopted individually in each core.
s
tCore 1:
su
s
tCore 2:
su
s
tCore 3:
su
s
tCore 4:
su = max {scrit,w4}
2Santiago Pagani and Jian-Jia Chen. “Energy Efficiency Analysis for the Single Frequency Approximation (SFA) Scheme”. In: Proceedings
of the 19th IEEE International Conference on Embedded and Real-Time Computing Systems and Applications (RTCSA). 2013
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Motivation
12 Dec. 2013 Santiago Pagani and Jian-Jia ChenEnergy Efficient Task Partitioning based on the Single Frequency Approximation Scheme
KIT
Combining LTF and SFA for energy minimization:
Is a practical solution.
Very easy to implement.
What is the worst-case performancein terms of energy efficiency?
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Problem Definition
13 Dec. 2013 Santiago Pagani and Jian-Jia ChenEnergy Efficient Task Partitioning based on the Single Frequency Approximation Scheme
KIT
For periodic real-time tasks, assigned on a voltage island.
Using Earliest-Deadline-First (EDF) on individual cores.
Contributions
Present a simple and practical solution for energy minimization.Task Partitioning: Double-Largest-Task-First (DLTF).
DVFS schedule: SFA.
Theoretically analyse such a solution:
AFDLTFSFA = max
EDLTFSFA
E∗OPT≤ max
EDLTFSFA
E∗↓
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Problem Definition
13 Dec. 2013 Santiago Pagani and Jian-Jia ChenEnergy Efficient Task Partitioning based on the Single Frequency Approximation Scheme
KIT
For periodic real-time tasks, assigned on a voltage island.
Using Earliest-Deadline-First (EDF) on individual cores.
Contributions
Present a simple and practical solution for energy minimization.Task Partitioning: Double-Largest-Task-First (DLTF).
DVFS schedule: SFA.
Theoretically analyse such a solution:
AFDLTFSFA = max
EDLTFSFA
E∗OPT≤ max
EDLTFSFA
E∗↓
![Page 33: Energy Efficient Task Partitioning based on the Single ...cesdownloads.itec.kit.edu/pdf/pagani/Pagani-RTSS... · 2 Dec. 2013 Santiago Pagani and Jian-Jia Chen Energy Efficient Task](https://reader034.vdocuments.us/reader034/viewer/2022052009/601e4ca0e754601a697c6af1/html5/thumbnails/33.jpg)
Problem Definition
13 Dec. 2013 Santiago Pagani and Jian-Jia ChenEnergy Efficient Task Partitioning based on the Single Frequency Approximation Scheme
KIT
For periodic real-time tasks, assigned on a voltage island.
Using Earliest-Deadline-First (EDF) on individual cores.
Contributions
Present a simple and practical solution for energy minimization.Task Partitioning: Double-Largest-Task-First (DLTF).
DVFS schedule: SFA.
Theoretically analyse such a solution:
AFDLTFSFA = max
EDLTFSFA
E∗OPT≤ max
EDLTFSFA
E∗↓
![Page 34: Energy Efficient Task Partitioning based on the Single ...cesdownloads.itec.kit.edu/pdf/pagani/Pagani-RTSS... · 2 Dec. 2013 Santiago Pagani and Jian-Jia Chen Energy Efficient Task](https://reader034.vdocuments.us/reader034/viewer/2022052009/601e4ca0e754601a697c6af1/html5/thumbnails/34.jpg)
Outline
14 Dec. 2013 Santiago Pagani and Jian-Jia ChenEnergy Efficient Task Partitioning based on the Single Frequency Approximation Scheme
KIT
Introduction
Motivation and Problem Definition
Task Partitioning Scheme: Double-Largest-Task-First (DLTF)
Approximation Factor Analysis (energy consumption): DLTF and SFANegligible Leakage Power Consumption
Non-negligible Leakage Power Consumption
Non-negligible Sleeping Overhead
Simulations
Conclusions
![Page 35: Energy Efficient Task Partitioning based on the Single ...cesdownloads.itec.kit.edu/pdf/pagani/Pagani-RTSS... · 2 Dec. 2013 Santiago Pagani and Jian-Jia Chen Energy Efficient Task](https://reader034.vdocuments.us/reader034/viewer/2022052009/601e4ca0e754601a697c6af1/html5/thumbnails/35.jpg)
Double-Largest-Task-First (DLTF)
15 Dec. 2013 Santiago Pagani and Jian-Jia ChenEnergy Efficient Task Partitioning based on the Single Frequency Approximation Scheme
KIT
Initial solution: Task partitioning with LTF.
Tasks are regrouped, shutting down all possible cores.
This reduces the energy consumption for idling under SFA:
Example: LTF and SFAs
ts
ts
ts
ts
tbreak-even time
Core 1: τ1
Core 2: τ2
Core 3: τ3
Core 4: τ4
Core 5: τ5
Example: DLTF and SFAs
ts
ts
ts
ts
tbreak-even time
Core 1: τ1
Core 2: τ2
Core 3: τ3
Core 4:
τ4
Core 5:
τ5
![Page 36: Energy Efficient Task Partitioning based on the Single ...cesdownloads.itec.kit.edu/pdf/pagani/Pagani-RTSS... · 2 Dec. 2013 Santiago Pagani and Jian-Jia Chen Energy Efficient Task](https://reader034.vdocuments.us/reader034/viewer/2022052009/601e4ca0e754601a697c6af1/html5/thumbnails/36.jpg)
Double-Largest-Task-First (DLTF)
15 Dec. 2013 Santiago Pagani and Jian-Jia ChenEnergy Efficient Task Partitioning based on the Single Frequency Approximation Scheme
KIT
Initial solution: Task partitioning with LTF.
Tasks are regrouped, shutting down all possible cores.
This reduces the energy consumption for idling under SFA:
Example: LTF and SFAs
ts
ts
ts
ts
tbreak-even time
Core 1: τ1
Core 2: τ2
Core 3: τ3
Core 4: τ4
Core 5: τ5
Example: DLTF and SFAs
ts
ts
ts
ts
tbreak-even time
Core 1: τ1
Core 2: τ2
Core 3: τ3
Core 4:
τ4
Core 5:
τ5
![Page 37: Energy Efficient Task Partitioning based on the Single ...cesdownloads.itec.kit.edu/pdf/pagani/Pagani-RTSS... · 2 Dec. 2013 Santiago Pagani and Jian-Jia Chen Energy Efficient Task](https://reader034.vdocuments.us/reader034/viewer/2022052009/601e4ca0e754601a697c6af1/html5/thumbnails/37.jpg)
Double-Largest-Task-First (DLTF)
15 Dec. 2013 Santiago Pagani and Jian-Jia ChenEnergy Efficient Task Partitioning based on the Single Frequency Approximation Scheme
KIT
Initial solution: Task partitioning with LTF.
Tasks are regrouped, shutting down all possible cores.
This reduces the energy consumption for idling under SFA:
Example: LTF and SFAs
ts
ts
ts
ts
tbreak-even time
Core 1: τ1
Core 2: τ2
Core 3: τ3
Core 4: τ4
Core 5: τ5
Example: DLTF and SFAs
ts
ts
ts
ts
tbreak-even time
Core 1: τ1
Core 2: τ2
Core 3: τ3
Core 4:
τ4
Core 5:
τ5
![Page 38: Energy Efficient Task Partitioning based on the Single ...cesdownloads.itec.kit.edu/pdf/pagani/Pagani-RTSS... · 2 Dec. 2013 Santiago Pagani and Jian-Jia Chen Energy Efficient Task](https://reader034.vdocuments.us/reader034/viewer/2022052009/601e4ca0e754601a697c6af1/html5/thumbnails/38.jpg)
Double-Largest-Task-First (DLTF)
16 Dec. 2013 Santiago Pagani and Jian-Jia ChenEnergy Efficient Task Partitioning based on the Single Frequency Approximation Scheme
KIT
Example:
8 tasks: {τ1, τ2, . . . , τ8}
Partitioned into 4 task sets:{
TDLTF1 ,TDLTF
2 , . . . ,TDLTF4
}
TDLTF1 TDLTF
2 TDLTF3 TDLTF
4
τ1
τ2 τ3 τ4
τ5τ6τ7
τ8
τ4
τ5
τ5
τ6
τ5
![Page 39: Energy Efficient Task Partitioning based on the Single ...cesdownloads.itec.kit.edu/pdf/pagani/Pagani-RTSS... · 2 Dec. 2013 Santiago Pagani and Jian-Jia Chen Energy Efficient Task](https://reader034.vdocuments.us/reader034/viewer/2022052009/601e4ca0e754601a697c6af1/html5/thumbnails/39.jpg)
Double-Largest-Task-First (DLTF)
16 Dec. 2013 Santiago Pagani and Jian-Jia ChenEnergy Efficient Task Partitioning based on the Single Frequency Approximation Scheme
KIT
Example:
8 tasks: {τ1, τ2, . . . , τ8}
Partitioned into 4 task sets:{
TDLTF1 ,TDLTF
2 , . . . ,TDLTF4
}
TDLTF1 TDLTF
2 TDLTF3 TDLTF
4
τ1
τ2 τ3 τ4
τ5τ6τ7
τ8
τ4
τ5
τ5
τ6
τ5
![Page 40: Energy Efficient Task Partitioning based on the Single ...cesdownloads.itec.kit.edu/pdf/pagani/Pagani-RTSS... · 2 Dec. 2013 Santiago Pagani and Jian-Jia Chen Energy Efficient Task](https://reader034.vdocuments.us/reader034/viewer/2022052009/601e4ca0e754601a697c6af1/html5/thumbnails/40.jpg)
Double-Largest-Task-First (DLTF)
16 Dec. 2013 Santiago Pagani and Jian-Jia ChenEnergy Efficient Task Partitioning based on the Single Frequency Approximation Scheme
KIT
Example:
8 tasks: {τ1, τ2, . . . , τ8}
Partitioned into 4 task sets:{
TDLTF1 ,TDLTF
2 , . . . ,TDLTF4
}
TDLTF1 TDLTF
2 TDLTF3 TDLTF
4
τ1
τ2 τ3 τ4
τ5τ6τ7
τ8
τ4
τ5
τ5
τ6
τ5
![Page 41: Energy Efficient Task Partitioning based on the Single ...cesdownloads.itec.kit.edu/pdf/pagani/Pagani-RTSS... · 2 Dec. 2013 Santiago Pagani and Jian-Jia Chen Energy Efficient Task](https://reader034.vdocuments.us/reader034/viewer/2022052009/601e4ca0e754601a697c6af1/html5/thumbnails/41.jpg)
Double-Largest-Task-First (DLTF)
16 Dec. 2013 Santiago Pagani and Jian-Jia ChenEnergy Efficient Task Partitioning based on the Single Frequency Approximation Scheme
KIT
Example:
8 tasks: {τ1, τ2, . . . , τ8}
Partitioned into 4 task sets:{
TDLTF1 ,TDLTF
2 , . . . ,TDLTF4
}
TDLTF1 TDLTF
2 TDLTF3 TDLTF
4
τ1
τ2 τ3 τ4
τ5τ6τ7
τ8
τ4
τ5
τ5
τ6
τ5
![Page 42: Energy Efficient Task Partitioning based on the Single ...cesdownloads.itec.kit.edu/pdf/pagani/Pagani-RTSS... · 2 Dec. 2013 Santiago Pagani and Jian-Jia Chen Energy Efficient Task](https://reader034.vdocuments.us/reader034/viewer/2022052009/601e4ca0e754601a697c6af1/html5/thumbnails/42.jpg)
Double-Largest-Task-First (DLTF)
16 Dec. 2013 Santiago Pagani and Jian-Jia ChenEnergy Efficient Task Partitioning based on the Single Frequency Approximation Scheme
KIT
Example:
8 tasks: {τ1, τ2, . . . , τ8}
Partitioned into 4 task sets:{
TDLTF1 ,TDLTF
2 , . . . ,TDLTF4
}
TDLTF1 TDLTF
2 TDLTF3 TDLTF
4
τ1
τ2 τ3 τ4
τ5τ6τ7
τ8
τ4
τ5
τ5
τ6
τ5
![Page 43: Energy Efficient Task Partitioning based on the Single ...cesdownloads.itec.kit.edu/pdf/pagani/Pagani-RTSS... · 2 Dec. 2013 Santiago Pagani and Jian-Jia Chen Energy Efficient Task](https://reader034.vdocuments.us/reader034/viewer/2022052009/601e4ca0e754601a697c6af1/html5/thumbnails/43.jpg)
Double-Largest-Task-First (DLTF)
16 Dec. 2013 Santiago Pagani and Jian-Jia ChenEnergy Efficient Task Partitioning based on the Single Frequency Approximation Scheme
KIT
Example:
8 tasks: {τ1, τ2, . . . , τ8}
Partitioned into 4 task sets:{
TDLTF1 ,TDLTF
2 , . . . ,TDLTF4
}
TDLTF1 TDLTF
2 TDLTF3 TDLTF
4
τ1
τ2 τ3 τ4
τ5τ6τ7
τ8
τ4
τ5
τ5
τ6
τ5
![Page 44: Energy Efficient Task Partitioning based on the Single ...cesdownloads.itec.kit.edu/pdf/pagani/Pagani-RTSS... · 2 Dec. 2013 Santiago Pagani and Jian-Jia Chen Energy Efficient Task](https://reader034.vdocuments.us/reader034/viewer/2022052009/601e4ca0e754601a697c6af1/html5/thumbnails/44.jpg)
Double-Largest-Task-First (DLTF)
16 Dec. 2013 Santiago Pagani and Jian-Jia ChenEnergy Efficient Task Partitioning based on the Single Frequency Approximation Scheme
KIT
Example:
8 tasks: {τ1, τ2, . . . , τ8}
Partitioned into 4 task sets:{
TDLTF1 ,TDLTF
2 , . . . ,TDLTF4
}
TDLTF1 TDLTF
2 TDLTF3 TDLTF
4
τ1
τ2 τ3 τ4
τ5τ6τ7
τ8
τ4
τ5
τ5
τ6
τ5
![Page 45: Energy Efficient Task Partitioning based on the Single ...cesdownloads.itec.kit.edu/pdf/pagani/Pagani-RTSS... · 2 Dec. 2013 Santiago Pagani and Jian-Jia Chen Energy Efficient Task](https://reader034.vdocuments.us/reader034/viewer/2022052009/601e4ca0e754601a697c6af1/html5/thumbnails/45.jpg)
Properties of Double-Largest-Task-First (DLTF)
17 Dec. 2013 Santiago Pagani and Jian-Jia ChenEnergy Efficient Task Partitioning based on the Single Frequency Approximation Scheme
KIT
If wLTFM < scrit, then:
wDLTF1 ≤ wDLTF
1 ≤ · · · ≤ wDLTFM < scrit
All cores run at the critical frequency: su = scrit
The energy consumption for execution is minimized.
EDLTFSFA = E∗OPT ⇒ AFDLTF
SFA = 1
If wLTFM ≥ scrit, then:
wDLTFM = wLTF
M
If there is only one task in TDLTFM ⇒ wDLTF
M ≤ w∗M
If there are at least two tasks in TDLTFM ⇒ wDLTF
Mw∗M≤ θLTF = 4
3 −1
3M
![Page 46: Energy Efficient Task Partitioning based on the Single ...cesdownloads.itec.kit.edu/pdf/pagani/Pagani-RTSS... · 2 Dec. 2013 Santiago Pagani and Jian-Jia Chen Energy Efficient Task](https://reader034.vdocuments.us/reader034/viewer/2022052009/601e4ca0e754601a697c6af1/html5/thumbnails/46.jpg)
Properties of Double-Largest-Task-First (DLTF)
17 Dec. 2013 Santiago Pagani and Jian-Jia ChenEnergy Efficient Task Partitioning based on the Single Frequency Approximation Scheme
KIT
If wLTFM < scrit, then:
wDLTF1 ≤ wDLTF
1 ≤ · · · ≤ wDLTFM < scrit
All cores run at the critical frequency: su = scrit
The energy consumption for execution is minimized.
EDLTFSFA = E∗OPT ⇒ AFDLTF
SFA = 1
If wLTFM ≥ scrit, then:
wDLTFM = wLTF
M
If there is only one task in TDLTFM ⇒ wDLTF
M ≤ w∗M
If there are at least two tasks in TDLTFM ⇒ wDLTF
Mw∗M≤ θLTF = 4
3 −1
3M
![Page 47: Energy Efficient Task Partitioning based on the Single ...cesdownloads.itec.kit.edu/pdf/pagani/Pagani-RTSS... · 2 Dec. 2013 Santiago Pagani and Jian-Jia Chen Energy Efficient Task](https://reader034.vdocuments.us/reader034/viewer/2022052009/601e4ca0e754601a697c6af1/html5/thumbnails/47.jpg)
Outline
18 Dec. 2013 Santiago Pagani and Jian-Jia ChenEnergy Efficient Task Partitioning based on the Single Frequency Approximation Scheme
KIT
Introduction
Motivation and Problem Definition
Task Partitioning Scheme: Double-Largest-Task-First (DLTF)
Approximation Factor Analysis (energy consumption): DLTF and SFANegligible Leakage Power Consumption
Non-negligible Leakage Power Consumption
Non-negligible Sleeping Overhead
Simulations
Conclusions
![Page 48: Energy Efficient Task Partitioning based on the Single ...cesdownloads.itec.kit.edu/pdf/pagani/Pagani-RTSS... · 2 Dec. 2013 Santiago Pagani and Jian-Jia Chen Energy Efficient Task](https://reader034.vdocuments.us/reader034/viewer/2022052009/601e4ca0e754601a697c6af1/html5/thumbnails/48.jpg)
Negligible Leakage Power Consumption
19 Dec. 2013 Santiago Pagani and Jian-Jia ChenEnergy Efficient Task Partitioning based on the Single Frequency Approximation Scheme
KIT
Energy Consumption for DLTF and SFA (when β = 0):
EDLTFSFA = P (su)
Lsu
M
∑i=1
wDLTFi ⇒ EDLTF
SFA = αL(
wDLTFM
γ−1) M
∑i=1
w∗i
Lower Bound Energy Consumption (when β = 0):
Unroll periodic tasks in a hyper-period⇒ frame-based tasks.
Use the results from the SFA analysis paper 3:
E∗↓(β=0) = αL
[M∑
i=1
(w∗i −w∗i−1
) γ√
M − i + 1]γ
3Santiago Pagani and Jian-Jia Chen. “Energy Efficiency Analysis for the Single Frequency Approximation (SFA) Scheme”. In: Proceedings
of the 19th IEEE International Conference on Embedded and Real-Time Computing Systems and Applications (RTCSA). 2013
![Page 49: Energy Efficient Task Partitioning based on the Single ...cesdownloads.itec.kit.edu/pdf/pagani/Pagani-RTSS... · 2 Dec. 2013 Santiago Pagani and Jian-Jia Chen Energy Efficient Task](https://reader034.vdocuments.us/reader034/viewer/2022052009/601e4ca0e754601a697c6af1/html5/thumbnails/49.jpg)
Negligible Leakage Power Consumption
19 Dec. 2013 Santiago Pagani and Jian-Jia ChenEnergy Efficient Task Partitioning based on the Single Frequency Approximation Scheme
KIT
Energy Consumption for DLTF and SFA (when β = 0):
EDLTFSFA = P (su)
Lsu
M
∑i=1
wDLTFi ⇒ EDLTF
SFA = αL(
wDLTFM
γ−1) M
∑i=1
w∗i
Lower Bound Energy Consumption (when β = 0):
Unroll periodic tasks in a hyper-period⇒ frame-based tasks.
Use the results from the SFA analysis paper 3:
E∗↓(β=0) = αL
[M∑
i=1
(w∗i −w∗i−1
) γ√
M − i + 1]γ
3Santiago Pagani and Jian-Jia Chen. “Energy Efficiency Analysis for the Single Frequency Approximation (SFA) Scheme”. In: Proceedings
of the 19th IEEE International Conference on Embedded and Real-Time Computing Systems and Applications (RTCSA). 2013
![Page 50: Energy Efficient Task Partitioning based on the Single ...cesdownloads.itec.kit.edu/pdf/pagani/Pagani-RTSS... · 2 Dec. 2013 Santiago Pagani and Jian-Jia Chen Energy Efficient Task](https://reader034.vdocuments.us/reader034/viewer/2022052009/601e4ca0e754601a697c6af1/html5/thumbnails/50.jpg)
Negligible Leakage Power Consumption
20 Dec. 2013 Santiago Pagani and Jian-Jia ChenEnergy Efficient Task Partitioning based on the Single Frequency Approximation Scheme
KIT
Approximation Factor for DLTF and SFA (when β = 0):
AFDLTFSFA
(β=0) ≤ max
(wDLTF
M
)γ−1 M∑
i=1w∗i[
M∑
i=1
(w∗i −w∗i−1
)γ√
M − i + 1]γ
Critical Cycle Utilization Distribution: Minimizes E∗↓ , for a fixed
M∑
i=1w∗i
· · ·w∗1
w∗2w∗M-1
w∗M
· · ·w ′1 w ′2 w ′M-1
w ′M
w ′1 = w ′2 = · · · = w ′M−1 = Average(w∗1 ,w
∗2 , . . . ,w∗M−1
)Utilization Ratio: 0 ≤ δ =
Average(w∗1 ,w∗2 ,...,w
∗M−1)
w∗M≤ 1
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Negligible Leakage Power Consumption
20 Dec. 2013 Santiago Pagani and Jian-Jia ChenEnergy Efficient Task Partitioning based on the Single Frequency Approximation Scheme
KIT
Approximation Factor for DLTF and SFA (when β = 0):
AFDLTFSFA
(β=0) ≤ max
(wDLTF
M
)γ−1 M∑
i=1w∗i[
M∑
i=1
(w∗i −w∗i−1
)γ√
M − i + 1]γ
Critical Cycle Utilization Distribution: Minimizes E∗↓ , for a fixed
M∑
i=1w∗i
· · ·w∗1
w∗2w∗M-1
w∗M
· · ·w ′1 w ′2 w ′M-1
w ′M
w ′1 = w ′2 = · · · = w ′M−1 = Average(w∗1 ,w
∗2 , . . . ,w∗M−1
)Utilization Ratio: 0 ≤ δ =
Average(w∗1 ,w∗2 ,...,w
∗M−1)
w∗M≤ 1
![Page 52: Energy Efficient Task Partitioning based on the Single ...cesdownloads.itec.kit.edu/pdf/pagani/Pagani-RTSS... · 2 Dec. 2013 Santiago Pagani and Jian-Jia Chen Energy Efficient Task](https://reader034.vdocuments.us/reader034/viewer/2022052009/601e4ca0e754601a697c6af1/html5/thumbnails/52.jpg)
Negligible Leakage Power Consumption
21 Dec. 2013 Santiago Pagani and Jian-Jia ChenEnergy Efficient Task Partitioning based on the Single Frequency Approximation Scheme
KIT
Approximation Factor for DLTF and SFA (when β = 0):
AFDLTFSFA
(β=0) ≤ max
(
wDLTFMw∗M
)γ−1
· h (δ)
where
h (δ) =1− δ + δM(
1− δ + δγ√
M)γ ≤ h (δmax)
and
δmax =
1γ−1
(γ− 1 + M − γ
γ√
M)
(M γ√
M −M − γ√
M + 1)
![Page 53: Energy Efficient Task Partitioning based on the Single ...cesdownloads.itec.kit.edu/pdf/pagani/Pagani-RTSS... · 2 Dec. 2013 Santiago Pagani and Jian-Jia Chen Energy Efficient Task](https://reader034.vdocuments.us/reader034/viewer/2022052009/601e4ca0e754601a697c6af1/html5/thumbnails/53.jpg)
Negligible Leakage Power Consumption
21 Dec. 2013 Santiago Pagani and Jian-Jia ChenEnergy Efficient Task Partitioning based on the Single Frequency Approximation Scheme
KIT
Approximation Factor for DLTF and SFA (when β = 0):
AFDLTFSFA
(β=0) ≤ max
(
wDLTFMw∗M
)γ−1
· h (δ)
where
h (δ) =1− δ + δM(
1− δ + δγ√
M)γ ≤ h (δmax)
and
δmax =
1γ−1
(γ− 1 + M − γ
γ√
M)
(M γ√
M −M − γ√
M + 1)
![Page 54: Energy Efficient Task Partitioning based on the Single ...cesdownloads.itec.kit.edu/pdf/pagani/Pagani-RTSS... · 2 Dec. 2013 Santiago Pagani and Jian-Jia Chen Energy Efficient Task](https://reader034.vdocuments.us/reader034/viewer/2022052009/601e4ca0e754601a697c6af1/html5/thumbnails/54.jpg)
Negligible Leakage Power Consumption
21 Dec. 2013 Santiago Pagani and Jian-Jia ChenEnergy Efficient Task Partitioning based on the Single Frequency Approximation Scheme
KIT
Approximation Factor for DLTF and SFA (when β = 0):
AFDLTFSFA
(β=0) ≤ max
(
wDLTFMw∗M
)γ−1
· h (δ)
where
h (δ) =1− δ + δM(
1− δ + δγ√
M)γ ≤ h (δmax)
and
δmax =
1γ−1
(γ− 1 + M − γ
γ√
M)
(M γ√
M −M − γ√
M + 1)
h (δ) for γ = 3:
0 0.5 11
1.5
2
2.5 M=32
δ
h(δ)
![Page 55: Energy Efficient Task Partitioning based on the Single ...cesdownloads.itec.kit.edu/pdf/pagani/Pagani-RTSS... · 2 Dec. 2013 Santiago Pagani and Jian-Jia Chen Energy Efficient Task](https://reader034.vdocuments.us/reader034/viewer/2022052009/601e4ca0e754601a697c6af1/html5/thumbnails/55.jpg)
Negligible Leakage Power Consumption
21 Dec. 2013 Santiago Pagani and Jian-Jia ChenEnergy Efficient Task Partitioning based on the Single Frequency Approximation Scheme
KIT
Approximation Factor for DLTF and SFA (when β = 0):
AFDLTFSFA
(β=0) ≤ max
(
wDLTFMw∗M
)γ−1
· h (δ)
where
h (δ) =1− δ + δM(
1− δ + δγ√
M)γ ≤ h (δmax)
and
δmax =
1γ−1
(γ− 1 + M − γ
γ√
M)
(M γ√
M −M − γ√
M + 1)
h (δ) for γ = 3:
0 0.5 11
1.5
2
2.5 M=32
δ
h(δ)
δmax
![Page 56: Energy Efficient Task Partitioning based on the Single ...cesdownloads.itec.kit.edu/pdf/pagani/Pagani-RTSS... · 2 Dec. 2013 Santiago Pagani and Jian-Jia Chen Energy Efficient Task](https://reader034.vdocuments.us/reader034/viewer/2022052009/601e4ca0e754601a697c6af1/html5/thumbnails/56.jpg)
Negligible Leakage Power Consumption
21 Dec. 2013 Santiago Pagani and Jian-Jia ChenEnergy Efficient Task Partitioning based on the Single Frequency Approximation Scheme
KIT
Approximation Factor for DLTF and SFA (when β = 0):
AFDLTFSFA
(β=0) ≤ max
(
wDLTFMw∗M
)γ−1
· h (δ)
where
h (δ) =1− δ + δM(
1− δ + δγ√
M)γ ≤ h (δmax)
and
δmax =
1γ−1
(γ− 1 + M − γ
γ√
M)
(M γ√
M −M − γ√
M + 1)
h (δ) for γ = 3:
0 0.5 11
1.5
2
2.5
δmax
M=2M=4
M=8
M=16
M=32
δ
h(δ)
![Page 57: Energy Efficient Task Partitioning based on the Single ...cesdownloads.itec.kit.edu/pdf/pagani/Pagani-RTSS... · 2 Dec. 2013 Santiago Pagani and Jian-Jia Chen Energy Efficient Task](https://reader034.vdocuments.us/reader034/viewer/2022052009/601e4ca0e754601a697c6af1/html5/thumbnails/57.jpg)
Negligible Leakage Power Consumption
22 Dec. 2013 Santiago Pagani and Jian-Jia ChenEnergy Efficient Task Partitioning based on the Single Frequency Approximation Scheme
KIT
Approximation Factor for DLTF and SFA (when β = 0):
If w∗M ≥ wDLTFM ⇒ w ′M = wDLTF
M → Same AF as for fixed task sets
0 8 16 24 321
2
3
M
AF
n.p.
SFA
(β=0)
1.81
1.41
1.17
AFSFAn.p. (β = 0) (γ=3)
AFSFAn.p. (β = 0) (γ=2)
Note: AFn.p.SFA
(β=0)only depends on the values of γ and M.
![Page 58: Energy Efficient Task Partitioning based on the Single ...cesdownloads.itec.kit.edu/pdf/pagani/Pagani-RTSS... · 2 Dec. 2013 Santiago Pagani and Jian-Jia Chen Energy Efficient Task](https://reader034.vdocuments.us/reader034/viewer/2022052009/601e4ca0e754601a697c6af1/html5/thumbnails/58.jpg)
Negligible Leakage Power Consumption
23 Dec. 2013 Santiago Pagani and Jian-Jia ChenEnergy Efficient Task Partitioning based on the Single Frequency Approximation Scheme
KIT
Approximation Factor for DLTF and SFA (when β = 0):
If w∗M < wDLTFM ⇒
If δ > δmax ⇒ h (δ) < h (δmax):
0 0.5 11
1.5
2
2.5
M=2M=4
M=8
M=16
M=32
δ
h(δ)
We prove that:
δ ≥w ′1w ′M≥ 4M + 1
6M≥ 0.66
The AF for this case is ≤ θγ−1LTF · h
(4M+1
6M
)
![Page 59: Energy Efficient Task Partitioning based on the Single ...cesdownloads.itec.kit.edu/pdf/pagani/Pagani-RTSS... · 2 Dec. 2013 Santiago Pagani and Jian-Jia Chen Energy Efficient Task](https://reader034.vdocuments.us/reader034/viewer/2022052009/601e4ca0e754601a697c6af1/html5/thumbnails/59.jpg)
Negligible Leakage Power Consumption
23 Dec. 2013 Santiago Pagani and Jian-Jia ChenEnergy Efficient Task Partitioning based on the Single Frequency Approximation Scheme
KIT
Approximation Factor for DLTF and SFA (when β = 0):
If w∗M < wDLTFM ⇒
If δ > δmax ⇒ h (δ) < h (δmax):
0 0.5 11
1.5
2
2.5
M=2M=4
M=8
M=16
M=32
δ
h(δ)
We prove that:
δ ≥w ′1w ′M≥ 4M + 1
6M≥ 0.66
The AF for this case is ≤ θγ−1LTF · h
(4M+1
6M
)
![Page 60: Energy Efficient Task Partitioning based on the Single ...cesdownloads.itec.kit.edu/pdf/pagani/Pagani-RTSS... · 2 Dec. 2013 Santiago Pagani and Jian-Jia Chen Energy Efficient Task](https://reader034.vdocuments.us/reader034/viewer/2022052009/601e4ca0e754601a697c6af1/html5/thumbnails/60.jpg)
Negligible Leakage Power Consumption
23 Dec. 2013 Santiago Pagani and Jian-Jia ChenEnergy Efficient Task Partitioning based on the Single Frequency Approximation Scheme
KIT
Approximation Factor for DLTF and SFA (when β = 0):
If w∗M < wDLTFM ⇒
If δ > δmax ⇒ h (δ) < h (δmax):
0 0.5 11
1.5
2
2.5
M=2M=4
M=8
M=16
M=32
δ
h(δ)
We prove that:
δ ≥w ′1w ′M≥ 4M + 1
6M≥ 0.66
The AF for this case is ≤ θγ−1LTF · h
(4M+1
6M
)
![Page 61: Energy Efficient Task Partitioning based on the Single ...cesdownloads.itec.kit.edu/pdf/pagani/Pagani-RTSS... · 2 Dec. 2013 Santiago Pagani and Jian-Jia Chen Energy Efficient Task](https://reader034.vdocuments.us/reader034/viewer/2022052009/601e4ca0e754601a697c6af1/html5/thumbnails/61.jpg)
Negligible Leakage Power Consumption
24 Dec. 2013 Santiago Pagani and Jian-Jia ChenEnergy Efficient Task Partitioning based on the Single Frequency Approximation Scheme
KIT
Worst-case Approximation Factor for DLTF and SFA (when β = 0):
AFDLTFSFA
(β=0) ≤ max{
h (δmax) , θγ−1LTF · h
(4M + 1
6M
)}
0 8 16 24 32 40 481
2
3
4
M
AFDLTF
SFA
(β=0)
AFDLTFSFA
(β=0 )whenγ = 3
θγ−1LTF · h(
4M +16M ) when γ = 3
h(δmax ) when γ = 3
AFDLTFSFA
(β=0 )whenγ = 2
θγ−1LTF · h(
4M +16M ) when γ = 2
h(δmax ) when γ = 2
Note: AFDLTFSFA
(β=0)only depends on the values of γ and M.
![Page 62: Energy Efficient Task Partitioning based on the Single ...cesdownloads.itec.kit.edu/pdf/pagani/Pagani-RTSS... · 2 Dec. 2013 Santiago Pagani and Jian-Jia Chen Energy Efficient Task](https://reader034.vdocuments.us/reader034/viewer/2022052009/601e4ca0e754601a697c6af1/html5/thumbnails/62.jpg)
Outline
25 Dec. 2013 Santiago Pagani and Jian-Jia ChenEnergy Efficient Task Partitioning based on the Single Frequency Approximation Scheme
KIT
Introduction
Motivation and Problem Definition
Task Partitioning Scheme: Double-Largest-Task-First (DLTF)
Approximation Factor Analysis (energy consumption): DLTF and SFANegligible Leakage Power Consumption
Non-negligible Leakage Power Consumption
Non-negligible Sleeping Overhead
Simulations
Conclusions
![Page 63: Energy Efficient Task Partitioning based on the Single ...cesdownloads.itec.kit.edu/pdf/pagani/Pagani-RTSS... · 2 Dec. 2013 Santiago Pagani and Jian-Jia Chen Energy Efficient Task](https://reader034.vdocuments.us/reader034/viewer/2022052009/601e4ca0e754601a697c6af1/html5/thumbnails/63.jpg)
Non-negligible Leakage Power Consumption
26 Dec. 2013 Santiago Pagani and Jian-Jia ChenEnergy Efficient Task Partitioning based on the Single Frequency Approximation Scheme
KIT
We approximate the Lower Bound Energy Consumption:
0 0.5 1 1.5 2 2.50
20
40
60
80 if wM
* > sdyn
:
P(s) = α sγ
if wM
* ≤ sdyn
:
P(s) = α scrit
γ + β
smin
scrit
sdyn
smax
w∗
M[GHz]
E∗ ↓(w
∗ M)[Joule]
![Page 64: Energy Efficient Task Partitioning based on the Single ...cesdownloads.itec.kit.edu/pdf/pagani/Pagani-RTSS... · 2 Dec. 2013 Santiago Pagani and Jian-Jia Chen Energy Efficient Task](https://reader034.vdocuments.us/reader034/viewer/2022052009/601e4ca0e754601a697c6af1/html5/thumbnails/64.jpg)
Non-negligible Leakage Power Consumption
26 Dec. 2013 Santiago Pagani and Jian-Jia ChenEnergy Efficient Task Partitioning based on the Single Frequency Approximation Scheme
KIT
We approximate the Lower Bound Energy Consumption:
0 0.5 1 1.5 2 2.50
20
40
60
80 if wM
* > sdyn
:
P(s) = α sγ
if wM
* ≤ sdyn
:
P(s) = α scrit
γ + β
smin
scrit
sdyn
smax
w∗
M[GHz]
E∗ ↓(w
∗ M)[Joule]
![Page 65: Energy Efficient Task Partitioning based on the Single ...cesdownloads.itec.kit.edu/pdf/pagani/Pagani-RTSS... · 2 Dec. 2013 Santiago Pagani and Jian-Jia Chen Energy Efficient Task](https://reader034.vdocuments.us/reader034/viewer/2022052009/601e4ca0e754601a697c6af1/html5/thumbnails/65.jpg)
Non-negligible Leakage Power Consumption
26 Dec. 2013 Santiago Pagani and Jian-Jia ChenEnergy Efficient Task Partitioning based on the Single Frequency Approximation Scheme
KIT
We approximate the Lower Bound Energy Consumption:
0 0.5 1 1.5 2 2.50
20
40
60
80 if wM
* > sdyn
:
P(s) = α sγ
if wM
* ≤ sdyn
:
P(s) = α scrit
γ + β
smin
scrit
sdyn
smax
w∗
M[GHz]
E∗ ↓(w
∗ M)[Joule]
![Page 66: Energy Efficient Task Partitioning based on the Single ...cesdownloads.itec.kit.edu/pdf/pagani/Pagani-RTSS... · 2 Dec. 2013 Santiago Pagani and Jian-Jia Chen Energy Efficient Task](https://reader034.vdocuments.us/reader034/viewer/2022052009/601e4ca0e754601a697c6af1/html5/thumbnails/66.jpg)
Negligible Leakage Power Consumption
27 Dec. 2013 Santiago Pagani and Jian-Jia ChenEnergy Efficient Task Partitioning based on the Single Frequency Approximation Scheme
KIT
Worst-case Approximation Factor for DLTF and SFA (when β 6= 0):
AFDLTFSFA ≤ max
γ− 1
[γγh (δmax)]1
γ−1
+ h (δmax) ,γ− 1
θLTF
[γγh
(4M+1
6M
)] 1γ−1
+ θγ−1LTF h
(4M + 1
6M
)
0 8 16 24 32 40 481
2
3
4
M
AFDLTF
SFA
AFDLTFSFA when γ = 3
γ−1
θL T F[γ γh( 4M +16M )]
1γ− 1
+ θγ−1LTFh(
4M +16M ) when γ = 3
γ−1
[γ γh(δmax)]1
γ− 1+ h(δmax) whenγ = 3
AFDLTFSFA when γ = 2
γ−1
θL T F[γ γh( 4M +16M )]
1γ− 1
+ θγ−1LTFh(
4M +16M ) when γ = 2
γ−1
[γ γh(δmax)]1
γ− 1+ h(δmax) whenγ = 2
Note: AFDLTFSFA only depends on the values of γ and M.
![Page 67: Energy Efficient Task Partitioning based on the Single ...cesdownloads.itec.kit.edu/pdf/pagani/Pagani-RTSS... · 2 Dec. 2013 Santiago Pagani and Jian-Jia Chen Energy Efficient Task](https://reader034.vdocuments.us/reader034/viewer/2022052009/601e4ca0e754601a697c6af1/html5/thumbnails/67.jpg)
Outline
28 Dec. 2013 Santiago Pagani and Jian-Jia ChenEnergy Efficient Task Partitioning based on the Single Frequency Approximation Scheme
KIT
Introduction
Motivation and Problem Definition
Task Partitioning Scheme: Double-Largest-Task-First (DLTF)
Approximation Factor Analysis (energy consumption): DLTF and SFANegligible Leakage Power Consumption
Non-negligible Leakage Power Consumption
Non-negligible Sleeping Overhead
Simulations
Conclusions
![Page 68: Energy Efficient Task Partitioning based on the Single ...cesdownloads.itec.kit.edu/pdf/pagani/Pagani-RTSS... · 2 Dec. 2013 Santiago Pagani and Jian-Jia Chen Energy Efficient Task](https://reader034.vdocuments.us/reader034/viewer/2022052009/601e4ca0e754601a697c6af1/html5/thumbnails/68.jpg)
Non-negligible Sleeping Overhead
29 Dec. 2013 Santiago Pagani and Jian-Jia ChenEnergy Efficient Task Partitioning based on the Single Frequency Approximation Scheme
KIT
Our strategy can be combined with any DPM schemes.
Two cases:
∑Mi=1 w∗i < scrit:
DLTF assigns all tasks on one core and SFA executes at scrit.
Uniprocessor scheduling problem.
For example, using Left-To-Right (LTR) algorithm 4 → 2-approximation.
∑Mi=1 w∗i ≥ scrit:
Using any DPM scheme, against the optimal solution:
AFDLTFSFA-DPM ≤ AFDLTF
SFA +γ− 1
γ
4Sandy Irani, Sandeep Shukla, and Rajesh Gupta. “Algorithms for power savings”. In: Symposium on Discrete Algorithms (SODA).
Baltimore, Maryland, 2003, pp. 37–46
![Page 69: Energy Efficient Task Partitioning based on the Single ...cesdownloads.itec.kit.edu/pdf/pagani/Pagani-RTSS... · 2 Dec. 2013 Santiago Pagani and Jian-Jia Chen Energy Efficient Task](https://reader034.vdocuments.us/reader034/viewer/2022052009/601e4ca0e754601a697c6af1/html5/thumbnails/69.jpg)
Non-negligible Sleeping Overhead
29 Dec. 2013 Santiago Pagani and Jian-Jia ChenEnergy Efficient Task Partitioning based on the Single Frequency Approximation Scheme
KIT
Our strategy can be combined with any DPM schemes.
Two cases:
∑Mi=1 w∗i < scrit:
DLTF assigns all tasks on one core and SFA executes at scrit.
Uniprocessor scheduling problem.
For example, using Left-To-Right (LTR) algorithm 4 → 2-approximation.
∑Mi=1 w∗i ≥ scrit:
Using any DPM scheme, against the optimal solution:
AFDLTFSFA-DPM ≤ AFDLTF
SFA +γ− 1
γ
4Sandy Irani, Sandeep Shukla, and Rajesh Gupta. “Algorithms for power savings”. In: Symposium on Discrete Algorithms (SODA).
Baltimore, Maryland, 2003, pp. 37–46
![Page 70: Energy Efficient Task Partitioning based on the Single ...cesdownloads.itec.kit.edu/pdf/pagani/Pagani-RTSS... · 2 Dec. 2013 Santiago Pagani and Jian-Jia Chen Energy Efficient Task](https://reader034.vdocuments.us/reader034/viewer/2022052009/601e4ca0e754601a697c6af1/html5/thumbnails/70.jpg)
Non-negligible Sleeping Overhead
29 Dec. 2013 Santiago Pagani and Jian-Jia ChenEnergy Efficient Task Partitioning based on the Single Frequency Approximation Scheme
KIT
Our strategy can be combined with any DPM schemes.
Two cases:
∑Mi=1 w∗i < scrit:
DLTF assigns all tasks on one core and SFA executes at scrit.
Uniprocessor scheduling problem.
For example, using Left-To-Right (LTR) algorithm 4 → 2-approximation.
∑Mi=1 w∗i ≥ scrit:
Using any DPM scheme, against the optimal solution:
AFDLTFSFA-DPM ≤ AFDLTF
SFA +γ− 1
γ
4Sandy Irani, Sandeep Shukla, and Rajesh Gupta. “Algorithms for power savings”. In: Symposium on Discrete Algorithms (SODA).
Baltimore, Maryland, 2003, pp. 37–46
![Page 71: Energy Efficient Task Partitioning based on the Single ...cesdownloads.itec.kit.edu/pdf/pagani/Pagani-RTSS... · 2 Dec. 2013 Santiago Pagani and Jian-Jia Chen Energy Efficient Task](https://reader034.vdocuments.us/reader034/viewer/2022052009/601e4ca0e754601a697c6af1/html5/thumbnails/71.jpg)
Outline
30 Dec. 2013 Santiago Pagani and Jian-Jia ChenEnergy Efficient Task Partitioning based on the Single Frequency Approximation Scheme
KIT
Introduction
Motivation and Problem Definition
Task Partitioning Scheme: Double-Largest-Task-First (DLTF)
Approximation Factor Analysis (energy consumption): DLTF and SFANegligible Leakage Power Consumption
Non-negligible Leakage Power Consumption
Non-negligible Sleeping Overhead
Simulations
Conclusions
![Page 72: Energy Efficient Task Partitioning based on the Single ...cesdownloads.itec.kit.edu/pdf/pagani/Pagani-RTSS... · 2 Dec. 2013 Santiago Pagani and Jian-Jia Chen Energy Efficient Task](https://reader034.vdocuments.us/reader034/viewer/2022052009/601e4ca0e754601a697c6af1/html5/thumbnails/72.jpg)
Simulation Results
31 Dec. 2013 Santiago Pagani and Jian-Jia ChenEnergy Efficient Task Partitioning based on the Single Frequency Approximation Scheme
KIT
For negligible overhead for sleeping:
Power parametersmodelled from SCC.
150 cases of synthetictasks for every M, withdifferent:
Amount of tasks.
Cycle utilizations.
Resulting hyper-periods.
Task Partitioning:DLTF for SFA.
Lower bound for theoptimal solution.
![Page 73: Energy Efficient Task Partitioning based on the Single ...cesdownloads.itec.kit.edu/pdf/pagani/Pagani-RTSS... · 2 Dec. 2013 Santiago Pagani and Jian-Jia Chen Energy Efficient Task](https://reader034.vdocuments.us/reader034/viewer/2022052009/601e4ca0e754601a697c6af1/html5/thumbnails/73.jpg)
Simulation Results
31 Dec. 2013 Santiago Pagani and Jian-Jia ChenEnergy Efficient Task Partitioning based on the Single Frequency Approximation Scheme
KIT
For negligible overhead for sleeping:
Power parametersmodelled from SCC.
150 cases of synthetictasks for every M, withdifferent:
Amount of tasks.
Cycle utilizations.
Resulting hyper-periods.
Task Partitioning:DLTF for SFA.
Lower bound for theoptimal solution.
0 8 16 24 32 40 481
2
3
4
M
EDLTF
SFA
(wDLTF
M)
E∗ ↓(w
∗ M)
pea
k
AFDLTFSFA
EDLTFSFA (wDLTF
M)
E∗
↓(w∗
M)
peak
![Page 74: Energy Efficient Task Partitioning based on the Single ...cesdownloads.itec.kit.edu/pdf/pagani/Pagani-RTSS... · 2 Dec. 2013 Santiago Pagani and Jian-Jia Chen Energy Efficient Task](https://reader034.vdocuments.us/reader034/viewer/2022052009/601e4ca0e754601a697c6af1/html5/thumbnails/74.jpg)
Outline
32 Dec. 2013 Santiago Pagani and Jian-Jia ChenEnergy Efficient Task Partitioning based on the Single Frequency Approximation Scheme
KIT
Introduction
Motivation and Problem Definition
Task Partitioning Scheme: Double-Largest-Task-First (DLTF)
Approximation Factor Analysis (energy consumption): DLTF and SFANegligible Leakage Power Consumption
Non-negligible Leakage Power Consumption
Non-negligible Sleeping Overhead
Simulations
Conclusions
![Page 75: Energy Efficient Task Partitioning based on the Single ...cesdownloads.itec.kit.edu/pdf/pagani/Pagani-RTSS... · 2 Dec. 2013 Santiago Pagani and Jian-Jia Chen Energy Efficient Task](https://reader034.vdocuments.us/reader034/viewer/2022052009/601e4ca0e754601a697c6af1/html5/thumbnails/75.jpg)
Conclusions
33 Dec. 2013 Santiago Pagani and Jian-Jia ChenEnergy Efficient Task Partitioning based on the Single Frequency Approximation Scheme
KIT
For periodic tasks, combining DLTF and SFA is a practical solution forenergy minimization.
Approximation factor of DLTF and SFA for energy efficiency:Considered cases: negligible leakage, non-negligible leakage, andcombinations with DPM.
Bounded by γ and M (for all cases).
Simulations show a small gap compared with our analysis (for theworst-case).
Combining DLTF and SFA is an acceptable scheme based on theworst-case analysis.
![Page 76: Energy Efficient Task Partitioning based on the Single ...cesdownloads.itec.kit.edu/pdf/pagani/Pagani-RTSS... · 2 Dec. 2013 Santiago Pagani and Jian-Jia Chen Energy Efficient Task](https://reader034.vdocuments.us/reader034/viewer/2022052009/601e4ca0e754601a697c6af1/html5/thumbnails/76.jpg)
34 Dec. 2013 Santiago Pagani and Jian-Jia ChenEnergy Efficient Task Partitioning based on the Single Frequency Approximation Scheme
KIT
Thank you!
Questions?
![Page 77: Energy Efficient Task Partitioning based on the Single ...cesdownloads.itec.kit.edu/pdf/pagani/Pagani-RTSS... · 2 Dec. 2013 Santiago Pagani and Jian-Jia Chen Energy Efficient Task](https://reader034.vdocuments.us/reader034/viewer/2022052009/601e4ca0e754601a697c6af1/html5/thumbnails/77.jpg)
34 Dec. 2013 Santiago Pagani and Jian-Jia ChenEnergy Efficient Task Partitioning based on the Single Frequency Approximation Scheme
KIT
Thank you!
Questions?