Soner Yaldiz , Alper Demir, Serdar Tasiran

Koç University, Istanbul, Turkey

Paolo Ienne, Yusuf Leblebici

Swiss Federal Institute of Technology (EPFL), Lausanne, Switzerland

Characterizing and ExploitingCharacterizing and ExploitingTask-Load Variability and Task-Load Variability and CorrelationCorrelationfor Energy Management for Energy Management in Multi-Core Systemsin Multi-Core Systems

ESTIMedia 2005ESTIMedia 2005

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Multi-Core Soft Real-Time Multi-Core Soft Real-Time SystemsSystems

processors

• Chip-level multiprocessing for massive performance– Energy management problem

• Real-time multimedia applications– Audio, video processing

• Soft real-time systems– Tolerance to deadline misses

t t + TDEADLINEtime

start end

T2

T4T3

T1task graph

MPEG2 video frames

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Variability and CorrelationVariability and Correlation

• Capture by Stochastic Models

• Exploit for Energy Management– Dynamic Voltage Scaling (DVS)

TimeV

olt

ag

e

V1

deadline

V2

workload

Taskivariability

probability

Task2

workload

Task

1

workload positivecorrelation

• This work: First approach to consider variability and correlations for multiprocessor energy management

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• Application composed of two tasks on a single processor

Motivating ExampleMotivating Example

start endT2T1

TDEADLINE = 2 sec

• Task loads low (2) or high (10) with equal probability

• Processor Operating Modes – Slow Mode -> 6 instructions-per-second– Fast Mode -> 10 instructions-per-second

2 10instructions

T1,T250%50%

probability

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start endT2T1

TDEADLINE = 2 sec 2 10

instructions

T1,T250%50%

probability

T1 T2

2 10

2 25%

25%

10 25%

25%

T1 T2

2 10

2 50%

0

10 0 50%

T1 T2

2 10

2 0 50%

10 50%

0

Probabilities for task load combinations:

Independent Positively Correlated Negatively Correlated

Task Load CombinationsTask Load Combinations

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T1 T2

2 10

2 25%

25%

10 25%

25%

Motivating Motivating ExampleExample

T1 T2

2 10

2 50%

0

10 0 50%

T1 T2

2 10

2 0 50%

10 50%

0

Independent

PositivelyCorrelated

NegativelyCorrelated

Slow mode -> 12 instructions in 2 secMisses desired performance

0.75 0.50 never happens !

Fast mode -> 20 instructions in 2 secSuboptimal energy

1.0

• Application– 2 tasks

• Processor modes– Slow 6 inst/sec– Fast 10 inst/sec

• Deadline– 2 sec

Target 75%

Assumption

Independent

Reality Positive Correlation

Target 100%

Assumption

Independent

Reality Negative Correlation

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• Stochastic Modeling

• Energy Management Scheme– OFFLINE Optimization– ONLINE Adjustments

• Experimental Results

• Conclusions

OUTLINEOUTLINE

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Stochastic Modeling FlowStochastic Modeling Flow

• Computational Demand (CD) of a task– Number of CPU cycles for execution

• Demands are represented by dist– Quantized for manageability

• dist is obtained from a set of traces

• Demand of tasks constitutes an ‘observation’

– (T1,T2) = ( 5, 5 ) observed 3 out of 8.

– dist ( 5,5 ) = 3/8

OBSERVATIONS

Task1 Task2

1 2 10

2 5 5

3 2 5

4 10 2

5 5 5

6 2 10

7 2 5

8 5 5

start endT2T1

T1 T2

2 5 10

2 2/8 2/8

5 3/8

10 1/8

disdistt

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• MPEG2 video decoding– Widely-used and computationally intensive

• Slice-based task decomposition(Olukotun et.al,1998) – VLD ( Variable-length decoding)– MC ( Motion compensation )

Case Study: MPEG2Case Study: MPEG2VLD0, MC0VLD1, MC1VLD2, MC2... ...

Experimental Data: – 10 movie segments– 19 slices, 38 tasks – 24 frames-per-second– ~ 14000 frames per movie

Task Assignment Processor Precedence

Data Precedence

slice0

slice1

slice2

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Variability of MPEG2 Task Variability of MPEG2 Task LoadsLoads

aggregate

one movie

aggregate

1- SimilarityTraning set predicts workload

for others

2- Long TailsWorst-Case causes overdesign

one movie

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Correlation among MPEG2 Task Correlation among MPEG2 Task LoadsLoads

High Correlation

aggregatestatistics

one movieSl

ice

9

Slice

14

Slice

18

Slice

0

Slice

5... ... ... ...

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Critical PathCritical Path

• Summation of worst-case task loads : 64 million cycles • Observed worst-case total load : 28 million cycles• Ignoring correlations lead to far from optimal

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• Stochastic Modeling

• Energy Management Scheme– OFFLINE Optimization– ONLINE Adjustments

• Experimental Results

• Conclusions

OUTLINEOUTLINE

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OFFLINE: OFFLINE: Optimization FormulationOptimization Formulation

• Nonlinear constrained optimization problem with 38 variables– One voltage per task

• Stochastic programming formulation– Based on stochastic application model

• Optimized voltages stored for run-time look-up

• Each task i has fixed voltage Vi for all periods• GOAL: Determine optimal Vi’s

minimizeaverage energy consumption

subject tocompletion probability

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ONLINE ONLINE AdjustmentsAdjustments

• When low load is detected, lower the task voltage– Preserving probabilistic performance

• Very small run-time expense– Few comparisons and arithmetic operations

Load lower than expectedSlow down further

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• Stochastic Modeling

• Energy Management Scheme– OFFLINE Optimization– ONLINE Adjustments

• Experimental Results

• Conclusions

OUTLINEOUTLINE

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Experimental SetupExperimental Setup

• Compared with approaches for multiprocessor systems:– I (Zhang et. al, DAC2002 )

• Ignores variability, correlations• 100% completion• Worst-case task load

– II ( Hua et. al, EMSOFT2003 )• Ignores correlations• Completion Probability• Marginal load distribution

• Training set: 8 movie segments out of 10

• Test set has 2 movies not included in training set.

• Three completion probabilities PCON– 0.90, 0.95, 0.99

• Two deadlines– Normal , Tight

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Experiment I : Normal DeadlineExperiment I : Normal Deadline

1. Significant energy savings 2. Desired completion probability achieved

Avg E 860

154

100 98 833 147

100 97 764 129

100 91

Avg Pr 0.9026 0.9511 0.9899

Movie #

PCON=0.90 PCON=0.95 PCON=0.99

I II OFLN ONLN

I II OFLN ONLN I II OFLN

ONLN

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Experiment II : Tight DeadlineExperiment II : Tight Deadline

Avg E 100 95 100 91 100 70

Avg Pr 0.9030 0.9515 0.9898

• II (Hua2003) fails with tight deadline– Ignores correlations

• ONLN improves more

• Accurate stochastic model

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Experiment III: Comparison with Experiment III: Comparison with GODGOD

Single Movie

OFFLINE

ONLINE GOD

PCON = 0.99 100 66 52

PCON = 0.95 100 86 72

PCON = 0.90 100 92 76• GOD

– Ideal, Unrealizable, Non-causal– For every individual frame

• Knows load of each task• Computes optimal voltages

• There is still room for future work– “application state” structure

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ConclusionsConclusions

• Demonstrated significant variability and correlations among workloads of MPEG2 tasks

• Our stochastic models capture essential characteristics of applications– Accurately predict performance

• Novel energy management scheme based on stochastic models– Significant energy savings

Soner Yaldiz , Alper Demir, Serdar Tasiran

Koç University, Istanbul, Turkey

Paolo Ienne, Yusuf Leblebici

Swiss Federal Institute of Technology (EPFL), Lausanne, Switzerland

Characterizing and ExploitingCharacterizing and ExploitingTask-Load Variability and CorrelationTask-Load Variability and Correlationfor Energy Management for Energy Management in Multi-Core Systemsin Multi-Core Systems

ESTIMedia 2005ESTIMedia 2005

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