Soner Yaldiz , Alper Demir, Serdar Tasiran Koç University, Istanbul, Turkey

1. Soner Yaldiz , Alper Demir, Serdar TasiranKoç University, Istanbul, Turkey Paolo Ienne, Yusuf Leblebici Swiss Federal Institute of Technology (EPFL), Lausanne, Switzerland Characterizing and ExploitingTask-Load Variability and Correlationfor Energy Management in Multi-Core Systems ESTIMedia 2005

2. Multi-Core Soft Real-Time Systems processors task graph T1 T2 end T3 T4 start t t + TDEADLINE time • Chip-level multiprocessing for massive performance • Energy management problem • Real-time multimedia applications • Audio, video processing • Soft real-time systems • Tolerance to deadline misses MPEG2 video frames ESTIMedia 2005

3. Variability and Correlation positive correlation probability workload variability Taski Task1 workload workload Task2 V2 V1 Voltage Time deadline • This work: First approach to consider variability and correlations for multiprocessor energy management • Capture by Stochastic Models • Exploit for Energy Management • Dynamic Voltage Scaling (DVS) ESTIMedia 2005

4. Motivating Example TDEADLINE = 2 sec probability T1 T2 end 50% 50% T1,T2 instructions 2 10 start • Application composed of two tasks on a single processor • 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 ESTIMedia 2005

5. Task Load Combinations TDEADLINE = 2 sec probability T1 T2 end 50% 50% T1,T2 instructions 2 10 start Probabilities for task load combinations: Independent Positively Correlated Negatively Correlated ESTIMedia 2005

6. Motivating Example 1.0 0.75 never happens ! 0.50 Positively Correlated Negatively Correlated Independent • Application • 2 tasks • Processor modes • Slow 6 inst/sec • Fast 10 inst/sec • Deadline • 2 sec Slow mode -> 12 instructions in 2 sec Misses desired performance Fast mode -> 20 instructions in 2 sec Suboptimal energy ESTIMedia 2005

7. OUTLINE • Stochastic Modeling • Energy Management Scheme • OFFLINE Optimization • ONLINE Adjustments • Experimental Results • Conclusions ESTIMedia 2005

8. Stochastic 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 T1 T2 end start dist ESTIMedia 2005

9. Case Study: MPEG2 Data Precedence Processor Precedence Task Assignment VLD0, MC0 VLD1, MC1 VLD2, MC2 ... .. . • MPEG2 video decoding • Widely-used and computationally intensive • Slice-based task decomposition(Olukotun et.al,1998) • VLD ( Variable-length decoding) • MC ( Motion compensation ) slice0 slice2 slice1 Experimental Data: • 10 movie segments • 19 slices, 38 tasks • 24 frames-per-second • ~ 14000 frames per movie ESTIMedia 2005

10. Variability of MPEG2 Task Loads 1- Similarity Traning set predicts workload for others 2- Long Tails Worst-Case causes overdesign aggregate aggregate one movie one movie ESTIMedia 2005

11. Correlation among MPEG2 Task Loads High Correlation aggregate statistics one movie ... ... ... ... Slice 14 Slice 18 Slice 0 Slice 5 Slice 9 ESTIMedia 2005

12. Critical 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 ESTIMedia 2005

13. OUTLINE • Stochastic Modeling • Energy Management Scheme • OFFLINE Optimization • ONLINE Adjustments • Experimental Results • Conclusions ESTIMedia 2005

14. OFFLINE: Optimization Formulation • Each task i has fixed voltage Vi for all periods • GOAL: Determine optimal Vi’s • 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 ESTIMedia 2005

15. ONLINE Adjustments Load lower than expected Slow down further • When low load is detected, lower the task voltage • Preserving probabilistic performance • Very small run-time expense • Few comparisons and arithmetic operations ESTIMedia 2005

16. OUTLINE • Stochastic Modeling • Energy Management Scheme • OFFLINE Optimization • ONLINE Adjustments • Experimental Results • Conclusions ESTIMedia 2005

17. Experimental 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 ESTIMedia 2005

18. Experiment I : Normal Deadline 1. Significant energy savings2. Desired completion probability achieved ESTIMedia 2005

19. Experiment II : Tight Deadline • II (Hua2003) fails with tight deadline • Ignores correlations • ONLN improves more • Accurate stochastic model ESTIMedia 2005

20. Experiment III: Comparison with GOD • 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 ESTIMedia 2005

21. Conclusions • 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 ESTIMedia 2005

22. Soner Yaldiz , Alper Demir, Serdar TasiranKoç University, Istanbul, Turkey Paolo Ienne, Yusuf Leblebici Swiss Federal Institute of Technology (EPFL), Lausanne, Switzerland Characterizing and ExploitingTask-Load Variability and Correlationfor Energy Management in Multi-Core Systems - Questions ? ESTIMedia 2005