Understanding and Predicting Host Load

1. Understanding and PredictingHost Load Peter A. Dinda Carnegie Mellon University http://www.cs.cmu.edu/~pdinda

2. Talk in a Nutshell Statistical analysis of two sets of week long, 1 Hz resolution traces of load on ~40 machines and evaluation of linear time series models for load prediction • Load is self-similar • Load exhibits epochal behavior • Load prediction benefits from capturing self-similarity

3. Why Study Load? ? [tmin,tmax] Load partially determines execution time We want to model and predict load Interactive Application Short tasks with deadlines Unmodified Distributed System

4. Load and Execution Time

5. Outline • Measurement methodology • Load traces • Load variance • New Results • Self-similarity • Epochal behavior • Benefits of capturing self similarity in linear models • Conclusions

6. Measurement Methodology Digital Unix Kernel User Level Measurement Tool RUN T=2 seconds Ready Queue lent lent-T Exponential Average (1 minute Load “Average”) lent-2T avgt ... lent-29T avgt-0.5T Our Measurements (1 Hz sample rate) lent-30T avgt-T ... ...

7. Load Traces

8. Absolute Variation

9. Relative Variation

10. Load Time Autocorrelation Lag Periodogram Frequency

11. Visual Self-Similarity Here

12. The Hurst Parameter

13. Self-similarity Statistics

14. Why is Self-Similarity Important? • Complex structure • Not completely random, nor independent • Short range dependence • Excellent for history-based prediction • Long range dependence • Possibly a problem • Modeling Implications • Suggests models that can capture • ARFIMA, FGN, TAR

15. Load Exhibits Epochal Behavior

16. Epoch Length Statistics

17. Why is Epochal Behavior Important? • Complex structure • Non-stationary • Modeling Implications • Suggests models • ARIMA, ARFIMA, etc. • Non-parametric spectral methods • Suggests problem decomposition

18. Linear Time Series Models Unpredictable Random Sequence Partially Predictable Load Sequence Fixed Linear Filter Choose weightsyj to minimize sa2 sa is the confidence interval for t+1 predictions

19. Realizable Pole-Zero Models ARFIMA(p,d,q) Self Similarity, d related to Hurst ARIMA(p,d,q) Non-stationarity, d integer ARMA(p,q) AR(p) MA(q) p,q are numbers of parameters d is degree of differencing

20. Real World Benefits of Models sa is the confidence interval for t+1 predictions Map work that would take 100 ms at zero load axp0: sz=0.54, m=1.0, sa(ARMA(4,4))= 0.109 sa(ARFIMA(4,d,4))= 0.108 no model: 1.0 +/- 1.06 (95%) => 100 to 306 ms ARMA: 1.0 +/- 0.22 (95%) => 178 to 222 ms ARFIMA: 1.0 +/- 0.21 (95%) => 179 to 221 ms axp7: sz=0.14, m=0.12, sa(ARMA(4,4))= 0.041 sa(ARFIMA(4,d,4))= 0.025 no model: 0.12 +/- 0.27 (95%) => 100 to 139 ms ARMA: 0.12 +/- 0.08 (95%) => 104 to 120 ms ARFIMA: 0.12 +/- 0.05 (95%) => 107 to 117 ms 1 % 40 %

21. t+1 prediction

22. t+8 prediction

23. Conclusions • Load has high variance • Load is self-similar • Load exhibits epochal behavior • Capturing self-similarity in linear time series models improves predictability

24. Load Traces • Would a web-accessible load trace database be useful? • Would you like to contribute?