Peter A. Dinda Carnegie Mellon University

1. Resource Signal Prediction andIts Application to Real-time Scheduling AdvisorsorHow to Tame Variability in Distributed Systems Peter A. Dinda Carnegie Mellon University

2. Outline • Bird’s eye view • Highly variable resource availability • Real-time scheduling advisor • Predicting task running times • Characterizing variability with confidence intervals • Performance results (feasible, practical, useful) • Prototype system • Host load prediction • Traces, structure, linear models, evaluation • RPS Toolkit • Conclusion

3. A Universal Challenge in High Performance Distributed Applications Highly variable resource availability • Shared resources • No reservations • No globally respected priorities • Competition from other users - “background workload” Running time can vary drastically Adaptation

4. A Universal Problem Which host should the application send the task to so that its running time is appropriate? ? Task Known resource requirements

5. Real-time Scheduling Advisor • Distributed interactive applications • Examples: CMU Dv/QuakeViz, BBN OpenMap • Assumptions • Sequential tasks initiated by user actions • Aperiodic arrivals • Resilient deadlines (soft real-time) • Compute-bound tasks • Known computational requirements • Best-effort semantics • Recommend host where deadline is likely to be met • Predict running time on that host • No guarantees

6. Running Time Advisor Predicted Running Time Application notifies advisor of task’s computational requirements (nominal time) Advisor predicts running time on each host Application assigns task to most appropriate host ? Task nominal time

7. Real-time Scheduling Advisor Application notifies advisor of task’s computational requirements (nominal time) and its deadline Advisor acquires predicted task running times for all hosts Advisor recommends one of the hosts where the deadline can be met Predicted Running Time deadline ? Task nominal time deadline

8. Variability and Prediction Prediction resource High Resource Availability Variability t Low Prediction Error Variability Predictor resource error t t Characterization of variability ACF t Exchange high resource availability variability for low prediction error variability and a characterization of that variability

9. Confidence Intervals to Characterize Variability “3 to 5 seconds with 95% confidence” Application specifies confidence level (e.g., 95%) Running time advisor predicts running times as a confidence interval (CI) Real-time scheduling advisor chooses host where CI is less than deadline CI captures variability to the extent the application is interested in it Predicted Running Time deadline ? Task nominal time deadline 95% confidence

10. Confidence Intervals And Predictor Quality Bad Predictor No obvious choice Good Predictor Two good choices Predicted Running Time Predicted Running Time deadline Good predictors provide smaller CIs Smaller CIs simplify scheduling decisions

11. Overview of Research Results • Predicting CIs is feasible • Host load prediction using AR(16) models • Running time estimation using host load predictions • Predicting CIs is practical • RPS Toolkit (inc. in CMU Remos, BBN QuO) • Extremely low-overhead online system • Predicting CIs is useful • Performance of real-time scheduling advisor Measured performance of real system Statistically rigorous analysis and evaluation

12. Experimental Setup • Environment • Alphastation 255s, Digital Unix 4.0 • Workload: host load trace playback • Prediction system on each host • Tasks • Nominal time ~ U(0.1,10) seconds • Interarrival time ~ U(5,15) seconds • Methodology • Predict CIs / Host recommendations • Run task and measure

13. Predicting CIs is Feasible Near-perfect CIs on typical hosts 3000 randomized tasks

14. Predicting CIs is Practical - RPS System <2% of CPU At Appropriate Rate 1-2 ms latency from measurement to prediction 2KB/sec transfer rate

15. Predicting CIs is Useful - Real-time Scheduling Advisor Predicted CI < Deadline Host With Lowest Load Random Host 16000 tasks

16. Outline • Bird’s eye view • Highly variable resource availability • Real-time scheduling advisor • Predicting task running times • Characterizing variability with confidence intervals • Performance results (feasible, practical, useful) • Prototype system • Host load prediction • Traces, structure, linear models, evaluation • RPS Toolkit • Conclusion

17. Design Space Can the gap between the resources and the application can be spanned? yes!

18. Resource Signals • Characteristics • Easily measured, time-varying scalar quantities • Strongly correlated with resource availability • Periodically sampled (discrete-time signal) • Examples • Host load (Digital Unix 5 second load average) • Network flow bandwidth and latency Leverage existing statistical signal analysis and prediction techniques

19. Prototype System RPS components can be composed in other ways

20. Host load on real hosts has exploitable structure Strong autocorrelation, self-similarity, epochal behavior Trace database and host load trace playback Host load is predictable using simple linear models Recommendation: AR(16) models or better for 1-30 sec predictions RPS Toolkit for low overhead systems (<2% of CPU) C++, ported to 5 OSes, incorporated in CMU Remos, BBN QuO Running time CIs can be computed from load predictions Load discounting, error covariances Effective real-time scheduling advice can be based on CIs Know if deadline will be met before running task Research Results Statistically rigorous analysis and evaluation

21. Outline • Bird’s eye view • Highly variable resource availability • Real-time scheduling advisor • Predicting task running times • Characterizing variability with confidence intervals • Performance results (feasible, practical, useful) • Prototype system • Host load prediction • Traces, structure, linear models, evaluation • RPS Toolkit • Conclusion

22. Questions • What are the properties of host load? • Is host load predictable? • What predictive models are appropriate? • Are host load predictions useful?

23. Overview of Answers • Host load exhibits complex behavior • Strong autocorrelation, self-similarity, epochal behavior • Host load is predictable • 1 to 30 second timeframe • Simple linear models are sufficient • Recommend AR(16) or better • Predictions are useful • Can compute effective CIs from them

24. Host Load Traces • DEC Unix 5 second exponential average • Full bandwidth captured (1 Hz sample rate) • Long durations

25. If Host Load Was “Random” (White Noise)... Time domain Autocorrelation Frequency domain Spectrogram

26. Host Load Has Exploitable Structure Time domain Autocorrelation Frequency domain Spectrogram

27. Linear Time Series Models Pole-zero / state-space models capture autocorrelation parsimoniously (2000 sample fits, largest models in study, 30 secs ahead)

28. Evaluation Methodology • Ran ~190,000 randomly chosen testcases on the traces • Evaluate models independently of prediction/evaluation framework • No monitoring • ~30 testcases per trace, model class, parameter set • Data-mine results Offline and online systems implemented using RPS Toolkit

29. Testcases • Models • MEAN, LAST/BM(32) • Randomly chosen model from: AR(1..32), MA(1..8), ARMA(1..8,1..8), ARIMA(1..8,1..2,1..8), ARFIMA(1..8,d,1..8)

30. Evaluating a Testcase Measurements in Fit Interval Model Type <zt-m,...,zt-2 ,zt-1> Modeler z’t+2,t+2+w z’t+1,t+1+w z’t,t+w ... Model ... ... ... z’t+2,t+4 z’t+1,t+3 Measurements in Test Interval z’t,t+2 ... z’t+2,t+3 z’t+1,t+2 Load Predictor z’t,t+1 ... zt+n-1,…,zt+1 ,zt Prediction Stream Error Estimates Characterization of variation Evaluator One-time use Measurement of variation Production Stream Error Metrics

31. (z’t+i,t+i+w - zt+i+w)2 (z’t+i,t+i+2 - zt+i+2 )2 Measured Prediction Variance: Mean Squared Error z’t+2,t+2+w z’t+1,t+1+w z’t,t+w ... w step ahead predictions ... ... ... ... Load Predictor z’t+2,t+4 z’t+1,t+3 z’t,t+2 …,zt+1 ,zt ... 2 step ahead predictions z’t+2,t+3 z’t+1,t+2 z’t,t+1 ... 1 step ahead predictions s2z = (m - zt+i)2 Variance of z s2aw= w step ahead mean squared error ... ... s2a2= 2 step ahead mean squared error (z’t+i,t+i+1 - zt+i+1 )2 s2a1= 1 step ahead mean squared error Good Load Predictor :s2a1,s2a2 ,…,s2aw << s2z

32. Unpaired Box Plot Comparisons Inconsistent low error Consistent high error 97.5% Mean Squared Error 75% Consistent low error Mean 50% 25% Model A Model B Model C 2.5% Good models achieve consistently low error

33. 1 second Predictions, All Hosts 97.5% 75% Mean 50% 25% 2.5% Predictive models clearly worthwhile

34. 30 second Predictions, All Hosts 97.5% 75% Mean 50% 25% 2.5% Predictive models clearly beneficial even at long prediction horizons

35. 30 Second Predictions, High Load, Dynamic Host 97.5% 75% Mean 50% 25% 2.5% Predictive models clearly worthwhile Begin to see differentiation between models

36. RPS Toolkit • Extensible toolkit for implementing resource prediction systems • Easy “buy-in” for users • C++ and sockets (no threads) • Prebuilt prediction components • Libraries (sensors, time series, communication) • Users have bought in • Incorporated in CMU Remos, BBN QuO • Used in research by Bruce Lowekamp, Nancy Miller, LeMonte Green

37. Outline • Bird’s eye view • Highly variable resource availability • Real-time scheduling advisor • Predicting task running times • Characterizing variability with confidence intervals • Performance results (feasible, practical, useful) • Prototype system • Host load prediction • Traces, structure, linear models, evaluation • RPS Toolkit • Conclusion

38. Related Work • Distributed interactive applications • QuakeViz/ Dv, Aeschlimann [PDPTA’99] • Quality of service • QuO, Zinky, Bakken, Schantz [TPOS, April 97] • QRAM, Rajkumar, et al [RTSS’97] • Distributed soft real-time systems • Lawrence, Jensen [assorted] • Workload studies for load balancing • Mutka, et al [PerfEval ‘91] • Harchol-Balter, et al [SIGMETRICS ‘96] • Resource signal measurement systems • Remos [HPDC’98] • Network Weather Service [HPDC‘97, HPDC’99] • Host load prediction • Wolski, et al [HPDC’99] (NWS) • Samadani, et al [PODC’95] • Hailperin [‘93] • Application-level scheduling • Berman, et al [HPDC’96] • Stochastic Scheduling, Schopf [Supercomputing ‘99]

39. Conclusions • Tame variability in distributed systems • Resource signal prediction • Predict running times as confidence intervals • Predicting CIs is feasible • Host load prediction using AR(16) models • Running time estimation using host load predictions • Predicting CIs is practical • RPS Toolkit (inc. in CMU Remos, BBN QuO) • Extremely low-overhead online system • Predicting CIs is useful • Performance of real-time scheduling advisor

40. Future Work (Near Term) • New resource signals • Network bandwidth and latency (Remos) • New prediction approaches • Wavelets, nonlinearity • Resource scheduler models • Better Unix scheduler model • Network models • Adaptation advisors • Applications and workloads • QuakeViz/DV, GIMP, Instrumentation

41. Tools/Venues for Future work • Resource signal methodolgy • RPS Toolkit • Remos • QuakeViz/DV • Grid Forum

42. Future Work (Long Term) • Experimental computer science research • Application-oriented view • Measurement studies and analysis • Statistical approach • Application services • Systems building systems X applications X statistics

43. Teaching • “Signals, systems, and statistics for computer scientists” • “Performance data analysis” • “Introduction to computer systems”