Using A Multiscale Approach to Characterize Workload Dynamics Tao Li taoli@ece.ufl

1. Using A Multiscale Approach to Characterize Workload Dynamics Tao Li taoli@ece.ufl.edu June 4, 2005 Dept. of Electrical and Computer Engineering University of Florida

2. Motivation • Workload dynamics reveals the changing of workload behavior over time • Understanding workload dynamics is important • emerging workload characterization • long-run (servers, e-commerce) • interactive (user, OS, DLL…) • non-deterministic (multithreaded) • run-time tuning, optimization, monitoring • performance, power, reliability, security • microarchitecture trends • CMP, SMT

3. Program Time Varying Behavior

4. Multiscale Workload Characterization • Characterize workload behavior across different time scales • “zoom-in” and “zoom-out”features • Apply wavelet analysis to study program scaling behavior • compact and parsimonious models • Complement with other approaches (aggregate measurement, phase analysis)

5. Outline • Scaling models and wavelet analysis • Experimental setup • Results of SPEC 2K integer benchmarks • On-line program scaling estimation • Conclusions

6. Scaling Models • Self-similarity: a dilated portion of the sample path of a process can not be statistically distinguished from the whole • H (Hurst parameter): the degree of self-similarity

7. Scaling Models (Contd.) • Long-Range Dependence (LRD): the correlation function of a process behaves like a power-law of the time lag k is a positive constant and the Hurst parameter • LRD: correlations decay so slowly that they sum to infinity

8. Scaling Analysis Technique: Discrete Wavelet Transform • Consider a series at the finest level of time scale resolution We can coarsen this event series by averaging (with a slightly unusual normalization factor) over non-overlapping blocks of size two (Equ. 1) and generates a new time series X1, which represents a coarser granularity picture of the original seriesX0

9. Discrete Wavelet Transform • The difference between the two, known as details, is (Equ. 2) The original time series X0 can be reconstructed from its coarser representation X1 by simply adding in the details d1 Repeat this process, we get

10. Discrete Wavelet Transform (Contd.) • Discrete wavelet coefficients: the collection of details • Discrete Wavelet Transform (DWT) iteratively uses Equ. 1 and Equ. 2 to calculate all • DWT divides data into a low-pass approximation and a high-pass detail at any level of resolution • The coefficients of wavelet decomposition can be used to study the scale dependent properties of the data

11. Energy Function and Log-scale Diagram • Given a time seriesand its discrete wavelet coefficientsthe average energy at resolution level is then defined as: • The log-scale diagram (LD) is the plot of Ej as a function of resolution level 2jon a scale, i.e. • The LD plot allows the detection of scaling through observation of strict alignment (linear trend) within some octave range

12. Experimental Setup • Simplescalar 3.0 Sim-outorder simulator

13. Experimental Setup (Contd.) • Program Traces

14. The LD Plots of Benchmarks gzip crafty

15. On-line Program Scaling Estimation • Pyramid algorithm for DWT computation

16. On-line Program Scaling Estimation (Contd.) • High-pass and low pass filters

17. On-line Program Scaling Estimation (Contd.) • FIR filter structure

18. Program Scaling Estimation Framework

19. Performance of On-line Estimator • Hurst parameter estimation

20. Conclusions • As software execution cycles become larger, its changing nature can span across a wide range of time scales • Various scaling properties can be used as a useful tool for unraveling the program dynamics over different time periods