1 Using A Multiscale Approach to Characterize Workload Dynamics Characterize Workload Dynamics Tao Li 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 X 1, which represents a coarser granularity picture of the original series X 0

9 Discrete Wavelet Transform  The difference between the two, known as details, is (Equ. 2) The original time series X 0 can be reconstructed from its coarser representation X 1 by simply adding in the details d 1 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 series and its discrete wavelet coefficients the average energy at resolution level is then defined as:  The log-scale diagram (LD) is the plot of E j as a function of resolution level 2 j on 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 gzipcrafty

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