Using A Multiscale Approach to

1

• Using A Multiscale Approach to
• Characterize Workload Dynamics
• Tao Li
• taoli_at_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 series X0

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 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 Ej as a
  function of resolution level 2j 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
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