1

Using A Multiscale Approach toUsing A Multiscale Approach to

Characterize Workload DynamicsCharacterize Workload Dynamics

Tao LiTao Li

taoli@ece.ufl.edutaoli@ece.ufl.edu

June 4, 2005June 4, 2005

Dept. of Electrical and Computer Dept. of Electrical and Computer

EngineeringEngineering

University of FloridaUniversity of Florida

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MotivationMotivation

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

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Program Time Varying BehaviorProgram Time Varying Behavior

710096.4 cycle bucket ( 1010096.4 cycles total)

IPC

/ b

uc

ket

61012.5 cycle bucket ( 91012.5 cycles total)

IPC

/ b

uc

ket

5104.6 cycle bucket

( 8104.6 cycles total)

IPC

/ b

uc

ket

4108 cycle bucket ( 7108 cycles total)

IPC

/ b

uc

ket

4101 cycle bucket ( 7101 cycles total)

IPC

/ b

uc

ket

(a) gzip (b) crafty

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Multiscale Workload Multiscale Workload CharacterizationCharacterization

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)

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OutlineOutline

Scaling models and wavelet analysis

Experimental setup

Results of SPEC 2K integer benchmarks

On-line program scaling estimation

Conclusions

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Scaling ModelsScaling 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

)(tX

)/( ctXcH

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Scaling Models Scaling Models (Contd.)(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

22~)(

H

rx kckr k

rc 121 H

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Scaling Analysis Technique: Discrete Wavelet Scaling Analysis Technique: Discrete Wavelet TransformTransform

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

,...,2,1,0,,0 kX kn2

)(2

112,02,0,1 kkk XXX

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Discrete Wavelet TransformDiscrete 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

)(2

112,02,0,1 kkk XXd

)(2 112/1

0 dXX

12/12/2/

0 2...22 ddXX nn

nn

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Discrete Wavelet Transform (Contd.)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

kjd ,

kjd ,

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Energy Function and Log-scale DiagramEnergy 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

,...,2,1,0,,0 kX k

,.)( jd X

j2

jn

kX

jj kjd

nE

1

2),(

1

22 loglog

)(log2 jj Ey

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Experimental SetupExperimental Setup

Simplescalar 3.0 Sim-outorder simulator

Parameter Configuration Processor Width

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ITLB 128 entries, 4-way, 200 cycle miss

Branch Prediction combined 8K tables, 10 cycle misprediction, 2 predictions/cycle

BTB

2K entries, 4-way Return Address Stack 32 entries

L1 Instruction Cache 32K, 2-way, 32 Byte/line, 2 ports, 4 MSHR, 1 cycle access RUU Size 128 entries

Load/ Store Queue 64 entries Store Buffer 16 entries Integer ALU

4 I-ALU, 2 I-MUL/DIV FP ALU

2 FP-ALU, 1FP-MUL/DIV DTLB 256 entries, 4-way, 200 cycle miss

L1 Data Cache 64KB, 4-way, 64 Byte/line, 2 ports, 8 MSHR, 1 cycle access

L1 Cache unified 1MB, 4-way, 128 Byte/line, 12 cycle access

Memory Access 100 cycles

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Experimental Setup (Contd.)Experimental Setup (Contd.)

Program Traces

Benchmark Input Duration (Cycles) mcf /ref/inp.in 570,689,841,862 gcc /ref/166.i 33,578,085,795 crafty /ref/crafty.in 337,250,101,460 gzip /ref/input.graphic 52,867,265,321 bzip2 /ref/input.source 70,644,828,028 eon /ref/chair.cook.ppm 93,485,005,275 gap /ref/ref.in 355,758,277,267 parser /ref/ref.in 247,035,615,983 perlbmk /ref/splitmail.pl 49,931,474,883 twolf /ref/ref 274,987,890,000 vortex /ref/lendian1.raw 93,677,830,341 vpr /ref/net.in 122,267,820,515

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The LD Plots of BenchmarksThe LD Plots of Benchmarks

2 4 6 8 10 12 14 16 18

-4

-2

0

2

4

6

8

Octave j

yj

gzip

2 4 6 8 10 12 14 16 18 20 22

-6

-4

-2

0

2

4

6

8

10

Octave j

yj

crafty

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On-line Program Scaling EstimationOn-line Program Scaling Estimation

Pyramid algorithm for DWT computation

x(n) N

cx(1,.) dx(1., )

H and decimate G and decimate

cx(J-1,.) dx(J-1,.)

cx(J,.) dx(J,.)

scalej

J

time shift k

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On-line Program Scaling Estimation (Contd.)On-line Program Scaling Estimation (Contd.)

High-pass and low pass filters

G 2

H 2G 2

H 2G 2

H 2

x(t) dx(1, .)

dx(2, .)

dx(3, .)

cx(3, .)

cx(1, .)

cx(2, .)

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On-line Program Scaling Estimation (Contd.)On-line Program Scaling Estimation (Contd.)

FIR filter structure

DD D D D......

......

D

h(0) h(1) h(2) h(3) h(4) h(N-1)

x(n)

y(n)

h(.): one delay register : filter coefficients

: multiplier : adder

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Program Scaling Estimation FrameworkProgram Scaling Estimation Framework

Clock

Perform anceCounters

Filter-banks(Mallat's Pyramid)

inpu tsequence DW T

coe ffic ien tsScaling Properties(Hurst Parameter)

Estimation

CPU

Feed-back Control

On-line Estimator

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Performance of On-line EstimatorPerformance of On-line Estimator

Hurst parameter estimation

0 2 4 6 8 10 12 14

x 104

0.5

0.6

0.7

0.8

0.9

1

Estimation Serial No.

Est

imate

d H

urs

t P

ara

mete

rcrafty

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ConclusionsConclusions

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