Load Analysis and Predictionfor

Responsive Interactive Applications

Peter A. Dinda

David R. O’Hallaron

Carnegie Mellon University

2

Overview

Responsive Interactive Applications(eg, BBN OpenMap)

Best Effort Real-time

Communication

Execution Time Predicition

Computation

History-based Load Prediction

Load Analysis Time Series Modelling

Remote Execution

Measurement

3

OpenMap (BBN)

“Move North”

New map dataIntegrator

Choice of Host

Terrain TerrainTerrain

BoundedResponseTime

ReplicatedSpecialists

4

Context

OpenMap (BBN)

Load Prediction (CMU)

QuO (BBN)

Remos (CMU)

JTF

Pla

nne

r

Adv

ance

d M

obili

ty P

latf

orm

Log

istic

s A

nch

or D

esk

ME

TO

C A

ncho

r D

esk

TR

AC

E2E

S

... Oth

erA

pplic

atio

ns

Frameworks

Adaptation

Measurement

Prediction

Applications

Distributed system Distributed system

5

StatisticalAnalysis

AppropriateTime SeriesModels

FittedModels

Evaluation/Comparison

On-linePredictors

Load TraceCollection

Load Analysis and Prediction

• Goal: accurate short term predictions– Few seconds for non-stale data

• Evaluation/comparison issues– Load generation vs. Load prediction

• Have to discover which properties are important

– Performance measure• Mean squared prediction error• Lack of lower bound to compare against• Simple, reasonable algorithm for comparison

6

Load Trace Analysis• Digital Unix one minute load average• Four classes of hosts (38 machines)• 1 Hz sample rate, >one week traces, two sets at

different times of the year• Analysis results to appear in LCR98

• Load is self-similar• Load exhibits epochal behavior

7

Self-similarity Statistics

0

0.2

0.4

0.6

0.8

1

1.2

Host

Production Cluster ResearchCluster

Desktops

+SDev

-SDev

Mean

8

Why is Self-Similarity Important?

• Complex structure– Not completely random, nor independent– Short range dependence

• Excellent for history-based prediction

– Long range dependence• Possibly a problem

• Modeling Implications– Suggests models

• ARFIMA, FGN, TAR

9

Load Exhibits Epochal Behavior

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10

Epoch Length Statistics

-200

0

200

400

600

800

1000

1200

Host

+SDev

-SDev

Mean

Production Cluster ResearchCluster

Desktops

11

Why is Epochal Behavior Important?

• Complex structure – Non-stationary

• Modeling Implications– Suggests models

• ARIMA, ARFIMA, etc.• Non-parametric spectral methods

– Suggests problem decomposition

12

Time Series Prediction of Load

Linear Nonlinear

Stationary Non-stationary

ARMA, AR, MA

ARIMAARFIMA, FGN

TARMarkov

Self-similar Non-self-similar

“Best Mean”

Non-parametricParametric

13

-20

0

20

40

60

80

100

Best Markov Improvement

Best ARMA Improvement

Production Cluster ResearchCluster

Desktops

t+1 Predictions

14

-50

-40

-30

-20

-10

0

10

20

30

Best Markov Gain

Best ARMA Gain

Production Cluster ResearchCluster

Desktops

t+5 Prediction

15

Conclusions

• Load has structure to exploit for prediction• Structure is complex (self-similarity, epochs)

• Simple time series models are promising• Benefits of more sophisticated models are unclear

• Current research questions• What are the benefits of more sophisticated models?• How to characterize prediction error to user?• Is there a measure of inherent predictability?• How to incorporate load prediction into systems?

16

0

0.002

0.004

0.006

0.008

0.01

0.012

0.014

0.016

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

Best Mean

Best Markov

Best ARMA

Best ARMA 95%

Production Cluster ResearchCluster

Desktops