A Forecasting Capability Study of Empirical Mode

Decomposition for the Arrival Time of a Parallel

Batch System

Linh Ngo and Amy Apon Doug Hoffman

University of Arkansas Acxiom Corporation

1

Introduction:

Empirical Mode Decomposition (EMD)

Huang et. al.

Represents non-stationary complex time signals as sum of Intrinsic Mode Function (IMF)

IMF:

The number of extremes and the number of zero crossing in the whole data set must either equal or differ at most by oneThe number of extremes and the number of zero crossing in the whole data set must either equal or differ at most by one

At any point, the mean value of the envelope defined by the local maxima and the envelope defined by the local minima is zero

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Introduction:

EMD Sifting Process

Construct upper envelope cubic spline and lower envelope

cubic spline

Find mean of upper and lower envelopes, and

subtract this mean from data

IMF?Data

Yes

No

Monotonic?Manual?

Subtract IMF from Data

StopYes

No

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Introduction:

IMF example

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Introduction:

Application to Arrival Histogram

150

200

250

300

Arrival Count Per Bucket

Arrival Histogram of March 2007

0

50

100

150

1 25 49 73 97 121 145 169 193 217 241 265 289 313 337 361 385 409 433 457 481 505 529 553 577 601 625 649 673 697 721

Arrival Count Per Bucket

One-Hour BucketBeginning on 00:00 Wednesday March 01

Ending on 23:58 Saturday March 31

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Introduction:

Application to Arrival Histogram

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Workload Characterization using EMD

EMD and Workload Characterization

Workload Histogram decomposition

Piecewise sine fitting

Characterization Results

Improvements over hyper-exponential distribution

Require non-trivial manual fine tuning

Impractical comparing to traditional distribution techniques

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Can EMD do anything else?

Workload Forecasting

Preprocessing data for forecasting techniques

Improve accuracy and flexibility of predicted data

A common preprocessing technique to both workload characterization and forecasting

Workload characterization model that reflects actual future workload

Forecasting model with extended range and modification capability

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Characterization and Forecasting:

Comparison

Original Workload

Characterization Model

StatisticalMeasurements

PastWorkload

Forecasting Model

ExactMeasurements

Future of Past Workload

NoNo

Measurements

System/Simulator

PerformanceMeasurements

Model modification to create hypothetical scenarios for capacity

planning

Real Time Prediction

ExactMeasurements

Scheduling/Resource Management based on prediction

Real Future Workload

Yes

No

Yes

Yes

Yes

No

No

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Forecasting Feasibility Study:

Data Preprocessing

Pattern isolation:

Workloads, enterprise workloads in particular, contain patterns

9-5, M-F, monthly, yearly, holidays,

Individual patterns = Individual Signals with unique frequencies

Signal decomposition techniques

Difficulties: Difficulties:

Different arrival sources carry different patterns

Patterns that exist only for a period of time

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Forecasting Feasibility Study:

Arrival Patterns

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Arrival Time Histogram Comparison (Wednesday and Thursday, last week of May 2006)

Arrival Time Histogram Comparison ( Wednesdays, June 2006)

Existence of daily arrival patterns

Forecasting Feasibility Study:

Arrival PatternsComparing IMFs ofadjacent groups:1.1, 1.2, 1.3, and 1.4are the IMFs of thefirst group (4193 10,000) - 2.1, 2.2,2.3, and 2.4 are forthe second group (0- 5,000), and 3.1, 3.2,3.3, and 3.4 are forthe overall group (0- 10,000)

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- 10,000)

IMFs generated from adjacent data subset exhibit a sense of continuity

Forecasting Feasibility Study:

Hypothesis

IMFs can be used to isolate signals with patterns to be inputs of a forecasting technique

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Forecasting Feasibility Study:

Algorithm and Evaluation Metric

Algorithm:

Using two set of data, estimation data and prediction data

Calculate the optimal estimated weights of the estimation data set

Apply the calculated weights to the prediction data set in order to find out the future dataorder to find out the future data

Evaluation:

Mean Average Percentage Error

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=

=

1

0

n

i i

ii

measured

measuredpredictedMAPE

Forecasting Feasibility Study:

Preliminary Results

Experiment 1:predict the first Thursday of June 2006 based on the original histograms of the first

Experiment IMF Count Estimation MAPE Prediction MAPE

1 0 0.0% 53.89%

2 2 13.68% 32.27%

3 10 2.65% 39.08%

4 12 0.9% 36.2%

predict the first Thursday of June 2006 based on the original histograms of the first Wednesday of June 2006, and the last Wednesday and Thursday of May 2006.

Experiment 2: predict the first Thursday of June 2006 with the same data set, but this time the days are

decomposed to IMFs.

Experiment 3 and 4: predict the first Thursday of June 2006, using the IMFs of the first Wednesday of June, and

the last Wednesday and Thursday of May to predict first Thursday of June.

The ranges of the empirical data used by the EMD process are extended.

Experiment 3: Full month of May until the first Wednesday of June.

Experiment 4: Full month of April and May until the first Wednesday of June.

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Forecasting Feasibility Study:

Preliminary Analysis

Experiments with EMD preprocessing offer a better prediction result.

An increases in data retention in Experiment 4 from Experiment 3 improved the prediction.

Experiment 2:

Low number of IMFs

Low estimation MAPE

High prediction MAPE

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Forecasting Feasibility Study:

Conclusion

EMD: Potential data processing platform

Need better predictive tools to increase the accuracy of EMD-based predictions

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Proposed Work

Prediction techniques for EMD-based data

Comparison of EMD as a data preprocessing tool against traditional decomposition techniques (Wavelet and Fourier)

Application on different workloads

Effect of the length of retained data for forecasting

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Questions?

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