Host Load Prediction in a Google Compute Cloud with a Bayesian Model

Sheng Di1, Derrick Kondo1, Walfredo Cirne2

1INRIA

2Google

2/28

OutlineMotivation of Load PredictionGoogle Load Measurements & CharacterizationPattern Prediction Formulation

Exponential Segmented Pattern (ESP) Prediction Transformation of Pattern Prediction

Mean Load Prediction based on Bayes ModelBayes ClassifierFeatures of Load Fluctuation

Evaluation of Prediction EffectConclusion

3/28

Motivation (Who needs Load Prediction)From the perspective of on-demand allocation

User’s resources/QoS are sensitive to host load.

From the perspective of system performanceStable load vs. Unstable load:

System is best to run in a load balancing state, where the load burst can be released asap.

From the perspective of Green computingResource Consolidation:

Shutting down idle machines can save electricity cost.

4/28

Google Load Measurements & Characterization

Overview of Google traceGoogle released one-month trace in Nov. of

2011 (40G disk space).10,000+ machines @ Google670,000 jobs, 25 million tasks in totalTask: the basic resource consumption unitJob: a logic computation object that

contains one or more tasks

5/28

Google Load Measurements & CharacterizationLoad Comparison between Google and Grid (GWA)

Google host load fluctuates with higher noises min noise / mean noise / max noise

Google: 0.00024, 0.028, 0.081AuverGrid: 0.00008, 0.0011, 0.0026

> 20 times

6/28

Pattern Prediction FormulationExponentially Segmented Pattern (ESP)

The hostload fluctuation over a period is split into a set of consecutive segments, whose lengths increase exponentially.

We predict the mean load over each time segment: l1, l2, …..

(Evidence window)

7/28

Pattern Prediction Formulation (Cont’d)Reduction of ESP Prediction Problem

Idea: Get Segmented Levels (li) always from the mean load (denoted as ηi ) during [t0, ti ]

We can get li , based on t0, (ti-1,ηi-1), (ti,ηi)

Two key steps in the Pattern Prediction AlgorithmPredict mean values with b2k lengths from current pointTransform the set of mean load prediction to ESP

Current time pointTime Seriest0 t1 t2 t3 t4

8/28

Traditional Approaches to Mean Load PredictionCan Feedback Control Model work? NO

Example: Kalman FilterReason: one-step look-ahead prediction doesn’t fit our long-int

erval prediction goal.Can we use

short-term prediction

error to instruct

long-term prediction

feed-back? NOCan the traditional methods like

Linear Model fit Google host load prediction?Such as Simple Moving Average, Auto-Regression (AR), etc.

16 hours 16 hours

9/28

Mean Load Prediction based on Bayes ModelPrinciple of Bayes Model (Why Bayes?)

We strongly believe the correctness of probabilityPosterior Probability rather than Prior Probability

Naïve Bayes Classifier (N-BC) Predicted Value:

Minimized MSE Bayes Classifier (MMSE-BC) Predicted Value:

10/28

Why do we use Bayes Model? Special Advantages of Bayes Model

Bayes Method can

1. effectively retain important features about load fluctuation and noises, rather than ignoring them.

2. dynamically improve prediction accuracy, with more accurate probability updated based on increasing samples.

3. estimate the future with low computation complexity, due to quick probability calculation.

4. only take limited disk space since it just needs to keep/update corresponding probability values

11/28

Mean Load Prediction based on Bayes ModelImplementation of Bayes Classifier

Evidence Window: an interval until current momentStates of Mean Load: for prediction interval

r states (e.g., r = 50 means there are 50 mean load states to predict: [0,0.02), [0.02,0.04),……, [0.98,1]

)

Key Point: How to extract features in Evidence Window?

12/28

Mean Load Prediction based on Bayes Model Features of Hostload in Evidence Window

1. Mean Load State (Fml(e))

2. Weighted Mean Load State (Fwml(e))

3. Fairness index (Ffi(e))

13/28

eg. α = 4

Mean Load Prediction based on Bayes Model

4. Noise-decreased fairness index (Fndfi(e)) Load outliers are kicked out

5. Type state (Fts(e)): for degree of jitter Representation: (α, β) α= # of types (or # of state levels) β= # of state changes

0.020.040.06

0.00

0.100.08

β=1β=2 β=3β=4 β=5 β=6β=7β=8Prediction Interval

eg. β = 8

14/28F4-sp(e)F3-sp(e)F2-sp(e)

Mean Load Prediction based on Bayes Model

6. First-Last Load (Ffll(e))

= {first load level, last load level }7. N-segment Pattern (FN-sp(e))

F2-sp(e): {0.01, 0.03}

F3-sp(e): {0.02, 0.04, 0.04}

F4-sp(e): {0.02, 0.02, 0.05, 0.05}

0.020.040.06

0.00

0.100.08

Prediction Interval

15/28

Mean Load Prediction based on Bayes ModelCorrelation of Features

Linear Correlation CoefficientRank Correlation Coefficient

16/28

Mean Load Prediction based on Bayes ModelCompatibility of Features

Four Groups split: {Fml, Fwml, F2-sp, F3-sp, F4-sp} , {Ffi, Fndfi} , {Fts} , {Ffll}

Total Number of Compatible Combinations:

17/28

Evaluation of Prediction Effect (Cont’d)List of well-known load prediction methods

Simple Moving Average Mean Value in the Evidence Window (EW)

Linear Weighted Moving Average Linear Weighted Moving Average Value in the EW

Exponential Moving AverageLast-State

use last state in the EW as the prediction valuePrior Probability

the value with highest prior probabilityAuto-Regression (AR): Improved Recursive ARHybrid Model [27]: Kalman filter + SG filter + AR

18/28

Evaluation of Prediction Effect (Cont’d)Training and Evaluation

Evaluation Type A: the case with insufficient samples Training Period: [day 1, day 25]: only 18,000 load samples Test Period: [day 26, day 29]

Evaluation Type B: ideal case with sufficient samples Training Period : [day 1, day 29]: emulation of larger set of samples Test Period: [day 26, day 29]

19/28

Evaluation of Prediction Effect (Cont’d)Evaluation Metrics for Accuracy

Mean Squared Error (MSE)

where are true mean values

and Success Rate (delta of 10%) in the test period

success rate = Number of Accurate Predictions

Total Number of Predictions

20/28

Evaluation of Prediction Effect (Cont’d)1. Exploration of Best Feature Combination

(Success Rate): Evaluation Type A Representation of Feature Combinations

101000000 denotes the combination of the mean load feature and fairness index feature

(a) s = 3.2 hour (b) s = 6.4 hour (c) s = 12.8 hour

21/28

Evaluation of Prediction Effect (Cont’d)1. Exploration of Best Feature Combination

(Mean Squared Error)

(a) s = 3.2 hour (b) s = 6.4 hour (c) s = 12.8 hour

22/28

Evaluation of Prediction Effect (Cont’d)2. Comparison of Mean Load Prediction Methods

(Success Rate of CPU load w.r.t. Evaluation Type A)

(a) s = 6.4 hour (b) s = 12.8 hour

23/28

Evaluation of Prediction Effect (Cont’d)2. Comparison of Mean Load Prediction Methods

(MSE of CPU load w.r.t. Evaluation Type A)

(a) s = 6.4 hour (b) s = 12.8 hour

24/28

Evaluation of Prediction Effect (Cont’d)4. Comparison of Mean-Load Prediction Methods

(CPU load w.r.t. Evaluation Type B)

Best feature Combination mean load fairness index type-state first-last

25/28

Evaluation of Prediction Effect (Cont’d)5. Evaluation of Pattern Prediction Effect

Mean Error & Mean MSE Mean Error:

26/28

Evaluation of Prediction Effect (Cont’d)5. Evaluation of Pattern Prediction Effect

Snapshot of Pattern Prediction (Evaluate Type A)

27/28

ConclusionObjective: predict ESP of host load fluctuationTwo-Step Algorithm

Mean Load Prediction for the exponential interval from the current moment

Transformation to ESPBayes Model (for Mean Load Prediction)

Exploration of best-fit combination of featuresComparison with 7 other well-known methods

Use Google Trace in the experimentEvaluation type A:

Bayes Model ({Fml}) outperforms others by 5.6-50%Evaluation type B: {Fml,Ffi,Fts,Ffll} is the best combination.MSE of Pattern Predictions: majority are in [10-8, 10-5]

28/28

Thanks QQueueststioionnss??