Host Load Prediction in a Google Compute Cloud with a Bayesian Model Sheng Di 1, Derrick Kondo 1, Walfredo Cirne 2 1 INRIA 2 Google

2/28 Outline Motivation of Load Prediction Google Load Measurements & Characterization Pattern Prediction Formulation Exponential Segmented Pattern (ESP) Prediction Transformation of Pattern Prediction Mean Load Prediction based on Bayes Model Bayes Classifier Features of Load Fluctuation Evaluation of Prediction Effect Conclusion

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 performance Stable 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 computing Resource Consolidation: Shutting down idle machines can save electricity cost.

4/28 Google Load Measurements & Characterization Overview of Google trace Google released one-month trace in Nov. of 2011 (40G disk space). 10,000+ Google 670,000 jobs, 25 million tasks in total Task: the basic resource consumption unit Job: a logic computation object that contains one or more tasks

5/28 Google Load Measurements & Characterization Load Comparison between Google and Grid (GWA) Google host load fluctuates with higher noises min noise / mean noise / max noise Google: , 0.028, AuverGrid: , , > 20 times

6/28 Pattern Prediction Formulation Exponentially 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: l 1, l 2, ….. (Evidence window)

7/28 Pattern Prediction Formulation (Cont ’ d) Reduction of ESP Prediction Problem Idea: Get Segmented Levels ( l i ) always from the mean load (denoted as η i ) during [t 0, t i ] We can get l i, based on t 0, (t i-1, η i-1 ), (t i, η i ) Two key steps in the Pattern Prediction Algorithm Predict mean values with b2 k lengths from current point Transform the set of mean load prediction to ESP Current time point Time Series t0t0 t1t1 t2t2 t3t3 t4t4

8/28 Traditional Approaches to Mean Load Prediction Can Feedback Control Model work? NO Example: Kalman Filter Reason: one-step look-ahead prediction doesn’t fit our long-interval prediction goal. Can we use short-term prediction error to instruct long-term prediction feed-back? NO Can the traditional methods like Linear Model fit Google host load prediction? Such as Simple Moving Average, Auto-Regression (AR), etc. 16 hours

9/28 Mean Load Prediction based on Bayes Model Principle of Bayes Model (Why Bayes?) We strongly believe the correctness of probability Posterior 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 Model Implementation of Bayes Classifier Evidence Window: an interval until current moment States 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 (F ml (e)) 2. Weighted Mean Load State (F wml (e)) 3. Fairness index (F fi (e))

13/28 eg. α = 4 Mean Load Prediction based on Bayes Model 4. Noise-decreased fairness index (F ndfi (e)) Load outliers are kicked out 5. Type state (F ts (e)): for degree of jitter Representation: (α, β ) α= # of types (or # of state levels) β= # of state changes β=1β=2β=3β=4β=5β=6β=7β=8 Prediction Interval eg. β = 8

14/28 F 4-sp (e)F 3-sp (e)F 2-sp (e) Mean Load Prediction based on Bayes Model 6. First-Last Load (F fll (e)) = { first load level, last load level } 7. N-segment Pattern (F N-sp (e)) F 2-sp (e): {0.01, 0.03} F 3-sp (e): {0.02, 0.04, 0.04} F 4-sp (e): {0.02, 0.02, 0.05, 0.05} Prediction Interval

15/28 Mean Load Prediction based on Bayes Model Correlation of Features Linear Correlation Coefficient Rank Correlation Coefficient

16/28 Mean Load Prediction based on Bayes Model Compatibility of Features Four Groups split: {F ml, F wml, F 2-sp, F 3-sp, F 4-sp }, {F fi, F ndfi }, {F ts }, {F fll } 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 Average Last-State use last state in the EW as the prediction value Prior Probability the value with highest prior probability Auto-Regression (AR): Improved Recursive AR Hybrid 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 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 Conclusion Objective: predict ESP of host load fluctuation Two-Step Algorithm Mean Load Prediction for the exponential interval from the current moment Transformation to ESP Bayes Model (for Mean Load Prediction) Exploration of best-fit combination of features Comparison with 7 other well-known methods Use Google Trace in the experiment Evaluation type A: Bayes Model ({F ml }) outperforms others by % Evaluation type B: {F ml,F fi,F ts,F fll } is the best combination. MSE of Pattern Predictions: majority are in [10 -8, ]

28/28 Questions ? Thanks Questions ?