A pattern fusion model for
multi-step-ahead CPU load prediction
Systems and Software
Dingyu Yanga, Jian Caoa,∗, Jiwen Fua, Jie Wangb,
Jianmei Guoc
鍾舜璽
1
Introduction
• Resource availability often changes from time to time
and schedulers needs a global view of all resources in
a distributed system.
• Sometimes high CPU load means performance
anomalies that may result in system collapse.
2
WNN and PSF
• Weighted Nearest Neighbors (WNN) algorithm
• Pattern Sequence-based Forecasting (PSF) algorithm
• Euclidean distance
– not enough to match the similar patterns.
3
WNN and PSF (cont.)
• One-step-ahead prediction strategy
– if the one-step-ahead value is not accurate, the predictions
for the following points in time will become more and
more inaccurate.
4
A pattern fusion model for multi-stepahead CPU load prediction
5
Pattern extraction
6
Pattern extraction (cont.)
7
Pattern extraction (cont.)
CPU load
9
8
7
6
5
CPU load
4
3
2
1
0
0
1
2
3
4
5
6
7
8
8
Pattern extraction (cont.)
• Pattern filtering
𝑛𝑢𝑚𝑏𝑒𝑟(𝑓𝑖𝑙𝑡𝑒𝑟(𝑄𝑖 ))
≤1−𝛼
𝑛𝑢𝑚𝑏𝑒𝑟(𝑄𝑖 )
𝑓𝑖𝑙𝑡𝑒𝑟 𝑄𝑖 : 𝑎 𝑓𝑢𝑛𝑐𝑡𝑖𝑜𝑛 𝑡ℎ𝑎 𝑟𝑒𝑡𝑢𝑟𝑛𝑠 𝑎 𝑝𝑎𝑡𝑡𝑒𝑟𝑛 𝑠𝑢𝑏𝑠𝑒𝑡 𝑤𝑖𝑡ℎ ℎ𝑖𝑔ℎ𝑒𝑟 𝑜𝑐𝑐𝑢𝑟𝑟𝑒𝑛𝑐𝑒
𝑓𝑟𝑒𝑞𝑢𝑒𝑛𝑐𝑦
𝑛𝑢𝑚𝑏𝑒𝑟 𝑄𝑖 : 𝑝𝑎𝑡𝑡𝑒𝑟𝑛 𝑛𝑢𝑚𝑏𝑒𝑟
𝑛𝑢𝑚𝑏𝑒𝑟 𝑓𝑖𝑙𝑡𝑒𝑟 𝑄𝑖 : 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑟𝑒𝑚𝑎𝑖𝑛𝑖𝑛𝑔 𝑝𝑎𝑡𝑡𝑒𝑟𝑛𝑠
• Pattern merging
↑↑↑↑↑↑↑↑
↑↑↑∗↑↑↑↑
↑↑↑↓↑↑↑↑
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Pattern matching
10
Pattern matching (cont.)
• Pattern similarity matching
– Euclidean distance matching
𝑑𝑖𝑠𝑡 𝑖, 𝑗 = 𝑋𝑖 − 𝑚𝑗
𝑇ℎ𝑒 𝑡𝑜𝑝 𝑘 𝑛𝑒𝑎𝑟𝑒𝑠𝑡 𝑝𝑎𝑡𝑡𝑒𝑟𝑛𝑠 𝑐𝑎𝑛 𝑏𝑒 𝑐ℎ𝑜𝑠𝑒𝑛
– Fluctuation pattern set matching
𝑋𝑖′ − 𝑚𝑗′
𝜆 ≥1−
𝑙𝑒𝑛𝑔𝑡ℎ(𝑋𝑖′ )
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Pattern weighting strategy
• Average rule strategy
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Pattern weighting strategy (cont.)
• Uniform decline strategy
𝜔𝑖 = 1 𝑙
𝑖
𝜔
𝜔𝑖′ = 𝑖
𝑑
𝑖=1 𝜔𝑖
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Pattern weighting strategy (cont.)
14
Pattern weighting strategy (cont.)
15
Prediction results function
• Adaboost algorithm
𝑡
𝑤
𝑖
1. 𝑠𝑒𝑡 𝜑𝑖𝑡 = 𝑛
𝑡
𝑖=1 𝑤𝑖
2. 𝑒𝑟𝑟𝑡 =
𝑛
𝑡
𝑖=1 𝜑𝑖
∗ 𝐼 𝑑𝑖 ≠ ℎ𝑚 𝑥𝑖
𝑛
𝑡
𝑖=1 𝜑𝑖
𝐼=
1 𝑑𝑖 ≠ ℎ𝑚 𝑥𝑖
0 𝑑𝑖 = ℎ𝑚 𝑥𝑖
1 1 − 𝑒𝑟𝑟𝑡
3. 𝛼𝑡 = ln
2
𝑒𝑟𝑟𝑡
4. 𝜑𝑖𝑡 = 𝜑𝑖𝑡 ∗ 𝑒𝑥𝑝 𝛼𝑡 ∗ 𝐼 𝑑𝑖 ≠ ℎ𝑚 𝑥𝑖
16
Prediction results function (cont.)
• Prediction values from different values of various
length patterns:
17
Experiment
• Experiment settings
– Mean absolute error (MAE)=
1
𝑁
𝑁
𝑖=1
– Mean relative error (MRE)= 100 ∗
1
𝑁
𝑥𝑖 − 𝑥
𝑁 𝑥𝑖 −𝑥
𝑖=1 𝑥
𝑖
18
Experiment (cont.)
19
Experiment (cont.)
• Pattern similarity measurement
• The influences of filter parameter
𝑛𝑢𝑚𝑏𝑒𝑟(𝑓𝑖𝑙𝑡𝑒𝑟(𝑄𝑖 ))
≤1−𝛼
𝑛𝑢𝑚𝑏𝑒𝑟(𝑄𝑖 )
20
Experiment (cont.)
• Different pattern weighting strategies
• Multi-step-ahead predictions
21
Experiment (cont.)
• Comparison with iterative one-step-ahead prediction
22
Experiment (cont.)
• Comparisons with other prediction approaches
• Run time
23
Conclusion
• The contribution of this paper is a fusion model for
multi-step-ahead CPU load prediction.
• We plan to consider longer steps and improve the
prediction accuracy in future.
• In addition, multivariate prediction, such as memory
usage and disk usage predictions are also interesting
topics.
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