| <Poster Width="1735" Height="2453"> |
| <Panel left="38" right="535" width="631" height="480"> |
| <Text>Motivation</Text> |
| <Text>For latency-aware applications, round-trip-time estimation has</Text> |
| <Text>been studied extensively. But there are also lots of bandwidth-</Text> |
| <Text>aware applications. Prediction of bottleneck bandwidth has</Text> |
| <Text>received much less attention.</Text> |
| <Text>Therefore, we attempt to design a new system to predict</Text> |
| <Text>bottleneck bandwidth, based on matrix factorization.</Text> |
| <Text>As a first step, we need to prove:</Text> |
| <Text>1) Low-rank nature</Text> |
| <Text>bandwidth matricesofbottleneck</Text> |
| <Text>2) Feasibility of reducing dimension of</Text> |
| <Text>bottleneck bandwidth data space</Text> |
| </Panel> |
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| <Panel left="35" right="1031" width="635" height="444"> |
| <Text>Matrix Factorization</Text> |
| <Text>The network bottleneck bandwidth data space can be modelled</Text> |
| <Text>as square matrix B. Apply Principle Component Analysis on B:</Text> |
| <Figure left="47" right="1185" width="616" height="253" no="1" OriWidth="0" OriHeight="0 |
| " /> |
| </Panel> |
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| <Panel left="40" right="1493" width="630" height="730"> |
| <Text>Principle Component Analysis</Text> |
| <Text>We attempt to analyze the magnitude of singular values of B.</Text> |
| <Figure left="80" right="1630" width="537" height="436" no="2" OriWidth="0.239331" OriHeight="0.150178 |
| " /> |
| <Text>It shows that singular values decrease very fast. Considering the</Text> |
| <Text>’Oct 26’ line, the 4th singular value (0.156) is the first one that is</Text> |
| <Text>smaller than 0.2.</Text> |
| </Panel> |
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| <Panel left="37" right="2243" width="634" height="153"> |
| <Text>Acknowledgement</Text> |
| <Text>This work is supported by National Science Foundation of China</Text> |
| <Text>(No.60850003).</Text> |
| </Panel> |
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| <Panel left="688" right="533" width="1020" height="282"> |
| <Text>Methodology</Text> |
| <Text>Based on HP Scalable Sensing Service (S3), 250 interconnected hosts are extracted out for our evaluation.</Text> |
| <Text>From September 23 to December 23 2009, we collect bottleneck bandwidth data every four hours. Finally we</Text> |
| <Text>have 491datasets across 3 months for evaluation.</Text> |
| <Text>We compare the approximated matrix with the original one for evaluation. Relative error is defined as follows:</Text> |
| <Text>If (i, j ) ∈ {(m, n) | b</Text> |
| <Text>mn ≠ −1}, relative error</Text> |
| <Text>ij =b</Text> |
| <Text>ij '−b</Text> |
| <Text>ij</Text> |
| <Text>b</Text> |
| <Text>ij</Text> |
| </Panel> |
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| <Panel left="687" right="836" width="1023" height="1124"> |
| <Text>Evaluation of Dimension Reduction</Text> |
| <Text>The figure right shows the median</Text> |
| <Text>relative error when the dimension of</Text> |
| <Text>all the 491 datasets are reduced to</Text> |
| <Text>2D, 5D, 10D and 20D.</Text> |
| <Text>The average of median relative error</Text> |
| <Text>for 10D approximation is only 8.65%</Text> |
| <Text>among all the 491 datasets.</Text> |
| <Figure left="1071" right="929" width="619" height="488" no="3" OriWidth="0.250288" OriHeight="0.152852 |
| " /> |
| <Figure left="703" right="1411" width="601" height="522" no="4" OriWidth="0.238178" OriHeight="0.1582 |
| " /> |
| <Text>Considering the tradeoff between</Text> |
| <Text>computation complexity and target</Text> |
| <Text>dimension of reduction, a 10D</Text> |
| <Text>approximation is carried out to show the</Text> |
| <Text>cumulative distribution function of</Text> |
| <Text>relative error in figure left.</Text> |
| <Text>The 90th percentile relative error is only</Text> |
| <Text>0.281, meaning that 90% of the data</Text> |
| <Text>have lower relative error than 0.281.</Text> |
| </Panel> |
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| <Panel left="688" right="1980" width="1019" height="241"> |
| <Text>Conclusion</Text> |
| <Text>1. Dimension of bottleneck bandwidth data space can be reduced from250D to 10D</Text> |
| <Text>2. The average of median relative error for approximation is only8.65% among 491 datasets.</Text> |
| <Text>3. The 90th percentile relative error of 10D approximation is only0.281</Text> |
| </Panel> |
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| <Panel left="687" right="2240" width="1022" height="157"> |
| <Text>Future work</Text> |
| <Text>We would design a scalable bottleneck bandwidth prediction system based on matrix factorization, utilizing</Text> |
| <Text>the low-rank nature and low relative error in dimension reduction.</Text> |
| </Panel> |
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| </Poster> |
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