Phoenix: Towards an Accurate, Practical and Decentralized Network Coordinate System Yang Chen 1, Xiao Wang 1, Xiaoxiao Song 1, Eng Keong Lua 2, Cong Shi 3, Xiaohan Zhao 1, Beixing Deng 1, Xing Li 1 1 Department of Electronic Engineering, Tsinghua University, Beijing , China 2 College of Engineering, Carnegie Mellon University, Pittsburgh, PA College of Computing, Georgia Institute of Technology, Atlanta, GA 30332

Outline Introduction Related Work Design of Phoenix Performance Evaluation Conclusion

Introduction Problem ▫Distance (Latency) information is very important in Internet applications: Server Selection, Overlay Construction, Overlay Multicast, Overlay Routing, Application Layer Anycast ▫Direct measurement: Bad scalability Network Coordinate (NC) System ▫Scalable way for Internet distance prediction ▫Use O(N) measurement to predict the distances of N 2 end-to-end links

Related Work Euclidean Distance based Network Coordinates and Triangle Inequality Violation (TIV) Dot Product based NC and IDES

Euclidean Distance based NC Euclidean distance based NC is an embedding of N hosts into d-dimensional Euclidean space R d Typical NC systems ▫GNP,Vivaldi,PIC,NPS… d=3

Triangle Inequality Violation (TIV) D(A,C)+D(C,B)<D(A, B) D E (A,C)+D E (C,B)>D E (A, B) Any three hosts with TIV cannot be embedded into Euclidean space within some level of accuracy, for the distances among them in Euclidean space must obey triangle inequality.

Dot Product based NC D E (A,C)+D E (C,B)>D E (A, B) tolerate the constraints of TIVs.

IDES First dot product based NC system Problems ▫Negative Distance ▫Fair Prediction Accuracy

Negative Distance in IDES Cause the malfunction of the system because the distance (Round Trip Time) can not be negative.

Fair Prediction Accuracy ▫Reason: Error Propagation ▫A certain host gives equal confidence to each referred NC ▫However, some NCs are very inaccurate due to different factors Prediction Accuracy: No better than GNP/Vivaldi/…!!

Design Goal of Phoenix Accurate ▫Dot Product based NC ▫Weighted Model Decentralized Practical ▫Never give negative predicted distance

Architecture of Phoenix Early Hosts Ordinary Hosts

Early Hosts If N ≤ m, the new host H new will be considered as one of the early hosts. ▫These early hosts will probe each other to obtain the N × N distance matrix ▫The system will use NMF (Non-negative Matrix Factorization) algorithm to get the NCs (incoming vectors and the outgoing vectors) of these early hosts.

Ordinary Hosts N>m ▫For each new host H new  select any m existing hosts randomly  H new measures its RTTs to these m hosts as well as retrieves the NCs (X new and Y new )of these m hosts.  NC can be calculated and updated periodically.

NC Calculation of Ordinary Hosts Calculation of X new and Y new Predicted Distance between H new and R i Different weights are assigned to each referred vectors

Weight Calculation C is set as 5 in our Phoenix implementation. The more accurate the referred vector is, the higher confidence (weight) should be given to this NC. In contrast, some referred vectors with abnormal high error will not be considered for NC calculation.

Performance Evaluation Setup of the Experiment Metrics Evaluation Results on Prediction Accuracy Convergence Behavior of Phoenix Robustness over Measurement Anomalies

Setup of the Experiment All of these three systems use 10-dimensional coordinates. Phoenix: each host has m reference hosts IDES: m randomly selected landmarks Vivaldi: each host has m neighbors. (c c =0.25,c e =0.25) m=32 10 runs are performed on each data set and the average results are reported.

Datasets

Metrics Relative Error (RE) ▫Smaller RE indicates higher prediction accuracy. When measured distance equals to predicted distance, the RE value will be zero. ▫More attention is paid to the 90th Percentile Relative Error (NPRE) since it can guarantee 90% of the hosts have lower RE values than it

Prediction Accuracy Compared with Vivaldi, the representative Euclidean distance based NC, Phoenix can reduce the NPRE by between 18.34% (P2PSim data set) and 52.17% (AMP data set). Our simulation results demonstrate that Phoenix can achieve high prediction accuracy in a decentralized and practical way.

Convergence Behavior of Phoenix  Basically, Phoenix will converge in less than 10 rounds.  the final median prediction error of Phoenix is about 31% smaller than Vivaldi. Therefore the convergence of Phoenix is very fast and effective.

Robustness over Measurement Anomalies Phoenix is very robust to small amount of measurements anomalies. The difference between Phoenix and Phoenix(Simple) demonstrates that the weighted model can eliminate the impact of measurement anomalies greatly.

Conclusion Phoenix achieves much higher prediction accuracy than state-of-the-art NC systems in different typical Internet data sets Phoenix is an accurate, practical and decentralized solution to scalable Internet distance prediction.

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Phoenix: Towards an Accurate, Practical and Decentralized Network Coordinate System Network Coordinate System Triangle Inequality Violation (TIV) Negative Distance Distance Prediction Accuracy Approach Vivaldi  ★★★ Euclidean Distance IDES  ★★★ Matrix Factorization Phoenix ★★★★★ Matrix Factorization + Weighted Model