Vivaldi: A Decentralized Network Coordinate System F. Dabak, R. Cox, F. Kaashoek, R. Morris MIT

Outline Introduction Vivaldi Algorithm Evaluation Coordinate Model Selection Conclusions

Outline Introduction Vivaldi Algorithm Evaluation Coordinate Model Selection Conclusions

Motivation Large-scale Internet applications can benefit from an ability to predict round-trip times to other hosts without having to contact them first.

Design Goal Finding a metric space that embeds the Internet with little error Scaling to a large number of hosts Decentralizing the implementation Minimizing probe traffic Adapting to changing network conditions

Contribution of the Paper A decentralized, low overhead, adaptive synthetic coordinate system that computes coordinates which predict Internet latencies with low error Vivaldi is used by the Chord P2P lookup system Introduces the notion of a directionless height that improves the prediction accuracy

Outline Introduction Vivaldi Algorithm Evaluation Coordinate Model Selection Conclusions

Prediction Error Let Lij be the actual RTT between nodes i and j, and xi be the coordinates assigned to node i. The errors in the coordinates can be characterized using a squared-error function: The goal is to make this error small.

The simple Vivaldi algorithm Called for each new RTT measurement timestep

An Adaptive Timestep The rate of convergence is governed by the δ timestep A small δ causes slow convergence A large δ causes oscillation Vivaldi varies δ depending on how certain the node is about its coordinates Each node compares each new measured RTT sample with the predicted RTT, and maintains local error

The Vivaldi Algorithm

Outline Introduction Vivaldi Algorithm Evaluation Coordinate Model Selection Conclusions

Evaluation Environment The experiments are conducted using a packet-level network simulator running with RTT data collected from the Internet. PlanetLab data set: 192 hosts on the PlanetLab network testbed King data set: 1740 Internet DNS servers

Evaluation: Convergence Slow convergence Oscillates Constant δ Adaptive δ Adaptive δ leads lower error than constant δ

Evaluation: Robustness Using the constant δ, the initial structure of the system has been destroyed, a result of placing to much faith in young high-error nodes. Using the adaptive δ preserves the established order. The evolution of a stable 200-node network after 200 new nodes join.

Evaluation: Communication Patterns When nodes only contact their neighbors, coordinates at the large scale is not accurate.

The effect of long-distance communication Even when only 5 % of the samples involve distant nodes, skewed coordinate placements will be avoided.

Evaluation: Adaptation Converges after 20 sec. Go back to shorter links Increase longer links

Performance Comparison Small network Large network Relative error of Vivaldi is close to that of GNP which requires landmarks.

Outline Introduction Vivaldi Algorithm Evaluation Coordinate Model Selection Conclusions

Model Selection Vivaldi works with any coordinate system that supports the magnitude, addition, and subtraction operations We consider a few possible coordinate spaces that might better capture the Internet’s underlying structure

Euclidean Spaces Small network Large network Increasing dimension decreases error but increases overhead.

Spherical Coordinates Small network Large network 2D coordinates is better.

Height Vectors A height vector consists of a Euclidean coordinate augmented with a height The Euclidean portion models a high-speed Internet core with latencies proportional to geographic distance, while the height models the time it takes packets to travel the access link from the node to the core (e.g. queuing delay).

Height Vector Performance Height vectors perform better than both 2D and 3D Euclidean coordinates.

Conclusions Proposed a decentralized, low overhead, adaptive synthetic coordinate system that computes coordinates which predict Internet latencies with low error Introduced the notion of a directionless height that improves the prediction accuracy