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

2. Outline Introduction Vivaldi Algorithm Evaluation
Coordinate Model Selection
Conclusions

3. Outline Introduction Vivaldi Algorithm Evaluation
Coordinate Model Selection
Conclusions

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

5. 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

6. 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

7. Outline Introduction Vivaldi Algorithm Evaluation
Coordinate Model Selection
Conclusions

8. 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.

9. The simple Vivaldi algorithm
Called for each new RTT measurement
timestep

10. 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

11. The Vivaldi Algorithm

12. Outline Introduction Vivaldi Algorithm Evaluation
Coordinate Model Selection
Conclusions

13. 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

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

15. 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.

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

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

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

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

20. Outline Introduction Vivaldi Algorithm Evaluation
Coordinate Model Selection
Conclusions

21. 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

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

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

24. 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).

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

26. 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