Vivaldi: A Decentralized Network Coordinate System

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 syste

m

• 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

Constant δ

Adaptive δ

Slow convergence

Oscillates

Adaptive δ leads lower error than constant δ

Evaluation: Robustness

The evolution of a stable 200-node network after 200 new nodes join.

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.

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

Increase longer links

Converges after 20 sec.

Go back to shorter links

Performance Comparison

Smallnetwork

Largenetwork

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

Increasing dimension decreases error but increases overhead.

Smallnetwork

Largenetwork

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