Vivaldi: A Decentralized Network Coordinate System

1
Vivaldi A Decentralized Network Coordinate
System

• Authors
• Frank Dabek, Russ Cox, Frans Kaashoek, Robert
  Morris
• MIT
• Published at SIGCOMM 04

2
Introduction

• Vivaldi is a simple, adaptive, distributed
  algorithm for computing network coordinates that
  accurately predict Internet latencies without
  requiring any fixed infrastructure
• Internet Hosts compute their coordinates in some
  coordinate space such that the distance between
  themselves and other hosts coordinates predicts
  the RTT between them without sending probing
  packets just for measuring latencies

3
Algorithm

• Use synthetic distance between nodes to
  accurately map to latencies (RTT) between nodes.
• Can not create an exact mapping due to violations
  of triangle inequality

A lt B C
4
Algorithm

• Use synthetic distance between nodes to
  accurately map to latencies (RTT) between nodes.
• Can not create an exact mapping due to violations
  of triangle inequality

100 ms
N1
N3
48 ms
48 ms
N2
100 lt 48 48 100 lt 96
5
Algorithm

• Use synthetic distance between nodes to
  accurately map to latencies (RTT) between nodes.
• Can not create an exact mapping due to
  violations of triangle inequality
• Tries to minimize the error of predicted RTT
  values
• Observation
• Minimizing the square error function of
  predicted RTT between two nodes is analogous to
  minimizing the energy in a mass-spring system

Where Lij Actual Measure RTT between Node j
and Node j xi Synthetic coordinates of Node
i xj Synthetic coordinates of Node j
6
Algorithm
100
N1
N2
7
Algorithm
150
N1
N2
F12 100 150 F12 -50
8
Algorithm
100
N1
N2
F12 100 100 F12 0
9
Algorithm
100
100
N1
N2
N3
10
Algorithm
100
150
N3
N2
N2
F32 100 150 F32 50
F12 0
System Error F122 F322 0 502 2500
11
Algorithm
150
100
N1
N2
N3
F12 100 150 F12 -50
F32 0
System Error F122 F322 502 0 2500
12
Algorithm
125
125
N3
N1
N2
F32 100 125 F32 25
F12 100 125 F12 25
System Error F122 F322 252 252 1300
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Centralized version

• Calculate net Force on node i
• Move a step in the direction of the net Force

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d setting

• Sampling inaccurate node will not significantly
  affect the movement

15
Full Vivaldi Version
Adjust time step
16
Impact of Adaptive time stamp
17
Evaluation Methodology

• Environment
• Packet-level network simulator using measured RTT
  values from the Internet
• Latency data
• Matrix of inter-host Internet RTTs
• Compute coordinates from a subset of these RTTs
• Check accuracy of algorithm by comparing
  simulated results to full RTT matrix
• 2 Data sets (Measured Data)
• 192 nodes Planet Lab network, all pair-ping gives
  fully populated matrix
• Median RTT 76 ms
• 1740 Internet DNS servers
• Median RTT 159 ms
• populate full matrix using the King method
• Continuously measure pairs over a week take
  median (other schemes just keep minim measured
  RTT since King can give estimates that are lower
  than actual RTT need to take median)
• During collection of data need to make sure
  unwanted forwarding of name request did not occur
  (give RTT for the wrong name server)

18
Evaluation Methodology

• 2 Data sets (Synthetically generated Data)
• Grid
• Vivaldi accurately recovers RTT values but
  coordinates are translated and rotated from the
  original grids coordinates
• ITM topology generation

19
Using data

• Simulation test setup
• Input RTT matrix
• Send a packet one a second
• Delay by ½ RTT time
• Send RPC packet
• Uses measured RTT of RPC to update coordinates

20
Evaluation (Robustness to high error nodes)

• Adding many new nodes that do not know their
  coordinates s, so are very uncertain (200 stable,
  then 200 new)
• Constant delta, already certain node get knock
  away from there good coordinates
• Adaptive delta, already certain nodes stay stable
  while new nodes move relatively quickly to their
  correct coordinates

21
Evaluation (Communication Patterns)

• In 21 (localization in sensor networks) shown
  that sampling only low latency nodes gives good
  local coordinates but poor global coordinates.
• 400 node sim (set 4 close neighbor, set 4 far
  neighbor) chose from far neighbor set is a
  probability p.
• p .5 quick convergence
• p gt .5 convergence slows
• p lt .5 convergence slows
• no distant communication

22
Evaluation (Adapt to network changes)

• Ability to adapt to changes in the network
  (tested with Transit-Stub)
• extend one stub by 10x

23
Evaluation (Accuracy vs. GNP)
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Model Selection
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Critique

• Cool points
• Proposes simple decentralized way for
  measuring network latency
• Fast convergence
• Bad points
• Limited scope of application area due to its
  dependency on traffic pattern
• Applications communicating neighbors are less
  benefited from Vivaldi
• The implication of delta(d) is profound but no
  guidance provided
• No proposed architecture for managing coordinates
  information

26
New idea

• Scalable and distributed VC management system
• SPoN control plane?
• Exploits vivaldi scheme in clustering operations
• Cluster member nodes have received VC of other
  head nodes
• They decide to migrate the cluster by computing
  the distance between them and the cluster head
  nodes
• Exploits the spring-relaxation scheme in
  selecting data delivery node and clustering
  operatios in SPoN cluster
• Construct n dimensional virtual space with data
  loss, network bandwidth and latency.
• Compute the best VC in terms of the minimization
• Select the real node deployed in that coordinates
  or close to it

27

• Backup slides

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Evaluation Methodology
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Using data

• Error definitions
• Error of Link
• Absolute difference between predicted RTT
  (coordinate math) and measured (RTT Matrix
  element)
• Error of Node
• Median of link errors involving this node
• Error of System
• Median of all node errors