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Towards Network Triangle Inequality Violation Aware Distributed Systems A C B AB + AC > BC > |AB – AC| Introduction Many distributed systems rely on the neighbor selection mechanisms to construct overlay structures with good network performance.

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introduction

A

C

B

AB + AC > BC > |AB – AC|

Introduction
  • Many distributed systems rely on the neighbor selection mechanisms to construct overlay structures with good network performance.
  • Neighbor selection mechanisms often assume triangle inequality holds for the Internet delays in order to infer delays without measuring them.
network t riangle i nequality v iolation

A: 128.42.129.40

65 ms

330ms

520 ms

B:76.194.27.220

C: 219.243.200.93

AB + AC < BC !

Network Triangle Inequality Violation
  • Real Internet delays violate triangle inequality in many cases.
  • Neighbor selection mechanisms make mistakes because of Triangle Inequality Violation (TIV).
what we do not know about tiv
What we do NOT know about TIV
  • Characteristics of TIVs for the Internet delays?
  • How do TIVs impact neighbor selection mechanisms?
  • Ways to reduce the impacts of TIVs?
outline
Outline
  • Analyzing TIV characteristics
  • Understanding the impact of TIVs on neighbor selection mechanisms
  • TIV alert mechanism
data sets
Data Sets
  • DS2 data
    • RTTs among 4000 DNS servers
    • One DNS server per domain
    • Measured by the King tool
    • http://www.cs.rice.edu/~bozhang/ds2/
  • Other data:
    • p2psim data, Meridian data, PlanetLab data
tiv severity metric

C

TIV Severity

B

A

1- fraction of TIV

Triangulation ratio of ABC =

AB

AC+BC

TIV Severity Metric

TIV severity:

Sum of the triangulation ratios for all the TIVs (normalized by the network size)

clustering property

0

TIV severity

255

C1-C3

C1

C1-C2

C2-C3

C3

C2

C1

C2

C3

- Picture from PlanetLab.org

Clustering Property
  • Can we predict TIV severity by clustering property?
  • Crossing cluster edges tend to cause more TIVs, but it is hard to predict TIV severity of an edge by this coarse-grain trend.
tiv severity vs delay
TIV Severity vs. Delay
  • Can we predict TIV severity by delay length?
  • Long edges tend to cause more TIVs.
  • Irregular relation between TIV severity and delay.
  • It is hard to predict the TIV severity of an edge just by its delay length.
proximity property

nearest pair (average RTT: 6.08 ms)

A

B

An

Bn

nearest-pair-edge

random pair (average RTT: 156 ms)

A

B

Ar

Br

random-pair-edge

Proximity Property
  • Can we predict TIV severity by proximity property?
  • Close-by nodes do not necessarily have similar TIV severity characteristic.
outline11
Outline
  • Analyzing TIV characteristics
    • TIV is a complex phenomenon in the Internet, and it is hard to predict TIV by naïve heuristics.
  • Understanding the impact of TIVs on neighbor selection mechanisms
  • TIV alert mechanism
the impact of tivs on neighbor selection

20 ms

20 ms

B

20 ms

A

d

T

(1-)d

(1+)d

Y

(20, 25.3)

20ms

20ms

(10,8)

(30,8)

20ms

X

The Impact of TIVs on Neighbor Selection
  • Representative neighbor selection mechanisms

Vivaldi: metric embedding

Meridian: online probing

  • To reduce overhead:
  • Termination factor 
  • Limit the number of ring members
the impacts of tivs on vivaldi

C

100ms

5ms

A

5 ms

B

The Impacts of TIVs on Vivaldi
  • High error
    • Median absolute error: 20 ms for all the edges in the data set.
  • Coordinates oscillation
    • Median oscillation speed: 1.6ms/step
    • Large oscillation range: 170ms for a 20 ms edge!
the impacts of tivs on meridian

3ms

N

6.5ms

4ms

6ms

25ms

2ms

T

12ms

B

11ms

N

A

6ms

18ms

=0.5

The Impacts of TIVs on Meridian

Misplacement: Given any two nodes A and T with delay d, because of TIV, the ring members within d delay of node A are not placed in the range (1-)d to (1+)d of node T.

  • Misplacement in ring construction happens on 12% of the ring members of all the nodes in the data set.
  • Meridian fails to find the nearest neighbor for 13% of the experiments even under idealized setting.
outline15
Outline
  • Analyzing TIV characteristics
  • Understanding the impact of TIVs on neighbor selection mechanisms
    • Vivaldi yields high error and rapid coordinate oscillation.
    • Meridian makes mistakes in ring construction and fails to find nearest neighbor even under idealized settings.
  • TIV alert mechanism
tiv alert mechanism

B

A

TIV Alert Mechanism
  • The edges causing severe TIVs are highly likely to be shrunk in when embedding them into a metric space.
  • Using the prediction ratio in metric embedding as a heuristic indicator of TIV severity.
tiv alert mechanism cont
TIV Alert Mechanism (cont.)

Worst 20%: The top 20% edges with highest TIV severity

  • Identify edges causing severe TIVs with reasonable accuracy and recall rate.
  • Easy to get prediction ratios in Vivaldi and Meridian.
experiment methodology
Experiment Methodology
  • Neighbor selection experiment methodology
    • Vivaldi: 32 random neighbor, 5D Euclidean space
    • Meridian: default setting (s = 2, =0.5, =1), no limitation on number of ring members.
    • Percentage penalty:
    • Aggregated over 5 runs
using tiv alert in vivaldi

A

Using TIV Alert in Vivaldi
  • Dynamic neighbor Vivaldi:
  • Identify the neighbors causing severe TIVs by prediction ratios and replace them by random neighbors
  • At each iteration, randomly sample another 32 neighbors, and from the 64 candidates, we remove the half with lowest prediction ratios.
using tiv alert in meridian

A

T

Using TIV Alert in Meridian
  • Identify the edges causing severe TIVs by prediction ratios and fix the mistakes in ring construction and online query.
conclusion
Conclusion
  • Analyzed the characteristics of TIVs based on the Internet delay measurement, and highlight the irregular behavior of TIVs.
  • Investigated the impacts of TIVs on two representative neighbor selection mechanisms.
  • Proposed a TIV alert mechanism that can identify edges causing severe TIVs.
  • TIV alert mechanism can provide TIV awareness in a variety of distributed systems.