Towards Network Triangle Inequality Violation Aware Distributed Systems
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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 l.jpg

A Distributed Systems

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 l.jpg

A: Distributed Systems128.42.129.40

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 l.jpg
What we do NOT know about TIV Distributed Systems

  • Characteristics of TIVs for the Internet delays?

  • How do TIVs impact neighbor selection mechanisms?

  • Ways to reduce the impacts of TIVs?


Outline l.jpg
Outline Distributed Systems

  • Analyzing TIV characteristics

  • Understanding the impact of TIVs on neighbor selection mechanisms

  • TIV alert mechanism


Data sets l.jpg
Data Sets Distributed Systems

  • 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 l.jpg

C Distributed Systems

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 l.jpg

0 Distributed Systems

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 l.jpg
TIV Severity vs. Delay Distributed Systems

  • 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 l.jpg

nearest pair (average RTT: 6.08 ms) Distributed Systems

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 l.jpg
Outline Distributed Systems

  • 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 l.jpg

20 ms Distributed Systems

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 l.jpg

C Distributed Systems

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 l.jpg

3ms Distributed Systems

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 l.jpg
Outline Distributed Systems

  • 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 l.jpg

B Distributed Systems

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 l.jpg
TIV Alert Mechanism (cont.) Distributed Systems

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 l.jpg
Experiment Methodology Distributed Systems

  • 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 l.jpg

A Distributed Systems

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 l.jpg

A Distributed Systems

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 l.jpg
Conclusion Distributed Systems

  • 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.


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