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Towards Network Triangle Inequality Violation Aware Distributed SystemsPowerPoint Presentation

Towards Network Triangle Inequality Violation Aware Distributed Systems

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Towards Network Triangle Inequality Violation Aware Distributed Systems

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.

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 Distributed Systems

- Characteristics of TIVs for the Internet delays?
- How do TIVs impact neighbor selection mechanisms?
- Ways to reduce the impacts of TIVs?

Outline Distributed Systems

- Analyzing TIV characteristics
- Understanding the impact of TIVs on neighbor selection mechanisms
- TIV alert mechanism

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

C Distributed Systems

TIV Severity

B

A

1- fraction of TIV

Triangulation ratio of ABC =

AB

AC+BC

TIV Severity MetricTIV severity:

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

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 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.

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.

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

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

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!

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 MeridianMisplacement: 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.

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

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.) 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 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

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.

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 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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