Yashar Ganjali, and Abtin KeshavarzianPresented by: Isaac Keslassy

Computer Systems LaboratoryDepartment of Electrical EngineeringStanford University

INFOCOM 2004

Load Balancing in Ad Hoc Networks:

Single-path Routing vs. Multi-path Routing

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Outline

1. Single-path vs. multi-path routing2. Comparison Criteria3. Network model4. Traffic distribution analysis

4-1. Single-path routing4-2. Multi-path routing

5. Simulations6. Optimal number of paths?7. Conclusion

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Single-path vs. Multi-path

s t

s t

Single-path routing

Multi-path routing

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Comparison Criteria

Overhead: Route discovery overhead Route maintenance overhead Data transmission overhead

Load distribution (throughput)

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Network ModelNodes: Distributed uniformly in a circle of radius one with density (high)Links: Any two nodes with distance <= T are connectedTraffic: Each node sends to any other node in the network with fixed rate

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Problem Statement

Find the amount of flow going through a node (load) at

distance r from the center.

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Any path starting at a node in S1 going to a node in S2 goes through node F.

Therefore, the traffic going through node F is proportional to S1 x S2.

S1

S2

Load Distribution Analysis:Single-path Routing

[P. Pham and S. Perreau, INFOCOM’03]

F

d

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[Pham and Perreau, INFOCOM’03]: Load is distributed uniformly using multi-path routing.

Load Distribution Analysis: Multi-path Routing

0102030405060

0 250 350 500 750 1000 1250

Distance from the Origin

Lo

ad

Single-path routing Multi-path routing

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Load Distribution Analysis: New Approach

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Load Distribution Analysis: New Approach

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Load Distribution Analysis

Problem: For a given node F in the network find the set of all node pairs (A,B) such that the rectangle defined by A and B contains F.

AF

B

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Load Distribution Analysis

A Fw

B

w

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Load Distribution Analysis

A F

B=(x,y)

d

L

y=L cosy=L sinL =d cosx=d cos2

y=d sin cosy2+(x-d/2)2=d2/4

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Load Distribution Analysis

A F

B

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Load Distribution Analysis

For a fixed node F, and and a given node A we can find all points B such that the traffic from A to B goes through F. If we sum up for all nodes A we can find the total traffic going through F.

F

A r

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How to choose w?

It is inversely proportional to .It depends on how nodes are connected.It depends on how paths are chosen: Length metric: hop-count, Euclidian

distance. Edge-disjoint vs. node disjoint.

It is increased by the number of paths in multi-path routing.

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How to choose w? (cont’d)

1. Keep all parameters fixed.2. Find w based on simulations for

single-path.3. For k paths use kw.

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Evaluation of the Model

500 Nodes - 2 Paths

0.00

1000.00

2000.00

3000.00

4000.00

5000.00

0.1 0.2 0.3 0.4 0.4 0.5 0.6 0.7 0.8 0.9

Distance

Lo

ad Simulation

Analysis

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Evaluation of the Model

500 Nodes - 4 Paths

0.00

2000.00

4000.00

6000.00

8000.00

10000.00

0.1 0.2 0.3 0.4 0.4 0.5 0.6 0.7 0.8 0.9

Distance

Lo

ad Simulation

Analysis

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Evaluation of the Model

500 Nodes - 10 Paths

0

20000

40000

60000

80000

100000

120000

0.1 0.2 0.3 0.4 0.4 0.5 0.6 0.7 0.8 0.9

Distance

Lo

ad Simulation

Analysis

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Effect of Increasing the Number of Paths in Multi-path routing

0

2

4

6

8

10

12

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

Distance from the Center

No

rmal

ized

Lo

ad

2 Paths

4 Paths

10 Paths

20 Paths

50 Paths

100 Paths

200 Paths

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Effect of Increasing the Number of Paths in Multi-path routing

0.00

0.50

1.00

1.50

2.00

2.50

3.00

3.50

4.00

4.50

Distance from the Center

Log(

Loa

d )

2 Paths

4 Paths

10 Paths

20 Paths

50 Paths

100 Paths

200 Paths

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Summary We introduced a new method for analyzing the traffic in Ad Hoc Networks.Advantages of the new model: Works for both single-path and multi-path Sensitive to the number of paths

We showed that increasing the number of paths in multi-path routing does not dramatically affect the load balance in the network. Open problem: What if we route on curves instead of shortest paths?

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Thank you!Thank you!

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Load Distribution Analysis

A F

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Load Distribution Analysis

A F

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Load Distribution Analysis

A F

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Load Distribution Analysis

FA

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Load Distribution Analysis