Yashar Ganjali, and Abtin Keshavarzian Presented by: Isaac Keslassy Computer Systems Laboratory Department of Electrical Engineering Stanford University.

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

INFOCOM 2004 Load Balancing in Ad Hoc Networks 2

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

INFOCOM 2004 Load Balancing in Ad Hoc Networks 3

Single-path vs. Multi-path

s t

s t

Single-path routing

Multi-path routing

INFOCOM 2004 Load Balancing in Ad Hoc Networks 4

Comparison Criteria

Overhead: Route discovery overhead Route maintenance overhead Data transmission overhead

Load distribution (throughput)

INFOCOM 2004 Load Balancing in Ad Hoc Networks 5

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

INFOCOM 2004 Load Balancing in Ad Hoc Networks 6

Problem Statement

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

distance r from the center.

INFOCOM 2004 Load Balancing in Ad Hoc Networks 7

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

INFOCOM 2004 Load Balancing in Ad Hoc Networks 8

[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

INFOCOM 2004 Load Balancing in Ad Hoc Networks 9

Load Distribution Analysis: New Approach

INFOCOM 2004 Load Balancing in Ad Hoc Networks 10

Load Distribution Analysis: New Approach

INFOCOM 2004 Load Balancing in Ad Hoc Networks 11

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

INFOCOM 2004 Load Balancing in Ad Hoc Networks 12

Load Distribution Analysis

A Fw

B

w

INFOCOM 2004 Load Balancing in Ad Hoc Networks 13

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

INFOCOM 2004 Load Balancing in Ad Hoc Networks 14

Load Distribution Analysis

A F

B

INFOCOM 2004 Load Balancing in Ad Hoc Networks 15

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

INFOCOM 2004 Load Balancing in Ad Hoc Networks 16

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.

INFOCOM 2004 Load Balancing in Ad Hoc Networks 17

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.

INFOCOM 2004 Load Balancing in Ad Hoc Networks 18

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

INFOCOM 2004 Load Balancing in Ad Hoc Networks 19

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

INFOCOM 2004 Load Balancing in Ad Hoc Networks 20

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

INFOCOM 2004 Load Balancing in Ad Hoc Networks 21

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

INFOCOM 2004 Load Balancing in Ad Hoc Networks 22

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

INFOCOM 2004 Load Balancing in Ad Hoc Networks 23

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?

INFOCOM 2004 Load Balancing in Ad Hoc Networks 24

Thank you!Thank you!

INFOCOM 2004 Load Balancing in Ad Hoc Networks 25

Load Distribution Analysis

A F

INFOCOM 2004 Load Balancing in Ad Hoc Networks 26

Load Distribution Analysis

A F

INFOCOM 2004 Load Balancing in Ad Hoc Networks 27

Load Distribution Analysis

A F

INFOCOM 2004 Load Balancing in Ad Hoc Networks 28

Load Distribution Analysis

FA

INFOCOM 2004 Load Balancing in Ad Hoc Networks 29

Load Distribution Analysis