Yashar Ganjali

Joint work with:Abtin Keshavarzian

June 4, 2003

Single-Path vs. Multi-Path Routing in Ad Hoc NetworksSingle-Path vs. Multi-Path Routing in Ad Hoc Networks

June 4, 2003 Single-path vs. Multi-path Routing in Ad Hoc Networks 2

Outline1. 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

June 4, 2003 Single-path vs. Multi-path Routing in Ad Hoc Networks 3

Single-path vs. Multi-path

s t

s t

Single-path routing

Multi-path routing

June 4, 2003 Single-path vs. Multi-path Routing in Ad Hoc Networks 4

Comparison Criteria

• Overhead:– Route discovery overhead– Route maintenance overhead– Data transmission overhead

• Load distribution (throughput)

June 4, 2003 Single-path vs. Multi-path Routing in Ad Hoc Networks 5

Network Model

• Nodes: Distributed uniformly in a circle of radius one with density (high)

• Links: Any two nodes with distance <= T are connected

• Traffic: Each node sends to any other node in the network with fixed rate

June 4, 2003 Single-path vs. Multi-path Routing in Ad Hoc Networks 6

Problem Statement

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

distance r from the center.

June 4, 2003 Single-path vs. Multi-path Routing in Ad Hoc Networks 7

Load Distribution Analysis:Single-path Routing

[P. Pham and S. Perreau, INFOCOM’03]

F

d

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

June 4, 2003 Single-path vs. Multi-path Routing 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

June 4, 2003 Single-path vs. Multi-path Routing in Ad Hoc Networks 9

Load Distribution Analysis: New Approach

June 4, 2003 Single-path vs. Multi-path Routing in Ad Hoc Networks 10

Load Distribution Analysis: New Approach (Cont’d)

June 4, 2003 Single-path vs. Multi-path Routing 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

June 4, 2003 Single-path vs. Multi-path Routing in Ad Hoc Networks 12

Load Distribution Analysis

A Fw

B

w

June 4, 2003 Single-path vs. Multi-path Routing 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

June 4, 2003 Single-path vs. Multi-path Routing in Ad Hoc Networks 14

Load Distribution Analysis

A F

B

June 4, 2003 Single-path vs. Multi-path Routing in Ad Hoc Networks 15

Load Distribution Analysis

A F

June 4, 2003 Single-path vs. Multi-path Routing in Ad Hoc Networks 16

Load Distribution Analysis

A F

June 4, 2003 Single-path vs. Multi-path Routing in Ad Hoc Networks 17

Load Distribution Analysis

A F

June 4, 2003 Single-path vs. Multi-path Routing in Ad Hoc Networks 18

Load Distribution Analysis

FA

June 4, 2003 Single-path vs. Multi-path Routing in Ad Hoc Networks 19

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

June 4, 2003 Single-path vs. Multi-path Routing in Ad Hoc Networks 20

Load Distribution Analysis

June 4, 2003 Single-path vs. Multi-path Routing in Ad Hoc Networks 21

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.

June 4, 2003 Single-path vs. Multi-path Routing in Ad Hoc Networks 22

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.

June 4, 2003 Single-path vs. Multi-path Routing in Ad Hoc Networks 23

Simulation Analysis

Evaluation of the Model

2 Paths -500 Nodes

0.00

500.00

1000.00

1500.00

2000.00

2500.00

3000.00

3500.00

4000.00

4500.00

0.1 0.2 0.3 0.4 0.4 0.5 0.6 0.7 0.8 0.9

Distance from the Center

Lo

ad

4 Paths - 500 Nodes

0.00

1000.00

2000.00

3000.00

4000.00

5000.00

6000.00

7000.00

8000.00

9000.00

0.1 0.2 0.3 0.4 0.4 0.5 0.6 0.7 0.8 0.9

Distance from the Center

Lo

ad

12 Paths - 500 Nodes

0.00

20000.00

40000.00

60000.00

80000.00

100000.00

120000.00

0.1 0.2 0.3 0.4 0.4 0.5 0.6 0.7 0.8 0.9

Distance from the Center

Lo

ad

7 Paths - 500 Nodes

0.00

2000.00

4000.00

6000.00

8000.00

10000.00

12000.00

14000.00

16000.00

0.1 0.2 0.3 0.4 0.4 0.5 0.6 0.7 0.8 0.9

Distance from the Center

Lo

ad

June 4, 2003 Single-path vs. Multi-path Routing in Ad Hoc Networks 24

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

Valiant’s Method?

June 4, 2003 Single-path vs. Multi-path Routing in Ad Hoc Networks 25

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

June 4, 2003 Single-path vs. Multi-path Routing in Ad Hoc Networks 26

Conclusion• 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– Takes into account the topology

• We showed that increasing the number of paths in multi-path routing does not dramatically affect the load balance in the network.

June 4, 2003 Single-path vs. Multi-path Routing in Ad Hoc Networks 27

Thank you!Thank you!