Post on 21-Dec-2015
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.
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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.
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!