1. Yashar Ganjali Joint work with: Abtin Keshavarzian June 4, 2003 Single-Path vs. Multi-Path Routing in Ad Hoc Networks

2. June 4, 2003Single-path vs. Multi-path Routing in Ad Hoc Networks 2 Outline 1.Single-path vs. multi-path routing 2.Comparison Criteria 3.Network model 4.Traffic distribution analysis 4-1. Single-path routing 4-2. Multi-path routing 5.Simulations 6.Optimal number of paths? 7.Conclusion

3. June 4, 2003Single-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

4. June 4, 2003Single-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)

5. June 4, 2003Single-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

6. June 4, 2003Single-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.

7. June 4, 2003Single-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d  Any path starting at a node in S 1 going to a node in S 2 goes through node F. Therefore, the traffic going through node F is proportional to S 1 x S 2. S1S1 S2S2

8. June 4, 2003Single-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

9. June 4, 2003Single-path vs. Multi-path Routing in Ad Hoc Networks 9 Load Distribution Analysis: New Approach

10. June 4, 2003Single-path vs. Multi-path Routing in Ad Hoc Networks 10 Load Distribution Analysis: New Approach (Cont’d)

11. June 4, 2003Single-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. A F B

12. June 4, 2003Single-path vs. Multi-path Routing in Ad Hoc Networks 12 Load Distribution Analysis AF w B w

13. June 4, 2003Single-path vs. Multi-path Routing in Ad Hoc Networks 13 Load Distribution Analysis A F B=(x,y) d L y=L cos  y=L sin  L =d cos  x=d cos 2  y=d sin  cos  y 2 +(x-d/2) 2 =d 2 /4

14. June 4, 2003Single-path vs. Multi-path Routing in Ad Hoc Networks 14 Load Distribution Analysis AF B

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

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

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

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

19. June 4, 2003Single-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

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

21. June 4, 2003Single-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.

22. June 4, 2003Single-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.

23. June 4, 2003Single-path vs. Multi-path Routing in Ad Hoc Networks 23 Simulation Analysis Evaluation of the Model

24. June 4, 2003Single-path vs. Multi-path Routing in Ad Hoc Networks 24 Effect of Increasing the Number of Paths in Multi-path routing Valiant’s Method?

25. June 4, 2003Single-path vs. Multi-path Routing in Ad Hoc Networks 25 Effect of Increasing the Number of Paths in Multi-path routing

26. June 4, 2003Single-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.

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