1. Yashar Ganjali, and Abtin Keshavarzian Presented by: Isaac Keslassy Computer Systems Laboratory Department of Electrical Engineering Stanford University INFOCOM 2004 Load Balancing in Ad Hoc Networks: Single-path Routing vs. Multi-path Routing

2. INFOCOM 2004Load Balancing in Ad Hoc Networks2 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. INFOCOM 2004Load Balancing in Ad Hoc Networks3 Single-path vs. Multi-path s t s t Single-path routing Multi-path routing

4. INFOCOM 2004Load Balancing in Ad Hoc Networks4 Comparison Criteria Overhead: Route discovery overhead Route maintenance overhead Data transmission overhead Load distribution (throughput)

5. INFOCOM 2004Load Balancing in Ad Hoc Networks5 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. INFOCOM 2004Load Balancing in Ad Hoc Networks6 Problem Statement Find the amount of flow going through a node (load) at distance r from the center.

7. INFOCOM 2004Load Balancing in Ad Hoc Networks7 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 Load Distribution Analysis: Single-path Routing [P. Pham and S. Perreau, INFOCOM’03] F  dd 

8. INFOCOM 2004Load Balancing in Ad Hoc Networks8 [Pham and Perreau, INFOCOM’03]: Load is distributed uniformly using multi-path routing. Load Distribution Analysis: Multi-path Routing

9. INFOCOM 2004Load Balancing in Ad Hoc Networks9 Load Distribution Analysis: New Approach

10. INFOCOM 2004Load Balancing in Ad Hoc Networks10 Load Distribution Analysis: New Approach

11. INFOCOM 2004Load Balancing in Ad Hoc Networks11 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. INFOCOM 2004Load Balancing in Ad Hoc Networks12 Load Distribution Analysis AF w B w

13. INFOCOM 2004Load Balancing in Ad Hoc Networks13 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. INFOCOM 2004Load Balancing in Ad Hoc Networks14 Load Distribution Analysis AF B

15. INFOCOM 2004Load Balancing in Ad Hoc Networks15 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

16. INFOCOM 2004Load Balancing in Ad Hoc Networks16 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.

17. INFOCOM 2004Load Balancing in Ad Hoc Networks17 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.

18. INFOCOM 2004Load Balancing in Ad Hoc Networks18 Evaluation of the Model

19. INFOCOM 2004Load Balancing in Ad Hoc Networks19 Evaluation of the Model

20. INFOCOM 2004Load Balancing in Ad Hoc Networks20 Evaluation of the Model

21. INFOCOM 2004Load Balancing in Ad Hoc Networks21 Effect of Increasing the Number of Paths in Multi-path routing

22. INFOCOM 2004Load Balancing in Ad Hoc Networks22 Effect of Increasing the Number of Paths in Multi-path routing

23. INFOCOM 2004Load Balancing in Ad Hoc Networks23 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?

24. INFOCOM 2004Load Balancing in Ad Hoc Networks24 Thank you!

25. INFOCOM 2004Load Balancing in Ad Hoc Networks25 Load Distribution Analysis AF

26. INFOCOM 2004Load Balancing in Ad Hoc Networks26 Load Distribution Analysis AF

27. INFOCOM 2004Load Balancing in Ad Hoc Networks27 Load Distribution Analysis AF

28. INFOCOM 2004Load Balancing in Ad Hoc Networks28 Load Distribution Analysis FA

29. INFOCOM 2004Load Balancing in Ad Hoc Networks29 Load Distribution Analysis