Yashar Ganjali and Abtin Keshavarzian Presented by: Isaac Keslassy Computer Systems Laboratory

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

2. Single-Path vs. Multi-Path Single-path routing A B A B Multi-path routing

3. Single-Path vs. Multi-Path • Multi-path  load-balancing • Higher throughput • Fault-tolerance • Main problems of multi-path • Route discovery overhead • Complexity • Reordering

4. Network Model • Nodes: Distributed uniformly in a circle of radius one with high density  • Links: Any two nodes with distance ≤ T are connected • Traffic: Each node sends to any other node with fixed rate 

5. Load-Distribution Analysis: Problem Statement Find the amount of flow going through a node at distance r from the center  load(r)

6. Load Distribution Analysis: Single-Path Routing • [Pham and Perreau, INFOCOM’03]

7. Question If we use multi-path routing with k disjoint shortest paths, is the load distribution more uniform?

8. Load-Distribution Analysis: Assumption • Multi-path routing uses k disjoint shortest paths: First choose shortest path, then second shortest path, and so on k times. • Simulation result: results of paper hold independently of many metric choices • “Disjoint”: edge-disjoint vs. node-disjoint • “Shortest”: minimum-hop-count vs. minimum-Euclidian-distance

9. Load Distribution Analysis: New Approach A B

10. 1 2 2w ≈ k / δ A B k 1/δ Intuition on Rectangle Width 2w • about independent of distance AB • about proportional to number of paths k • about inversely proportional to density  • width also depends on • how nodes are connected • how paths are chosen (edge-disjoint vs. node-disjoint, minimum-hop-count vs. minimum-Euclidian-distance) • Simulation result: results of paper hold for all these choices

11. Load Distribution Analysis • Duality Problem:For a given node Ffind the set of all node pairs (A,B)such that the rectangle defined by A and B of width 2w contains F. B A F

12. B A ≤ w F Load Distribution Analysis • Two criteria: • Distance(F,[AB)) ≤ w • Angle(ABF) ≤ 90 °

13. Load Distribution Analysis Distance(F,[AB)) ≤ w A w F

14. Load Distribution Analysis Distance(F,[AB)) ≤ w B w A F w

15. Load Distribution Analysis Distance(F,[AB)) ≤ w B w A F w

16. Load Distribution Analysis Angle(ABF) ≤ 90 ° B A F

17. Load Distribution Analysis Angle(ABF) ≤ 90 ° B A F

18. Load Distribution Analysis Angle(ABF) ≤ 90 ° B A F

19. Load Distribution Analysis • Distance(F,[AB)) ≤ w • Angle(ABF) ≤ 90 ° B A F

20. Load Distribution Analysis • For each F, sum up load over all appropriate (A,B) • This gives load(F) F A

21. How to Choose w? • Load(F) depends on w. • w depends on many factors (how nodes are connected, edge-disjoint vs. node-disjoint, minimum-hop-count vs. minimum-Euclidian-distance)  hard to provide analytical expression • To compute w for multi-path routing with k paths: • Find w based on simulations for single-path. • For k paths use w = k * (w for single path). Finally, check that model corresponds to simulations to validate model assumptions.

22. Evaluation of the Model

23. Evaluation of the Model

24. Evaluation of the Model

25. Increasing the Number of Paths in Multi-Path Routing

26. (Personal) Conclusion • The rectangle model seems to work… which was not obvious • Multi-path with k shortest paths does not significantly decrease load (with high-density networks) • Route on curves instead of shortest paths? • Decrease load  sacrifice extreme nodes and increase delay?

27. Thank you!

28. Load Distribution Analysis Distance(F,[AB]) ≤ w B w A F w

29. Load Distribution Analysis: Single-Path Routing [P. Pham and S. Perreau, INFOCOM’03] d S2 Any path from a node in S1to a node in S2 goes through node F. Therefore load(F)= ∫ S1 x S2 F S1 r d +β  depends on density

30. Outline • Single-path vs. multi-path routing • Comparison Criteria • Network model • Traffic distribution analysis 4-1. Single-path routing 4-2. Multi-path routing • Simulations • Optimal number of paths? • Conclusion

31. What this talk is about…. • Single-path vs. multi-path routing • Comparison Criteria • Network model • Traffic distribution analysis 4-1. Single-path routing 4-2. Multi-path routing • Simulations • Optimal number of paths? • Conclusion

32. Load Distribution Analysis: Multi-Path Routing • [Pham and Perreau, INFOCOM’03]: Load is distributed nearly uniformly using multi-path routing.

33. 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?

34. Effect of Increasing the Number of Paths in Multi-path routing

35. Comparison Criteria • Overhead: • Route discovery overhead • Route maintenance overhead • Data transmission overhead • Load distribution (throughput)

36. Load Distribution Analysis A F

37. Load Distribution Analysis A F

38. Load Distribution Analysis A F

39. Load Distribution Analysis A F

40. Load Distribution Analysis