1. On Optimal Geographic Routing in Wireless Networks with Holes and Non-Uniform Traffic Sundar Subramanian, Sanjay Shakkottai and Piyush Gupta INFOCOM 2007

2. Outline Introduction Network Model Randomway Algorithm Routing for non-uniform traffic patterns Extending non uniform traffic to networks with Holes Conclusion

3. Introduction Geographic forwarding based techniques have been widely suggested as an efficient routing method for wireless and sensor networks not required to maintain extensive routing tables make simple routing decisions based on the local geographic position

4. Introduction The geographic forwarding strategies in non-uniform networks may fail due to a forwarding node does not have any neighboring nodes that are closer to the destination may get stuck in routing “ holes ” or local minima

5. Introduction

6. X

7. switching to a boundary tracing scheme

8. Introduction

9. Currently known schemes only allow for small variations (within Θ(1/√n)) in node data rates (The capacity of wireless networks) Wireless networks may demand widely varying data rates mixture of video flows short messaging

10. Introduction -GOAL Randomized geographic routing scheme that can achieve a throughput capacity Construct a geographic forwarding based routing scheme that can support wide variations in the traffic requirements

11. Network Model nodes are uniformly and randomly distributed over a unit toroidal region Nodes have a uniform circular transmission range

12. Network Model To model the effect of network “ holes ” due to various factors physical obstacles clusters of failed nodes

13. Network Model X

14. X X X

15. X

16. Assume n/2 random source nodes and randomly choose destination nodes for each traffic source node uniformly and independently The throughput capacity T(n) of a network is defined as the maximum data-rate

17. Randomway (n,K) Algorithm To have a few extra fields

18. Randomway (n,K) Algorithm (1) The source node for every traffic flow creates Rlog(n) copies of its packet to send It chooses Rlog(n) independent and uniformly distributed points To sets the NEXT-DEST field to the randomly generated location in each of these copies WAYPOINT-NUM is set to 4K + 1

19. Randomway (n,K) Algorithm (2) The Rlog(n) packets are routed from the source in a Greedy geographic manner to the location in NEXTDEST.

20. Randomway (n,K) Algorithm (3) If it is not the NEXT-DEST location it searches within its neighboring nodes is closest to the NEXT-DEST location if none of its neighbor nodes are closer to the NEXT-DEST drop the packet

21. Randomway (n,K) Algorithm (4) If it is the NEXT-DEST location If WAYPOINT-NUM > 1 sets WAYPOINTNUM = WAYPOINT-NUM – 1 Repeat the first step If WAYPOINT-NUM = 1, sets NEXT-DEST = FINAL-DEST WAYPOINT-NUM = 0 If WAYPOINT-NUM = 0, the packet is received at the destination

22. Randomway (n,K) Algorithm

23. For general Geographic forwarding based X

24. Randomway (n,K) Algorithm For general Geographic forwarding based

25. Randomway (n,K) Algorithm X X

26. X

27. X

33. H(j) be the number of source-destination pairs that generate a line that touches tile j 2(Rlog(n)) 4K+1 √n The number of paths passing though any tile j is at most H(j) ∗ (Rlog(n)) 4K+1 = √n(Rlog(n)) 8K+2

34. Randomway (n,K) Algorithm The number of packet routes is no more than√n(Rlog(n)) 8K+2 T(n) = Θ( 1 /√n(log n) P ) P <∞ is achievable

35. Routing for non-uniform traffic patterns In many scenarios the traffic demands could be non-uniform Video flows, short messaging To provide a constructive scheme (RANDOMSPREAD) to distribute the traffic flows uniformly over the region

36. Routing for non-uniform traffic patterns Create √n routes simultaneously to the destination Using a three meta-hop path

37. Routing for non-uniform traffic patterns

39. Partition the packet-routes in the network into 4 disjoint classes T1: Packet routes generated by type-a source nodes to their corresponding destinations. T2: Outward lines radiating from source nodes to their first intermediate way-point T3: Inward lines radiating into destination nodes from their last intermediate way-points T4: The rest of the packet routes generated between the first and the last intermediate way- points Type-a traffic requirement: Θ( 1 /√n) Type-b traffic requirement: Θ(1)

40. Extending non uniform traffic to networks with holes The modification to the RANDOMWAY(n,K) is only at the source nodes If a source is a type-b node with Θ(1) traffic requirement transmits √n / (R log(n)) P packets simultaneously 4K+2 way points

41. Conclusion Presented algorithms for throughput optimal routing in networks with holes and non-uniform traffic preserve the inherent advantages of geographic scalability and fast convergence

42. Thank you!!