1. Ad Hoc Networking Course Instructor: Carlos Pomalaza-Ráez Geographical Routing Using Partial Information for Wireless Ad Hoc Networks Rahul Jain, Anuj Puri, and Raja Sengupta University of California, Berkeley Published on IEEE Personal Communications, Vol.8, Issue 1, Feb2001 Presented by Jani Saloranta at Ad Hoc Networking Course 27.1.2004

2. 2 Outline Introduction Geograhical Routing Algorithm (GRA) Algorithm Related Issues Teardown protocol Performance Simulation Results Conclusion

3. 3 Introduction The algorithm for routing in wireless ad hoc networks using information about geographical location of the nodes. Why? –Setting up a communication infrastructure is difficult. –Mobility –Money

4. 4 The Geographical Routing Algorithm Doesn’t assume any hierarchical network architecure Doesn’t do source routing Assumes nodes position via global positioning system (GPS) and existence of geographical location service (GLS). Optimal power Symmetric links Medium access schedule such that each node can transmit at a certain bit rate without interference.

5. 5 Wireless network can be modellad as a graph G = ( N, L ), where nodes N = {1, 2,..., n} and edges (links) L = { ( i, j ) | nodes i and j are neighbours }. Each node knows about a small number of nodes in the network. More about the those who are nearer to it than those about those further away.

6. 6 S D

7. 7 The Algorithm Start point: Each node knows only about its neighbours. Routing table for node S is a list, where p i is a geographical position and S i is neighbour of S. Node S checks from its routing table which p i is closest for packet destination D. Each node thus forwards the packet in the same way till the packet reaches the destination.

8. 8 S D If node S discovers that it is closer to the destination than any other p i we say the packet is ”stuck”. Route discovery protocol handles these situations. Route discovery protocol: –Finds a path from S to D. ( Path(S, D) = ) and updates the routing table of the node k i. ?

9. 9 1) from A to C2) from A to D3) from A to E

10. 10 Related Issues Positional Errors –Node i gets its position from GPS and there is an error. i advertises wrong position p i instead of correct position p i ’. –If error is big enough packet most propably get ”stuck”  Route discovery protocol. Multiple Route Discoveries –Avoided by timestamps.

11. 11 Teardown protocol Extension which tries to maintain the centers property ans keep the routing tables consistent. Node S updates its routing table: 1.S receives hello msg from node N i  it puts (N i, pos(N i ), N i ) 2.If S doesn’t hear anything from node N i for certain time  it removes (D i, pos(N i ), N i ) for every D i. 3.If Table(S) contains the entry (D i, p i, N i ) and S receives Table(N i ) which contains the entry (D i, p j, –), then S updates its entry to (D i, p j, N i ). 4.If Table(S) contains the entry (D i, p i, N i ) and S receives Table(N i ) which does not contain an entry (D i, –, –), then S removes the entry (D ii, p i, N i ) from its table. 5.After any change to its routing table, S broadcasts the new Table(S).

12. 12 Performance Convergence of Routing Tables –One of the advantages of algorithm is that a node does not need to have a routing entry for every other node in the network. Number of route discoveries per node –O (log n) Routing Table Size –The mean routing table size is bounded above by O ( L 1 log n )), where L 1 is the mean length of the shortest path between any pair of nodes in an n- node random network.

13. 13 Assumption: network has n nodes in a unit area and each node has transmission radius r. Overhead from a single link going down –O ( L log(n) / r 2 ) Number of links going down due to mobility –O (r v n 2 ), where v is speed of certain node.  Total overhead –O ( L v n 2 log(n ) / r ) packets get generated in the network per unit time.

14. 14 Simulation Results Figure 7aFigure 7b

15. 15 Figure 8aFigure 8b

16. 16 Figure 9aFigure 9b

17. 17 Conclusions Algorithm is asynchronous, real-time, distributed, and scalable. It does not require an architecture or hierarchy to be imposed on the network, but provides each node with a distance-dependent aggregated view of the network topology. Correctness of algorithm has been shown via theoretic calculus and verified through simulations.

18. 18 Teardown misspelling Correct form can be found from [19]. Says: (d i, p i, n i ) Should say: (d i, p j, n i )

19. 19 Blurry math ”We assume the network has n nodes in a unit area and each node has a transmission radius r.” ”On average, each node has n π r 2 neighbors and cLlog(n) entries in its routing table. So on average a = cLlog(n)/(n π r 2 ) entries in the routing table of A are using a link from node A to a neighbor B.”  nodesradiusneighboursentries nr nπr2nπr2 cLlog(n) 0.11031cL* (-1) 1103140 10 3141cL 2225cL* (0.3)