1. S. K. S. Gupta, Arizona State Univ On Maximizing Lifetime of Multicast Trees in Wireless Ad hoc Networks Bin Wang and Sandeep K. S. Gupta Computer Science and Engineering Department Arizona State University Tempe, AZ, USA {Bin.Wang,Sandeep.Gupta}@asu.edu

2. S. K. S. Gupta, Arizona State Univ Outline Multicasting in Wireless Network Node Metric Problem Statement Current State of Art L-REMiT Algorithm Performance Results Conclusions

3. S. K. S. Gupta, Arizona State Univ Multicasting Allow one entity to send messages to multiple entities residing in a subset of the nodes in the network Why multi-destination delivery in a single message? –Transparency; Efficiency; Concurrency Applications –distributed database, distributed games, teleconferencing

4. S. K. S. Gupta, Arizona State Univ Why Multicasting is different in Wireless Networks? Wireless medium is broadcast medium (Wireless multicast Advantage) –One time local transmission can possibly reach all the neighbors

5. S. K. S. Gupta, Arizona State Univ Power control allows a node to determine who are its neighbors. More power used  –more interference –Reduces # simultaneous transmissions (thrput) –Consumes energy at a faster rate  node can die faster leading to disconnections. Why Multicasting is different in wireless network?

6. S. K. S. Gupta, Arizona State Univ Why Not Single-Hop Multicast? Single source multicast: reach a subset of nodes from a given source s –s increases its transmission range to such an extent that it can reach all the group members Increased interference and power wastage source may have limited transmission range

7. S. K. S. Gupta, Arizona State Univ Multi-hop Approach Multi-hop Solution  Problem of constructing multicast tree 1.What is a link? Depends on power level Using maximum transmission power results in too many links 2.link weight? 1. & 2.  Link-based view not appropriate! –Node-based view: construct tree with “minimum/maximum summation of node cost”

8. S. K. S. Gupta, Arizona State Univ Node Cost? Depends upon the optimization goals: –Minimizing total energy consumption [Gupta, Globcom2003] 1 2 3

9. S. K. S. Gupta, Arizona State Univ Lifetime Node Cost –Maximizing multicast tree’s lifetime (#packets transmitted before the first node dies) 1 2 3

10. S. K. S. Gupta, Arizona State Univ Node’s Multicast Lifetime Metric Node i’s multicast lifetime: maximum number of multicast packets that may be forwarded by the node i: T: source-based multicast tree R i : remaining battery energy of node i, E(T,i): forwarding energy cost of node i

11. S. K. S. Gupta, Arizona State Univ Node’s Forwarding Energy Cost Energy consumed (per bit) at node i in a Source-based Tree T where and are energy cost (per bit) of transmission processing and reception processing, is length of the link between node i and i’s farthest children.  is propagation loss exponent, K is a constant dependent upon the antenna.

12. S. K. S. Gupta, Arizona State Univ Lifetime of Multicast Tree The lifetime of a multicast tree T is the minimum lifetime of any node in T: The maximum lifetime multicast tree T * is: where T G is the set of all possible multicast trees for the multicast group G in a given graph o. Maximizing multicast tree lifetime  maximizing the lifetime of tree’s bottleneck node

13. S. K. S. Gupta, Arizona State Univ REMiT Approach Refinement-based- (Take an initial solution and make it better) ? –Needed anyways because of dynamic changes in the network Battery level interference Distributed? –Sensor networks may have millions of nodes –High overhead to obtain global knowledge

14. S. K. S. Gupta, Arizona State Univ Challenges to Distributed Tree Construction? NP-complete problem [Li, LCN2001], [Singh, PIMRC99], heuristic algorithm is needed How to distribute the computation?

15. S. K. S. Gupta, Arizona State Univ Refinement Operation: Change Increase the lifetime of the multicast tree by moving the farthest child (say node i) of bottleneck node x to another node (say node j)

16. S. K. S. Gupta, Arizona State Univ Refinement Criterion

17. S. K. S. Gupta, Arizona State Univ Oscillation & Disconnection Avoidance Lemma 1: Nodes j and x are the only nodes in the multicast tree whose multicast lifetime may be affected by Change i x,j Lemma 2: If j is not in the sub-tree of i, then the tree remains connected after Change i x,j.

18. S. K. S. Gupta, Arizona State Univ L-REMiT Algorithm Two phases –First Phase: Build a MST [Gallager, TPLS1983]. –Second Phase: 1.Bottleneck node election, say node x. 2.Identify the farthest child of node x, say node i. 3.Select the new parent for node i with the highest lifetime gain, say node j. If the highest lifetime is not positive, go to step 5. 4.Node i changes its parent from x to j, then go to Step 1. 5.Terminate L-REMiT algorithm.

19. S. K. S. Gupta, Arizona State Univ Example of L-REMiT Algorithm 1 2 3 4 Initial MST 3 1)Bottleneck node election: node 2 2)Farthest child of node 2 is node 4. 3)Moving 4 to node 3 results in the the highest positive lifetime gain. 4)Node 4 changes its parent from node 2 to 3. 5)New bottleneck node election. Node 1 6)Farthest child of node 1 is node 3. 7)Moving 3 to node 2 results in the highest lifetime gain, however, gain is negative. 8)Terminate 1 2 4 L-REMiT Tree

20. S. K. S. Gupta, Arizona State Univ Related Work: BIP/MIP –BIP/MIP [Wieselthier, CN2002]); Dist-BIP-A, Dist-BIP- G [Wieselthier, Milcom2002]. The node metric is : Limitations: Even  =1, C i is not node i’s lifetime metric. As  increases, it will choose those nodes with higher remaining battery level as the relay nodes, 0<  <2.

21. S. K. S. Gupta, Arizona State Univ Example of BIP/MIP Algorithm 1 2 3 1 2 3

22. S. K. S. Gupta, Arizona State Univ Related Work: Refinement –Refine a minimum spanning tree (MST) to conserve energy consumption EWMA, Dist-EWMA[Cagalij, Mobicom2002] i j k

23. S. K. S. Gupta, Arizona State Univ Performance Results

24. S. K. S. Gupta, Arizona State Univ Performance Results

25. S. K. S. Gupta, Arizona State Univ Performance Results

26. S. K. S. Gupta, Arizona State Univ Performance Results

27. S. K. S. Gupta, Arizona State Univ Conclusions L-REMiT is a distributed algorithm to extend the lifetime of source-based multicast tree. L-REMiT performs better than BIP/MIP, L-MIP, EWMA-Dist algorithms.

28. S. K. S. Gupta, Arizona State Univ Future Work Lifetime extension for group-shared multicast trees Other schemes for maximizing lifetime of multicast tree –Directional antenna –Scheduling sleep mode among the nodes

29. S. K. S. Gupta, Arizona State Univ Reference [1] J. E. Wieselthier, G. D. Nguyen, and A. Ephremides, Resource management in energy-limited, bandwidth-limited, transceiver-limited wireless networks for session-based multicasting. Computer Networks, 39(2):113–131, 2002. [2] J. E. Wieselthier, G. D. Nguyen, and A. Ephremides, Distributed algorithms for energy- efficient broadcasting in ad hoc networks, Proceedings of MilCom, Anaheim, CA, Oct. 2002. [3] M. Cagalj, J.P. Hubaux, and C. Enz. Minimum-energy broadcast in All-wireless networks: NP-completeness and distribution issues. In Proceedings of ACM MobiCom 2002, pages 172 – 182, Atlanta, Georgia, September 2002. [4] F. Li and I. Nikolaidis. On minimum-energy broadcasting in all-wireless networks. In Proceedings of the 26th Annual IEEE Conference on Local Computer Networks (LCN 2001), pages 193–202, Tampa, Florida, November 2001. [5] R.G. Gallager, P. A. Humblet, and P. M. Spira. A distributed algorithm for minimum weight spanning trees. ACM Transactions on Programming Languages and Systems, 5(1):66– 77, January 1983. [6] B. Wang and S. K. S. Gupta. S-REMiT: An algorithm for enhancing energy-efficiency of multicast trees in wireless ad hoc networks. In Proceedings of IEEE GlobleCOM, San Francisco, CA, Dec. 2003. [7] S. Singh, C. S. Raghavendra and J. Stepanek. Power-Aware Broadcasting in Mobile Ad Hoc Networks. In Proceedings of PIMRC, pages 22 – 31, Osaka, Japan, September, 1999.