Author ： JEFFREY E. WIESELTHIER GAM D. NGUYEN

1. Algorithms for Energy-Efficient Multicasting in Static Ad Hoc Wireless NetworksMobile Networks and Applications 6,251-263,2001 Author：JEFFREY E. WIESELTHIER GAM D. NGUYEN Information Technology Division, Naval Research Laboratory, Washington Presented by 資管碩一 R92725034 林明源

2. Outline • Introduction • Architecture issues in all wireless networks • Multicast in wireless networks • Construction of minimum-energy broadcast trees • Multicasting problem and related algorithms • Simulation and Performance evaluation • Conclusions

3. Introduction • Considerations in ad hoc wireless networks - Physical layer issues • Transmission power, network connectivity etc. - Network layer issues • Routing, accessibility, reliability, latency etc. • Static or mobile ad hoc wireless networks • Fixed cellular infrastructure or not • Environmental factors - Propagation - Fading - Interference (multi-hop, co-channel interference)

4. Introduction (cont.) • Source initiated multicasting of session and connection-oriented traffic • Different power control level, elastic network topology and handoff tracking • Basic assumptions - Unlimited bandwidth (frequencies or time slot ) - Collision-free coordination - “All-admitted” admission control policy

5. Architecture issues in all-wireless networks • Decision variable - Different power control, elastic network topology and handoff tracking - No. of transceivers (network resources) • Constraints - SIR (signal to noise ratio) - Distance - BER (bit error rate) - Propagation loss and limit received power - omni-directional antennas - Others’ interference

6. Architecture issues in all-wireless networks (cont.) • Trade-off between high transmission power and low transmission power - range, connectivity, interference and energy consumption

7. Multicast in wireless networks • Two basic approaches to construct multicast tree and using PIM (Spare mode of the protocol independent Multicasting) on the trees - Source-Based Tree (SBT) - Core-Based Tree (CBT) • Transmission power range affect connectivity and construction of spanning tree • Additional nodes may be needed as relay to provided connectivity to all memberships of the multicast group

8. Multicast in wireless networks (cont.) • Normalize transmission power on link (I,j) by range r and proportional factor Pij = power needed to support link between nodes i and j =rαwhere r is the distance between nodes i and j and α is the decade factor • Single transmission power (two destinations) Pi,(j,k) = max{Pij, Pik } is sufficient to reach both node j and node k, based on our assumption of omnidirectional antennas. “Wireless Multicast advantage”

9. Multicast in wireless networks (cont.)

10. Construction of minimum-energy broadcast trees • Link-based nature of wired networks and node-based nature of wireless networks • Base case (one source and two destination)

11. Construction of minimum-energy broadcast trees (base case)

12. Alternative power control strategies of base case • Two strategies (a) S transmits using PS2: both D1 and D2 are reached (b) S transmits using PS1: only D1 is reached. D1 then transmits to D2 with power P12, resulting in a total power of PS1 + P12. • Selecting criteria (a) use strategy (a) if r1 > r2 cos θ, (b) use strategy (b) otherwise.

13. Alternative power control strategies of base case (cont.) • For propagation behavior 1/rα , we get - If xα−1 < (1+x2−2xcosθ)α/2 ,use strategy (a) - Otherwise use strategy (b) • The incentive to use the shortest available links increases as α increases. (When path loss is high, lower transmission range with less cost is more attractive.)

14. Alternative power control strategies of base case (cont.)

15. Minimum-energy broadcasting：Three destinations

16. Minimum-energy broadcasting：Three destinations (cont.) • We enumerate the alternative strategies: (a) S transmits using PS3：all three destinations are reached. (b) S transmits using PS2：destinations D1 and D2 are reached by this transmission. One of these nodes must then transmit to D3. The two alternatives are: (1) D1 transmits to D3: total power = PS2 + P13, (2)D2 transmits to D3: total power = PS2 + P23. (c) S transmits using PS1：only D1 is reached by this transmission.D1 must then form a tree to nodes D2 and D3. The three alternatives are: (1) D1 transmits with sufficient power to reach D2 andD3： total power = PS1 + max{P12, P13}, (2)D1 transmits to D2, which transmits to D3: total power= PS1 + P12 + P23 (3)D1 transmits to D3, which transmits to D2: total power= PS1 + P13 + P32.

17. Minimum-energy broadcasting (Recursive formulation) • In recursive formulation, broadcasting to two destinations is the simple base case. • When transmission power of the source is determined, we can remap the original to the new connected nodes. In general, the solution to ND destinations can be expressed in terms of the solutions for various subsets of the solutions for a smaller number of destinations. • Complexity is to evaluate the times of the two-destinations base case.

18. Multicasting problem and related algorithms • Admission control policies - For particular request - For particular destinations - Other considerations (ex. cost) • Default assumption：”admit-all” admission control policy

19. Multicasting problem and related algorithms (performance metric) • Notations - ni: the number of intended destinations by ith multicast arrival - mi: the number of destinations reached by ith multicast session - di: duration of ith multicast session (assumed exponentially distributed with mean = 1) - pi: sum of the transmitter powers used by all nodes in ith multicast session - Ei: total energy used by ith multicast session = pidi - vi: multicast value of ith multicast session • Value definition： vi=midi

20. performance metric (cont.) • Average (per call) multicast value per unit energy Use this metric alone trends to favor the high transmission power for maximization. • Multicast efficiency This metric is maximized when all destinations are reached without regarding to the energy required.

21. performance metric (cont.) • Yardstick metricTo take into consideration both of the criteria discussed above, namely accessibility per unit energy and reaching a large fraction of the number of the desired destinations • Local yardstick • Global yardstick

22. performance metric (cont.) • Blocking probability We define kx is number of multicast sessions that are completed blocked during an multicast request interval. • Local cost metric (for specific request and not average measurement) - Link-based cost - Node-based cost

23. Alternative algorithm for multicast • Algorithm 1：Multicast trees that consist of the superposition of the best unicast paths to each individual destination. The algorithm is simple and scalable but not the best (without using the wireless advantage).

24. Alternative algorithm for multicast(cont.) • Algorithm 2：First follow the standard MST formulation and then eliminate all transmission links that are not need to reach the members of the multicast group. (without using the wireless advantage). • Algorithm 3：Consider the wireless advantage and use the recursive method to construct MST and then eliminate the useless links.

25. Alternative algorithm for multicast(cont.) • Algorithm 4(pruned node-based spanning tree)：Construct the spanning tree at source node and maximize the “n/p” metric (selecting criteria) • Algorithm 5：Exhaustive search all possible multicast tree and chose the lowest cost one. • Algorithm 6：For each arriving multicast request i, select the multicast tree with the maximal local yardstick yi

26. Simulation and Performance evaluation • Pmax=10、 propagation α=2、n=5 (5x5 region)、λ (exponential distribution)、μ=1(service duration time per multicast) • Pmax is unlimited、α=4 propagation、n=100 5x5 region、λ (exponential distribution)、μ=1(service duration time per multicast) • For N nodes, there are 2N-N-1possible group types

27. Simulation and Performance evaluation

28. Simulation and Performance evaluation (cont.) • Algo6 provides approximately 19% better yardstick than algo1 by “using wireless advantage”

29. Simulation and Performance evaluation (cont.) • Algo6 is the only one that e is not close to 1 when lower traffic load because considering the link cost.

30. Simulation and Performance evaluation (cont.)

31. Simulation and Performance evaluation (cont.)

32. Simulation and Performance evaluation (cont.) • As path loss α increases, the incentive to use the shortest possible links increases.

33. Simulation and Performance evaluation (cont.)

34. Simulation and Performance evaluation (cont.)

35. Simulation and Performance evaluation (cont.)

36. Simulation and Performance evaluation (cont.)

37. Conclusion • Modeling the wireless multicast problem • Heuristic algorithm for benchmark • Scalability and polynomial executing time • Future work More practical considerations of physical layer and network layer