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

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

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

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

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

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

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

Multicast in wireless networks (cont.) Normalize transmission power on link (I,j) by range r and proportional factor Normalize transmission power on link (I,j) by range r and proportional factor Pij = power needed to support link between nodes i and j =r α where r is the distance between nodes i and j and α is the decade factor Pij = power needed to support link between nodes i and j =r α where r is the distance between nodes i and j and α is the decade factor Single transmission power (two destinations) 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. 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 ” “ Wireless Multicast advantage ”

Multicast in wireless networks (cont.)

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

Construction of minimum-energy broadcast trees (base case)

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

Alternative power control strategies of base case (cont.) For propagation behavior 1/r α, we get For propagation behavior 1/r α, we get - If x α −1 < (1+x 2 −2xcosθ) α/2,use - If x α −1 < (1+x 2 −2xcosθ) α/2,use strategy (a) strategy (a) - Otherwise use strategy (b) - 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.) 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.)

Alternative power control strategies of base case (cont.)

Minimum-energy broadcasting ： Three destinations

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

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

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

Multicasting problem and related algorithms (performance metric) Notations Notations - n i : the number of intended destinations by ith multicast arrival - m i : the number of destinations reached by ith multicast session - d i : duration of ith multicast session (assumed exponentially distributed with mean = 1) distributed with mean = 1) - p i : sum of the transmitter powers used by all nodes in ith multicast session multicast session - E i : total energy used by ith multicast session = p i d i - v i : multicast value of ith multicast session Value definition ： Value definition ： v i =m i d i v i =m i d i

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

performance metric (cont.) Yardstick metric To 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 Yardstick metric To 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 Local yardstick Global yardstick Global yardstick

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

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). 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).

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 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. Algorithm 3 ： Consider the wireless advantage and use the recursive method to construct MST and then eliminate the useless links.

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 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 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 y i Algorithm 6 ： For each arriving multicast request i, select the multicast tree with the maximal local yardstick y i

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

Simulation and Performance evaluation

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

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. Algo6 is the only one that e is not close to 1 when lower traffic load because considering the link cost.

Simulation and Performance evaluation (cont.)

As path loss α increases, the incentive to use the shortest possible links increases. As path loss α increases, the incentive to use the shortest possible links increases.

Simulation and Performance evaluation (cont.)

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