Algorithms for Energy-Algorithms for Energy-Efficient Multicasting in Static Efficient Multicasting in Static

Ad Hoc Wireless NetworksAd Hoc Wireless NetworksMobile Networks and Applications 6,251-263,2001Mobile Networks and Applications 6,251-263,2001

AuthorAuthor ：： JEFFREY E. JEFFREY E. WIESELTHIER WIESELTHIER GAM D. NGUYENGAM D. NGUYEN Information Technology Division, Naval Information Technology Division, Naval Research Laboratory, WashingtonResearch Laboratory, Washington Presented by Presented by 資管碩一 資管碩一 R92725034 R92725034 林明源 林明源

OutlineOutline

• IntroductionIntroduction

• Architecture issues in all wireless networksArchitecture issues in all wireless networks

• Multicast in wireless networksMulticast in wireless networks

• Construction of minimum-energy broadcast Construction of minimum-energy broadcast treestrees

• Multicasting problem and related algorithmsMulticasting problem and related algorithms

• Simulation and Performance evaluation Simulation and Performance evaluation

• Conclusions Conclusions

IntroductionIntroduction• Considerations in ad hoc wireless Considerations in ad hoc wireless

networksnetworks- Physical layer issues- Physical layer issues

•Transmission power, network connectivity etc. Transmission power, network connectivity etc. - Network layer issues - Network layer issues

•Routing, accessibility, reliability, latency etcRouting, accessibility, reliability, latency etc..• Static or mobile ad hoc wireless Static or mobile ad hoc wireless

networksnetworks• Fixed cellular infrastructure or notFixed cellular infrastructure or not• Environmental factorsEnvironmental factors - Propagation- Propagation - Fading - Fading - Interference (multi-hop, co-channel interference)- Interference (multi-hop, co-channel interference)

Introduction Introduction (cont.)(cont.)

• Source initiated multicasting Source initiated multicasting of of session and session and connection-orientedconnection-oriented traffic traffic

• Different Different power control levelpower control level, elastic , elastic network topology and handoff trackingnetwork topology and handoff tracking

• Basic assumptions Basic assumptions - Unlimited bandwidth (frequencies or time slot - Unlimited bandwidth (frequencies or time slot

) )

- Collision-free coordination - Collision-free coordination

- “All-admitted” admission control policy- “All-admitted” admission control policy

Architecture issues in all-Architecture issues in all-wireless networkswireless networks• Decision variableDecision variable

- - Different power controlDifferent power control, elastic network topology and , elastic network topology and handoff trackinghandoff tracking - - No. of transceiversNo. of transceivers (network resources) (network resources)• ConstraintsConstraints - 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-Architecture issues in all-wireless networks (cont.)wireless networks (cont.)

• Trade-off between high transmission Trade-off between high transmission power and low transmission power power and low transmission power

- - range, connectivity, interference and range, connectivity, interference and energy consumption energy consumption

Multicast in wireless Multicast in wireless networksnetworks• Two basic approaches to construct Two basic approaches to construct

multicast tree and using PIM multicast tree and using PIM (Spare mode of (Spare mode of the protocol independent Multicasting)the protocol independent Multicasting) on the on the trees trees

- Source-Based Tree (SBT)- Source-Based Tree (SBT) - Core-Based Tree (CBT)- Core-Based Tree (CBT)

• Transmission power range affect Transmission power range affect connectivity connectivity and construction of spanning treeand construction of spanning tree

• Additional nodesAdditional nodes may be needed as relay to may be needed as relay to provided connectivity to all memberships of the provided connectivity to all memberships of the multicast group multicast group

Multicast in wireless networks Multicast in wireless networks (cont.)(cont.)• Normalize transmission power on link (I,j) by Normalize transmission power on link (I,j) by

range r and proportional factorrange r and proportional factor Pij Pij = power needed to support link between nodes = power needed to support link between nodes i i and and jj =r =rαα

where where r r is the distance between nodes is the distance between nodes i i and and j and j and α is the decα is the decade factor ade factor

• Single transmission power (two destinations)Single transmission power (two destinations) Pi,(j,k) Pi,(j,k) = max{= max{Pij, Pik Pij, Pik } is sufficient to reach both node } is sufficient to reach both node j j aa

nd node nd node kk, based on our assumption of omnidirectional , based on our assumption of omnidirectional antennas.antennas.

“ “Wireless Multicast advantage”Wireless Multicast advantage”

Multicast in wireless networks Multicast in wireless networks (cont.)(cont.)

Construction of minimum-Construction of minimum-energy broadcast treesenergy broadcast trees

• Link-based nature of wired networks and Link-based nature of wired networks and node-based nature of wireless node-based nature of wireless networksnetworks

• Base case (one source and two Base case (one source and two destination)destination)

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

Alternative power control Alternative power control strategies of base casestrategies of base case

• Two strategiesTwo strategies (a) S (a) S transmits using Ptransmits using PS2: both D1 and D2 are reachedS2: both D1 and D2 are reached (b) S (b) S transmits using Ptransmits using PS1: only D1 is reached. D1 then S1: only D1 is reached. D1 then transmits to D2 with power transmits to D2 with power PP12, resulting in a total 12, resulting in a total power of power of PPS1 + S1 + PP12.12.• Selecting criteriaSelecting criteria (a) use strategy (a) if (a) use strategy (a) if rr1 1 > r> r2 cos 2 cos θθ,, (b) use strategy (b) otherwise.(b) use strategy (b) otherwise.

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

• For propagation behavior 1/rFor propagation behavior 1/rαα , we get , we get

- If x- If xαα−1 < (1+x−1 < (1+x22−2xcosθ)−2xcosθ)α/2 α/2 ,use ,use

strategy (a)strategy (a)

- Otherwise use strategy (b)- Otherwise use strategy (b)• The incentive to use the shortest The incentive to use the shortest

available links increases as α increases. available links increases as α increases. (When path loss is high, lower transmission range (When path loss is high, lower transmission range with less cost is more attractive.)with less cost is more attractive.)

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

Minimum-energy broadcastingMinimum-energy broadcasting ：：Three destinationsThree destinations

Minimum-energy broadcastingMinimum-energy broadcasting ：：Three destinations (cont.)Three destinations (cont.)• We enumerate the alternative strategies:We enumerate the alternative strategies: (a) S (a) S transmits using Ptransmits using PS3S3 ：： all three destinations are reached.all three destinations are reached. (b) S (b) S transmits using Ptransmits using PS2S2 ：： destinations D1 and D2 are reached by this 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:(1) D1 transmits to D3: total power = total power = PPS2 + S2 + PP13,13, (2)D2 transmits to D3:(2)D2 transmits to D3: total power = total power = PPS2 + S2 + PP23.23. (c) S (c) S transmits using Ptransmits using PS1S1 ：： only D1 is reached by this transmission.D1 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 =total power = P PS1 + max{S1 + max{PP1212, P, P13},13}, (2)D1 transmits to D2, which transmits to D3:(2)D1 transmits to D2, which transmits to D3: total power= total power= PPS1 + S1 + PP12 +12 + P P2323 (3)D1 transmits to D3, which transmits to D2:(3)D1 transmits to D3, which transmits to D2: total power= total power= PPS1 + S1 + PP13 +13 + P P32.32.

Minimum-energy broadcasting Minimum-energy broadcasting (Recursive formulation)(Recursive formulation)

• In recursive formulation, broadcasting to two In recursive formulation, broadcasting to two destinations is the simple base case.destinations is the simple base case.

• When transmission power of the source is When transmission power of the source is determined, we can remap the original to the determined, we can remap the original to the new connected nodes. In general, the solution new connected nodes. In general, the solution to Nto NDD destinations can be expressed in terms destinations can be expressed in terms of the solutions for various subsets of the of the solutions for various subsets of the solutions for a smaller number of solutions for a smaller number of destinations. destinations.

• Complexity is to evaluate the times of the Complexity is to evaluate the times of the two-destinations base case. two-destinations base case.

Multicasting problem and Multicasting problem and related algorithmsrelated algorithms

• Admission control policiesAdmission control policies- For particular request - For particular request

- For particular destinations- For particular destinations - Other considerations (ex. cost)- Other considerations (ex. cost)• Default assumptionDefault assumption ：”：” admit-all” adadmit-all” ad

mission control policy mission control policy

Multicasting problem and Multicasting problem and related algorithms related algorithms (performance (performance metric)metric)• NotationsNotations- n- nii: the number of intended destinations by : the number of intended destinations by iith multicast arrivalth multicast arrival- m- mii : the number of destinations reached by : the number of destinations reached by iith multicast sessionth multicast session- d- dii : duration of : duration of iith multicast session (assumed exponentially th multicast session (assumed exponentially distributed with mean = 1)distributed with mean = 1)- p- pii : sum of the transmitter powers used by all nodes in : sum of the transmitter powers used by all nodes in iith th multicast sessionmulticast session- E- Eii: total energy used by : total energy used by iith multicast session = pth multicast session = piiddii

- v- vii : : multicast value multicast value of of iith multicast sessionth multicast session• Value definitionValue definition ：： vvii=m=miiddii

performance metricperformance metric (cont.) (cont.)

• Average (per call) multicast value per unit Average (per call) multicast value per unit energyenergy

Use this metric alone trends to favor the high transmission Use this metric alone trends to favor the high transmission

power for maximization.power for maximization.

• Multicast efficiencyMulticast efficiency

This metric is maximized when all destinations are reached This metric is maximized when all destinations are reached without regarding to the energy requiredwithout regarding to the energy required..

performance metricperformance metric (cont.) (cont.)

• Yardstick metricYardstick metric To take into consideration To take into consideration both of the criteria discussed above, namely both of the criteria discussed above, namely accessibility per unit energyaccessibility per unit energy and and reaching a reaching a large fractionlarge fraction of the number of the desired of the number of the desired destinationsdestinations

• Local yardstickLocal yardstick

• Global yardstickGlobal yardstick

performance metricperformance metric (cont.) (cont.)

• Blocking probability Blocking probability We define kWe define kx x is number of multicis number of multicast sessions that are completed blocked during an multicast reqast sessions that are completed blocked during an multicast req

uest interval.uest interval.

• Local cost metric Local cost metric (for specific request and not average (for specific request and not average measurement)measurement)

- Link-based cost- Link-based cost - Node-based cost- Node-based cost

Alternative algorithm for Alternative algorithm for multicast multicast

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

Alternative algorithm for multicastAlternative algorithm for multicast (cont.)(cont.)

• Algorithm 2Algorithm 2 ：： First follow the standard MST First follow the standard MST formulation and then eliminate all transmissioformulation and then eliminate all transmission links that are not need to reach the membern links that are not need to reach the members of the multicast groups of the multicast group. . (without using the wi(without using the wireless advantage).reless advantage).

• Algorithm 3Algorithm 3 ：： Consider the wireless advConsider the wireless advantage and use the recursive method to antage and use the recursive method to construct MST and then eliminate the uconstruct MST and then eliminate the useless links.seless links.

Alternative algorithm for multicastAlternative algorithm for multicast (cont.)(cont.)

• Algorithm 4Algorithm 4 (pruned node-based spanning tree)(pruned node-based spanning tree) ：： CoConstruct the spanning tree at source node and maximize tnstruct the spanning tree at source node and maximize the “n/p” metric (selecting criteria)he “n/p” metric (selecting criteria)

• Algorithm 5Algorithm 5 ：： Exhaustive search all possible multicast Exhaustive search all possible multicast tree and chose the lowest cost one. tree and chose the lowest cost one.

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

Simulation and Performance Simulation and Performance evaluationevaluation

• PPmaxmax=10=10 、 、 propagation propagation α=2α=2 、、 n=5 (5x5 ren=5 (5x5 region)gion) 、、 λ (exponential distribution)λ (exponential distribution) 、、 μ=μ=1(service duration time per multicast) 1(service duration time per multicast)

• PPmaxmax is unlimited is unlimited 、、 α=4 α=4 propagationpropagation 、、 n=n=100 5x5 region100 5x5 region 、、 λ (exponential distributiλ (exponential distribution)on) 、、 μ=1(service duration time per multiμ=1(service duration time per multicast) cast)

• For N nodes, there are 2For N nodes, there are 2NN-N-1possible gro-N-1possible group typesup types

Simulation and Performance Simulation and Performance evaluationevaluation

Simulation and Performance Simulation and Performance evaluation evaluation (cont.)(cont.)

• Algo6 provides approximately 19% better yardstick than Algo6 provides approximately 19% better yardstick than algo1 by “using wireless advantage”algo1 by “using wireless advantage”

Simulation and Performance Simulation and Performance evaluation evaluation (cont.)(cont.)

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

Simulation and Performance Simulation and Performance evaluation evaluation (cont.)(cont.)

Simulation and Performance Simulation and Performance evaluation evaluation (cont.)(cont.)

Simulation and Performance Simulation and Performance evaluation evaluation (cont.)(cont.)

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

Simulation and Performance Simulation and Performance evaluation evaluation (cont.)(cont.)

Simulation and Performance Simulation and Performance evaluation evaluation (cont.)(cont.)

Simulation and Performance Simulation and Performance evaluation evaluation (cont.)(cont.)

Simulation and Performance Simulation and Performance evaluation evaluation (cont.)(cont.)

ConclusionConclusion

• Modeling the wireless multicast Modeling the wireless multicast problemproblem

• Heuristic algorithm for benchmarkHeuristic algorithm for benchmark

• Scalability and polynomial executing Scalability and polynomial executing timetime

• Future work Future work

More practical considerations of More practical considerations of physical layer and network layerphysical layer and network layer