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Topology Control of Multihop Wireless Networks using Transmit Power Adjustment INFOCOM 2000 Ram Ramanathan, Regina Rosales-Hain Bae Chi-Sung Jan. 20, 2005 Network Systems Lab. KAIST No.1 Network Systems Lab. Outline Introduction Problem formulation Centralized Algorithms Connected Min-Max Power (CMP) Bi-Connectivity Augmentation with Min-Max Power Distributed Heuristic Algorithms LINT (Local Information No Topology) LILT (Local Information Link-state Topology) Simulation Result Summary Critique KAIST No.2 Network Systems Lab. Introduction Topology The set of communication links between node pairs used by routing mechanism Uncontrollable factor: Mobility, Weather, Interference, Noise Controllable factor: Transmit power, Antenna direction. Drawback of Wrong Topology Reduce the capacity Increase interference Increase end-to-end packet delay Decrease the robustness to node failure Consider transmit power adjustment problem in a multi- hop wireless network to create a desired topology KAIST No.3 Network Systems Lab. Topology Control KAIST No.4 Network Systems Lab. K-vertex/edge-connected A graph is k-vertex/edge-connected if and only if there are k vertex/edge-disjoint paths between every pair of vertices (a)1-vertex/edge-connected (b) 2-vertex/edge-connected (connected) (bi-connected) KAIST No.5 Network Systems Lab. Problem formulation Connected Min-Max power Given an M=(N, L) Find a per-node minimal assignment of transmit powers p : N Z such that (1) the induced graph of (M, ,p) is connected (2) MAX uN ( p(u )) is minimum. Bi-connectivity Augmentation with Min-Max Power Given M=(N,L), and initial transmit power p : N Z such that the induced graph (M, , p) is connected Find a per node minimal set of power increases (u) such that (1) induced graph of (M, , p(u ) (u )) is bi-connected (2) MAX uN ( p(u ) (u )) is minimum KAIST No.6 Network Systems Lab. Algorithm CONNECT Input: (1) Multi-hop wireless network M= (N, L) (2) Least-power function Output: Power levels for each node that induces a connected graph Begin 1. Sort node pairs in non-decreasing order of mutual distance 2. initialize |N| clusters, one per node 3. for each (u,v) in sorted order do 4. if cluster(u)cluster(v) 5. p(u)=p(v)=(d(u,v)) 6. merge cluster(u) with cluster(v) 7. if number of cluster is 1 then end 8. perNodeMinimalize(M,,p,1) end KAIST No.7 Network Systems Lab. Per Node Minimize Procedure perNodeMinimalize(M,,p,k) Begin 1. let S = sorted node pair list 2. for each node u do 3. T={(n1,n2)S: u=n1 or u=n2} 4. sort T in no-increasing order of distance 5. discard from T all (x, y) such that (d(x,y))>p(u) 6. for (x, y) T using binary search do 7. if graph with p(u)=(d(x,y)) is not k- connected, Stop 8. else p(u)= (d(x,y) end KAIST No.8 Network Systems Lab. Algorithm BICONN-AUGMENT Input: (1) Multi-hop wireless network M= (N, L) (2) Least-power function (3) Initial power assignment inducing connected network Output: Power levels for each node that induces a bi-connected graph. Begin 1. sort node pairs in non-decreasing order of distance 2. G=graph induced by (M,,p) 3. For each (u,v) in sorted order do 4. if biconn-comp(G,u) biconn-comp(G,v) 5. q= (d(u,v)) 6. p(u)=max(q,p(u)) 7. q(u)=max(q,p(v)) 8. add (u,v) to G 9. perNodeMinimalize(M,, p, 2) end KAIST No.9 Network Systems Lab. Example (a) Connected Networks (b) Bi-connected Networks (c) Without Topology Control KAIST No.10 Network Systems Lab. Local Information No Topology Algorithm (LINT) Use locally available neighbor propagation model information (r ) (rthr ) if r rthr Attempts to keep the degree (r ) (rthr ) 10 log( r ), if r rthr rthr of each node If node degree > dh reduces transmit power d c D rc 2 If node degree < dl d d D rd2 increases transmit power rc pc ( (rthr ) 10 log( )) T rthr Power update equation pd ( (rthr ) 10 log( rd )) T dd pd pc 5 log( ) rthr dc dd pd pc 5 log( ) dc KAIST No.11 Network Systems Lab. Local Information Link-state Topology Algorithm (LILT) Uses freely available neighbor information and global topology information Triggered whenever an event driven or periodic link-state update A node determine topology states and take following action Bi-connected No Action Connected but not Bi-connected 1. Finds its distance form the closest articulation point 2. Set a timer for a value t 3. If acter time t the network is still not bi-connected, the node increase its power to the maximum possible. Disconnected Increases its transmit power to maximum possible value KAIST No.12 Network Systems Lab. Experiment Environment 40 node network, 3 minutes simulation time Use link-state routing mechanism Radio and its emulation Use Utilicom Logranger 2020 900MHz ISM band (raw data rate 300Kbps) Transmission range: 6Miles Use software emulation of radio and its MAC layer Protocol Mobility and Propagation model Mobility: pseudo-random mobility model (72miles/hour) h1 Propagation model: (d ) 156 40log(d ) 15log( ) ( g1 g 2) h2 12 data stream (random chosen source-destination pair, mean rate is 4kbps) KAIST No.13 Network Systems Lab. Simulation Result (static networks) For grater than 1.5nodes/sq, interference reduces spatial reuse BICONN gives the best throughput and adapt well to changing density BICONN uses significantly more power than CONNECT KAIST No.14 Network Systems Lab. Simulation Result (mobile networks) Above a density of 1 node/sq mile increased density causes a decrease in throughput Both LINT and LILT appropriately reduce interference and improve throughput LINT does better than LILT Only slight gains in delay performance KAIST No.15 Network Systems Lab. Concluding remarks Propose Centralized algorithms and distributed heuristics for transmit power control Relevant to Commercial Static network algorithms improve the throughput and battery life of infrequently mobile instant infrastructure networks (Metricom’s Ricochet networks) KAIST No.16 Network Systems Lab.

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