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Energy-Efficient Topology Control for Wireless Ad Hoc Sensor Networks

Energy-Efficient Topology Control for Wireless Ad Hoc Sensor Networks. Authors : Yu-Chee Tseng, Yen-Ning Chang, and Bour-Hour Tzeng ICPADS 2002. Outline. Introduction Problem Definition Topology Control under Fixed Powers

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Energy-Efficient Topology Control for Wireless Ad Hoc Sensor Networks

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  1. Energy-Efficient Topology Control for Wireless Ad Hoc Sensor Networks Authors:Yu-Chee Tseng, Yen-Ning Chang, and Bour-Hour Tzeng ICPADS 2002

  2. Outline • Introduction • Problem Definition • Topology Control under Fixed Powers • Topology Control under Variable Powers • Simulation Results • Conclusions

  3. Introduction • Smart sensors • are created by combining tiny sensing materials with electrical circuits • have been proposed recently for various applications

  4. Introduction (cont.) • How to manage the limited battery resource that constrains the life of the network • [4,16] : using power control to reduce interference and improve throughput • [3,9,14] : topology control achieved by tuning transmission powers • [1,10,11,12] : power-aware routing for ad hoc networks • [2,15] : both IEEE 802.11 and Bluetooth support low- power modes • [13] : to design low-power modes on 802.11-based multi-hop networks

  5. Introduction (cont.) • The topology control problem in an ad hoc sensor network • Topology in ad hoc networks is not static since it changes as one changes the transmission powers of hosts • To maximize the lifetime of the network • Hosts’ powers can be fixed or variable throughout the lifetime of the network • We show that optimal lifetimes can be obtained by using a simple minimum spanning tree construction under the fixed power assumption

  6. Introduction (cont.) • Our work is most related to [9], • “Topology control of multihop wireless networks using transmit power adjustment”, IEEE INFOCOM 2000 • Topology control algorithms to form 1-vertex and 2-vertex-connected graphs were presented • To minimize the maximal transmission power of each host in the network • Employs a minimum spanning tree construction • The result is optimal • However, the initial energies of all hosts were assumed to be the same • Our contribution is to extend the applicability of [9] to an environment where hosts’ initial energies are not necessarily equal

  7. Problem Definition • Definition • The network topology is a function of time • G(t)=(V,E(t)), • where E(t) is the link set induced by the power setting at time t • Our goal is to maintain a certain property of G(t) while keeping its lifetime as long as possible • V : a set of hosts

  8. Problem Definition (cont.) • dist(x,y) : the distance between two hosts • λ(x,y) : the least transmission power needed for x and y to communicate correctly λ(x,y) =c × dist(x,y)d where c is a constant, and d is an environment-dependent constant • Bx(t) : the energy level of host x, where t≧0 represents time • Bx(0) is representing x’sinitial energy

  9. Problem Definition (cont.) • For example: • At time t, to connect two hosts, x and y, together using the least power λ(x,y) • Then this link can be sustained for the following length of time

  10. Problem Definition (cont.) • Suppose x had energy Bx(t) at time t and uses power Ps to send. Then after Δt, its remaining energy becomes Bx(t+Δt)= Bx(t)-(Ps × αx × Δt+ Pr × Δt) where αx is the fraction of time that x transmits during Δt (traffic ratio) • Pris the power consumed in data reception (is a constant) • Ps can be a variable

  11. Problem Definition (cont.) • To consider topology control by tuning transmission powers • we can control the network topology • Ps,x(t) : the transmission power of x • For example: • At instant t, two hosts x and y both Ps,x(t) and Ps,y(t) ≧λ(x,y) • Then there is a communication link between x and y • αx : traffic ratio of each host x • Assume x’s traffic ratio αx remains constant at all times • Different hosts’ traffic ratios are not necessarily the same

  12. Problem Definition (cont.) • PAv(k) : power adjustment problem • to determine the transmission power of each host such that the induced network G(t) remains k-vertex-connected during the time interval [0,T], and such that T is maximized • PAe(k) : power adjustment problem • to determine the transmission power of each host such that the induced network G(t) remains k-edge-connected during the time interval [0,T], and such that T is maximized

  13. Problem Definition (cont.) • Three remarks: • A graph is k-edge(vertex)-connected if the deletion of any k-1 links(vertices) in the network does not partition the network • 1-edge-connected is equivalent to 1-vertex-connected, but this is not true when k≧2 • Vertex-connected is stronger than edge-connected • If all the hosts have the same initial energy, then this problem degenerates to the case considered in [9] • Unidirectional links may exist in the network since hosts may have different transmission powers • However, only bi-directional links are included G(t) since in practice, unidirectional links are difficult to use

  14. Topology Control under Fixed Powers • “Fixed power”:the power function Ps,x(t) remains unchanged throughout the lifetime of the network • The topology G(t) remains unchanged, too • An optimal solution for PAe(1) and PAv(1) • An optimal solution for PAe(2) and PAv(2)

  15. Topology Control under Fixed PowersSolution for PAe(1) andPAv(1) • Is similar to the typical minimum spanning tree construction • How long a link can be sustained as the metric in the construction • The lifetime of link (x,y) is defined as • A link with a longer lifetime implies a lower cost

  16. F A 1 6 5 G E 4 5 6 2 3 B C 4 D Topology Control under Fixed PowersSolution for PAe(1) andPAv(1)(cont.)

  17. Topology Control under Fixed PowersSolution for PAe(1) andPAv(1)(cont.) AlgorithmFPA(1)//Fixed power adjustment for PAe(1) and PAv(1) • From V, construct all possible C2|V| node pairs. Sort these node pairs into a list(PAIR), based on their lifetimes in descending order • Construct |V| clusters of node(s) by placing each node into one separate cluster • Retrieve the first node pair (x,y) from PAIR.If x and y are not in the same cluster, proceed to the next step.Otherwise, repeatedly retrieve more node pairs from PAIR until one (x,y), such that x and y are in different clusters, is found.

  18. Topology Control under Fixed PowersSolution for PAe(1) andPAv(1)(cont.) • Connect link (x,y) by performing the following two steps • If Ps,x(t)<λ(x,y), set Ps,x(t)=λ(x,y) • If Ps,y(t)<λ(x,y), set Ps,y(t)=λ(x,y) • Merge the two clusters containing x and y into one cluster.If all the nodes in V are already in one cluster, terminate the algorithm; otherwise, go to step 3 and repeat.

  19. Topology Control under Fixed PowersSolution for PAe(1) andPAv(1)(cont.) • FPA(1) employs a greedy approach similar to the standard minimum spanning tree construction by using the lifetimes of links as the costs. • The resulting network is not necessarily a spanning tree — cycles may exist • Whether or not two nodes are connected is not determined by their link lifetime, but by how much power they use

  20. F A 1 6 5 G E 4 5 6 2 3 B C 4 D Topology Control under Fixed PowersSolution for PAe(1) andPAv(1)(cont.)

  21. Topology Control under Fixed PowersSolution for PAe(2) andPAv(2)(cont.) • FPA(2) algorithm • utilizes the resulting network of FPA(1) • Further extends the network to the 2-edge or 2-vertex-connected cases

  22. Topology Control under Fixed PowersSolution for PAe(2) andPAv(2)(cont.) AlgorithmFPA(2) • Run FPA(1) to obtain the transmission power Ps,x(t) of each host x.Identify all 2-edge-/2-vertex-connected components in the resulting network • Again, let PAIR be the sorted list of all C2|v| node pairs • Retrieve the first node pair (x,y) from PAIR.If x and y are not in the same 2-edge-/2-vertex-connected component, then proceed to the next step.Otherwise, retrieve more node pairs from PAIR until one (x,y), such that x and y are in different components, is found.

  23. Topology Control under Fixed PowersSolution for PAe(2) andPAv(2)(cont.) • Connect link (x,y) by performing the following two steps • If Ps,x(t)<λ(x,y), set Ps,x(t)=λ(x,y) • If Ps,y(t)<λ(x,y), set Ps,y(t)=λ(x,y) • Identify all 2-egde-/2-vertex-connected components in the network.If only one component remains, terminate the algorithm; otherwise, go to step3.

  24. Topology Control under Variable Powers • FPA(1) and FPA(2) are optimal only when the nodes’ transmission powers, once selected, remain unchanged • Under the variable power assumption, • FPA(1) and FPA(2) are not necessarily optimal

  25. Topology Control under Variable Powers (cont.) AlgorithmVPA(k) //Variable power adjustment for PAe(k) and PAv(k), k=1 or2 • Run FPA(k) on the current network to determine hosts’ transmission powers • After a fixed interval Δt, check hosts’ remaining energies.If none of the hosts are dead, go back to step 1;otherwise, terminate the algorithm

  26. Topology Control under Variable Powers (cont.) • This implies that we only need to reevaluate the network topology when the order of links in PAIR changes

  27. Simulation Results • Environment • hosts:are randomly generated • 10 × 10 plane on the real domain • Where each unit is 1 kilometer • The electricity in each host is randomly set between 80 to 120 units with a uniform distribution • A time unit is one hour long • The power-consumption constant c is set to 1 • A pair of hosts with 100 units of electricity separated by 1 km has a lifetime of 100 hours, while such hosts separated by 10 km has a lifetime of 1 hour

  28. Simulation Results 50 randomly generated hosts RH(1) :28.27, FPA(1) :34.53, VPA(1) :38.23 RH(2) :16.70, FPA(2) :20.33, VPA(2) :26.33

  29. Simulation Results 100 randomly generated hosts RH(1) :36.65, FPA(1) :42.83, VPA(1) :49.78 RH(2) :22.62, FPA(2) :25.13, VPA(2) :32.11

  30. Conclusions • To address the ad hoc network topology control problem by taking into account hosts’ remaining energies • The contribution lies in extending the applicability of the work in [9] to the case where hosts’ initial energies can differ

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