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Maximum Network lifetime in Wireless Sensor Networks with


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									          Maximum Network lifetime
          in Wireless Sensor Networks
          with Adjustable Sensing Ranges
Mihaela Cardei, Jie Wu, Mingming Lu, and Mohammad O. Pervaiz
Department of Computer Science and Engineering,Florida Atlantic University
WIMOB August, 2005

 Introduction
 Problem  definition
 Solution for the AR-SC problem
 Simulation results
 Conclusions
   Application of wireless sensor networks:
    National security、Surveillance、Military、
    Health care 、Environment monitoring
   An important issue in sensor networks is power
    scarcity, driven in part by battery size and weight
   Power saving techniques can generally be
    classified in two categories: scheduling and
    adjusting the range (sensing or transmission).
   Design a scheduling mechanism in which only
    some of the sensors are active and other are in
    sleep mode.
   Address the target coverage problem.
   The goal is to maximize the network lifetime of a
    power constrained, deployed for monitoring a
    set of targets with known locations.
   Using the property that sensors have adjustable
    sensing ranges. The goal is to set up minimum
    sensing ranges for the active sensors, while
    satisfying the coverage requirements.
Problem definition
   Assume
    N   sensors s1,s2,…,sN
     M targets t1,t2,…,tM
     Initial energy E
     Sensing range r1,r2,…rp , corresponding energy
      consumptions e1,e2,…,ep
   Assume a base station located within the
    communication range of each sensor.
Target Coverage Problem
   Definition
    M    targets with known location
     N sensors randomly deployed in the closed proximity
      of the targets
     schedule the sensor nodes activity
     all the targets are continuously observed and network
      lifetime is maximized.
   The approach is to organize the sensors in sets,
    such that only one set is monitoring the targets ,
    and all other sensors are in sleep mode.
AR-SC Problem
   Given a set of targets and a set of sensors with
    adjustable sensing ranges.
   Find a family of set covers c1,c2,…,ck and
    determine the sensing range of each sensor in
    each set.
   Such that :
    K  is maximized
     Each sensor set monitors all targets
     Each sensor appearing in the sets c1,c2,…,ck
      consumes at most E energy.
   In AR-SC definition, the requirement to
    maximize K is equivalent with maximizing the
    network lifetime.
   AR-SC problem is NP-complete, by restriction
   Maximum set cover[3] is a special case of AR-
    SC problem when the number of sensing ranges

[3] M. Cardei, M. Thai, Y. Li, and W. Wu, Energy-Efficient Target Coverage
in Wireless Sensor Networks, IEEE INFOCOM 2005, Mar. 2005.
[7] M. R. Garey and D. S. Johnson, Computers and Intractability: A guide
to the theory of NP-completeness, W. H. Freeman, 1979.
Example of AR-SC

   Assume, E= 2 ,e1=0.5 ,e2=1
   Each cover is active for a unit time of 1
   (si,rp) : sensor i with range rp
Sensors without adjustable sensing ranges:


                                    Lifetime = 5


             Lifetime = 6
Solution for the AR-SC problem

   Integer Programming based Heuristic
     IP   is NP-Hard.
   Greedy based Heuristics
     Centralized Greedy Heuristic
     Distributed Heuristic
Integer Programming based Heuristic
   Given:
       N sensor nodes s1,s2,…,sN
       M targets t1,t2,…,tM
       P sensing ranges r1,r2,…,rp and corresponding energy
        consumption e1,e2,…,ep
       Initial sensor energy E
       The coefficients showing the relationship between sensor, radius
        and target : aipj =1, if sensor si with radius rp covers the target tj.
   Variables:
       Ck, boolean variable, for k=1…k if this subset is a set cover
       Xikp,boolean variable, for i=1…N, k=1…K, p=1…P; xikp=1 if
        sensor I with range rp is in cover k
   Integer programming based formulation:

   Since Integer Programming is NP-Hard, we use
    a relaxation and rounding mechanism.
   First, relax the IP to Linear Programming, solve
    the LP in polynomial time, and then round the
    solutions to get a feasible solution for the IP.
   Relaxed Linear Programming:
   LP-based Heuristic:
     Step1: solve the LP and get the optimal solution
     Step2: for variable      taken in nonincreasing order
                sort       in nonincreasing order
                for all      do
                    if    covers new targets and have at least ep
                    then set up the range of sensor I to rp,
     Step3: if all targets are covered by
             then set
                  update residual energy Ei=Ei-ep
       Step4:Return the total number of set cover
Greedy based Heuristics
   Notations:
     Tip: the set of uncovered targets within the sensing
                   range rp of sensor i
     Bip :the contribution of sensor i with range rp ,
     △Bip: the incremental contribution of the sensor i
              when its sensing range is increased to rp.

            : the set of targets uncovered by the set Ck
Centralized Greedy Heuristics

   A sensor that covers more targets per unit of energy
    should have higher priority.
   Using the incremental contribution parameter △Bip as
    the selection decision parameter.
   Assume that a sensor with the highest contribution △Bip
    is selected to be added to the current set cover, then the
    sensor i updates its sensing range from rq to tp.
Centralized greedy algorithm
   Step1:While each target is covered by at least one (si,rp)
                 and Ei>ep do
              for each si compute △Bip and Tip
              While            do
               select si with the highest △Bil
               sensing range form rp to rl

   Step2: For all sensors update the uncovered target set
           and the incremental contribution
   Step3: For all sensors in Ck , update the residual energy
   Step4: Output the number of set covers k
Distributed Heuristics

   It is desirable in WSNs since it adapts better to dynamic
    and large topologies.
   Each round begins with an initialization phase, which
    take W time, where W is far less than the duration of a
   Each sensor maintains a waiting time, after which it
    decide its status and its sensing range, and then
    broadcasts the list of targets it covers to its one-hop
Distributed Heuristics

   Waiting time,                       where BMAX is the
    largest possible contribution, BMAX= M/e1
   If the waiting times of two sensor si and sj are too close,
    |Wi-Wj|<d, where d is the length of the time slot, thus
    they are not update their uncover target set.
Distributed Greedy
   Step1: Compute the waiting time Wi and start timer t.
   Step2: while                        do
              if message from neighbor sensor is received
              then update Tip and set-up the sensing range to
                   the smallest value ru need cover Tip
              update si’s contribution to Biu
              update the waiting time Wi to
   Stpe3: si broadcasts information the set of targets Tiu it
           will monitor during this round.
Simulation Results
   Sensor nodes and targets randomly located in a
    100m x 100m area.
   Tunable parameters:
     The   number of sensor nodes N, between 25 and 250
     The number of target M, between 5 and 50
     Sensing range p, between 1 and 6, and the range
      values between 10m and 60m.
     Energy consumption model ep(rp) , we evaluate
      lifetime under linear (ep = Θ(rp)) and quadratic
      (ep=Θ(rp2)) model.
     Time slot d in the distributed greed heuristic, between
      0.2 and 0.75
   Network lifetime with number of sensors
   Network lifetime for different sensing range values
   Network lifetime for different values of the time slot d
   Linear and quadratic energy models
   The network lifetime output by our heuristics increases
    with the number of sensors deployed.
   Network lifetime increases with the number of adjustable
    sensing ranges.
   Even if the two centralized solutions perform better than
    the distributed solution, using a distributed heuristic is
    an important characteristic for a solution in wireless
    sensor networks environment.
   Transfer delay affects the network lifetime. Smaller
    transfer delays results in longer network lifetime.
   In future work, we will integer the sensor network
    connectivity requirement.

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