1. 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

2. Outline ： Introduction Problem definition Solution for the AR-SC problem Simulation results Conclusions

3. Introduction 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 limitations. Power saving techniques can generally be classified in two categories: scheduling and adjusting the range (sensing or transmission).

4. 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.

5. Problem definition Assume  N sensors s 1,s 2,…,s N  M targets t 1,t 2,…,t M  Initial energy E  Sensing range r 1,r 2,…r p, corresponding energy consumptions e 1,e 2,…,e p Assume a base station located within the communication range of each sensor.

6. 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.

7. AR-SC Problem Given a set of targets and a set of sensors with adjustable sensing ranges. Find a family of set covers c 1,c 2,…,c k 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 c 1,c 2,…,c k consumes at most E energy.

8. In AR-SC definition, the requirement to maximize K is equivalent with maximizing the network lifetime. AR-SC problem is NP-complete, by restriction method[7]. Maximum set cover[3] is a special case of AR- SC problem when the number of sensing ranges P=1 [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.

9. Example of AR-SC Assume, E= 2,e 1 =0.5,e 2 =1 Each cover is active for a unit time of 1 (s i,r p ) : sensor i with range r p

10. Sensors without adjustable sensing ranges: C1={(s1,r2)(s2,r2)} C2={(s1,r2)(s3,r2)} C3={(s2,r2)(s3,r2)} C4={(s4,r2)} C5={(s4,r2)} Lifetime = 5

11. AR-SC : C1={(s1,r1)(s2,r2)} C2={(s1,r2)(s3,r1)} C3={(s2,r1)(s3,r2)} C4={(s4,r2)} C5={(s1,r1)(s2,r1)(s3,r1)} C6={(s4,r2)} Lifetime = 6

12. Solution for the AR-SC problem Integer Programming based Heuristic  IP is NP-Hard. Greedy based Heuristics  Centralized Greedy Heuristic  Distributed Heuristic

13. Integer Programming based Heuristic Given:  N sensor nodes s 1,s 2,…,s N  M targets t 1,t 2,…,t M  P sensing ranges r 1,r 2,…,r p and corresponding energy consumption e 1,e 2,…,e p  Initial sensor energy E  The coefficients showing the relationship between sensor, radius and target : a ipj =1, if sensor s i with radius r p covers the target t j. Variables:  C k, boolean variable, for k=1…k if this subset is a set cover  X ikp,boolean variable, for i=1…N, k=1…K, p=1…P; x ikp =1 if sensor I with range r p is in cover k

14. Integer programming based formulation: Since Integer Programming is NP-Hard, we use a relaxation and rounding mechanism.

15. 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:

16. 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 e p then set up the range of sensor I to r p, else  Step3: if all targets are covered by then set update residual energy E i =E i -e p  Step4:Return the total number of set cover

17. Greedy based Heuristics Notations:  T ip : the set of uncovered targets within the sensing range r p of sensor i  B ip :the contribution of sensor i with range r p, B ip =|T ip |/e p  △ B ip : the incremental contribution of the sensor i when its sensing range is increased to r p.  : the set of targets uncovered by the set C k

18. Centralized Greedy Heuristics A sensor that covers more targets per unit of energy should have higher priority. Using the incremental contribution parameter △ B ip as the selection decision parameter. Assume that a sensor with the highest contribution △ B ip is selected to be added to the current set cover, then the sensor i updates its sensing range from r q to t p.

19. Centralized greedy algorithm Step1:While each target is covered by at least one (s i,r p ) and E i >e p do for each s i compute △ B ip and T ip While do select s i with the highest △ B il sensing range form r p to r l Step2: For all sensors update the uncovered target set and the incremental contribution Step3: For all sensors in C k, update the residual energy Step4: Output the number of set covers k

20. 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 round. 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 neighbors.

21. Distributed Heuristics Waiting time, where B MAX is the largest possible contribution, B MAX = M/e 1 If the waiting times of two sensor s i and s j are too close, |W i -W j |<d, where d is the length of the time slot, thus they are not update their uncover target set.

22. Distributed Greedy Step1: Compute the waiting time W i and start timer t. Step2: while do if message from neighbor sensor is received then update T ip and set-up the sensing range to the smallest value r u need cover T ip update s i ’s contribution to B iu update the waiting time W i to Stpe3: s i broadcasts information the set of targets T iu it will monitor during this round.

23. 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 e p (r p ), we evaluate lifetime under linear (e p = Θ(r p )) and quadratic (e p =Θ(r p 2 )) model.  Time slot d in the distributed greed heuristic, between 0.2 and 0.75

24. Network lifetime with number of sensors

25. Network lifetime for different sensing range values

26. Network lifetime for different values of the time slot d

27. Linear and quadratic energy models

28. Conclution 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.