Maximum Network lifetime in Wireless Sensor Networks with Adjustable Sensing Ranges

1. Maximum Network lifetimein 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 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.

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 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.

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 ,e1=0.5 ,e2=1 • Each cover is active for a unit time of 1 • (si,rp) : sensor i with range rp

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 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

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 ep then set up the range of sensor I to rp, else • Step3: if all targets are covered by then set update residual energy Ei=Ei-ep • Step4:Return the total number of set cover

17. 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=|Tip|/ep • △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

18. 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 △Bipis selected to be added to thecurrent set cover, then the sensor i updates its sensing range from rq to tp.

19. 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

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 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.

22. 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.

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 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

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.