1. Strong Barrier Coverage of Wireless Sensor Networks Benyuan Liu, Olivier Dousse, Jie Wang and Anwar Saipulla University of Massachusetts Lowell and Deutsche Telekom Laboratories (Germany) MobiHoc 2008, Hong Kong

2. Outline  Introduction  Network Model  Critical Conditions for Strong Barrier Coverage  Constructing Barriers  Performance Evaluation  Conclusions

3. Introduction  Sensor Barriers is used to detect intruders crossing a randomly-deployed sensor network  1-Barrier Coverage Intruder

4. Introduction  Strong Coverage and Weak Coverage

5. Introduction  Sensor Network Futures Random Deployment Random Deployment Power supply by Battery Power supply by Battery  Goal Constructing Strong Barrier Coverage Constructing Strong Barrier Coverage Finding Multiple Barriers Finding Multiple Barriers

6. Network Model  Two-dimensional strip area of size A 2-dim strip = [ 0, n ] × [ 0, w(n) ] A 2-dim strip = [ 0, n ] × [ 0, w(n) ]  Poisson point process of density λ  The expected number of nodes in the network is λnw(n)  Boolean sensing model  The communication range is 2 times of the sensing range

7. Network Model  A path is said to be k -covered if it intercepts at least k distinct sensors.  We say an event occurs with high probability (w.h.p.) if its probability tends to 1 as n →∞

8. Critical Condition for Strong Barrier Coverage  Theorem1. Consider a sensor network deployed on a two-dimensional rectangular area A 2-dim strip =[0,n] × [0, w(n)], where sensors are distributed according to a Poisson point process with density λ n w(n)w(n) The density :λ

9. Critical Conditions for Strong Barrier Coverage  If w(n) = Ω ( log n), the network is strongly barrier covered w.h.p. when the sensor density reaches a certain value. There exists a positive constant β such that w.h.p. there exist β w(n) disjoint horizontal sensor barriers crossing the strip.

10. Critical Conditions for Strong Barrier Coverage  If w(n) = o(log n), the network has no strong barrier coverage w.h.p. regardless what the sensor density is in the underlying sensor network. That is, w.h.p. there exist crossing paths that an intruder can cross the strip without being detected.

11. Constructing Barriers  Typical wireless sensors are powered by conventional batteries, and they are energy stringent  Important Issue Scheduling sensors so that at any given moment there are just enough active sensors to cover the barrier Scheduling sensors so that at any given moment there are just enough active sensors to cover the barrier  [6] shows that whether a sensor network is strongly k-barrier covered cannot be determined using local algorithms.

12. Constructing Barriers  Vertical Strip and Segment

13. Constructing Barriers  Selecting a sensor to be delegate  Collecting the location information of the strip or segment by broadcasting  Convert sensor network to flow network For any two vertices u and v in V, if their sensing area overlap, connect them with an edge capacity of 1. For any two vertices u and v in V, if their sensing area overlap, connect them with an edge capacity of 1. Add node s and d to the flow network Add node s and d to the flow network

14. Constructing Barriers  The Flow Network

15. Constructing Barriers

16.  Divide-and Conquer Algorithm 1. Divide the given strip into small segments interleaved by thin vertical strips 2. In each vertical strip, sensor nodes use ComputeBarrier to find al of the disjoint vertical barriers and the horizontal barriers that connect the vertical barrier together. 3. For each strip segment, use ComputeBarriers to find disjoint horizontal barriers intersecting the vertical barriers on both ends of the segment

17. ComputeBarriers Contributions  Lower Communication Overhead and computation costs  Improved robustness of the barrier coverage  Strengthened local barrier coverage

18. Performance Evaluation  The network of size l × w according to a two-dimensional Poisson point process of densityλ.  The simulation is repeated 500 times.  l =10,000 meters  Sensing range r = 10 meters

19. Condition for Strong Barrier Coverage

20. Strengthened Local Barrier Coverage Ten segments 20m to 350m Three kinds of density Barrier improvement ratio: the number of horizontal barriers in each segment / the number of global barriers for the whole strip

21. Strengthened Local Barrier Coverage

22. Conclusions  Theoretical foundations and practical algorithm  Below the critical width to length ration, there is n strong barrier coverage  Based on this result, they further devise an distributed algorithm to construct disjoint barriers with low delay, communication overhead, and computation cost.

23. The End