Barrier Coverage With Wireless Sensors

1. Barrier Coverage With Wireless Sensors Santosh Kumar, Ten H. Lai and Anish Arora Department of Computer Science and Engineering The Ohio State University MobiCom 2005

2. Outline • Introduction • The network Model • Algorithm for k-Barrier coverage • Simulation • Conclusions

3. Introduction • Wireless sensor networks can replace such barriers

4. Introduction : Barrier Coverage USA Intruder

5. Introduction : Belt Region

6. The network model: Crossing Paths • A crossing path is a path that crosses the complete width of the belt region. Crossing pathsNot crossing paths

7. The network model:Two special belt regions • Rectangular: • Donut-shaped:

8. k-Covered • A crossing path is said to be k-covered if it intersects the sensing disks of at least k sensors. 3-covered 1-covered 0-covered

9. k-Barrier Covered • A belt region is k-barrier covered if all crossing paths are k-covered. Not barrier covered 1-barrier covered

10. Barrier coverage vs. Blanket coverage • A belt region is k-barriercovered if all crossing paths are k-covered. • A region is k-blanket covered if all points are k-covered. • k-blanket covered k-barrier covered 1-barrier covered but not 1-blanket covered

11. Algorithm for k-Barrier coverage: • Local? Global ? • Open Belt Region • Closed Belt Region • Optimal configuration for deterministic deployments • Min # sensors in random deployment

12. Algorithm for k-Barrier coverage:Non-locality of k-barrier Coverage

13. Algorithm for k-Barrier coverage:Non-locality of k-barrier Coverage

14. Open Belt Region • Given a sensor network over a belt region • Construct a coverage graph G(V, E) • V: sensor nodes, plus two dummy nodes L, R • E: edge (u,v) if their sensing disks overlap • Region is k-barrier covered iff L and R are k-connected in G.

15. Open Belt Region R L

16. Closed Belt Region • Coverage graph G • k-barrier covered iff G has kessential cycles (that loop around the entire belt region).

17. Closed Belt Region

18. Optimal Configuration for deterministic deployments • Assuming sensors can be placed at desired locations • What is the minimum number of sensors to achieve k-barrier coverage? • kxS / (2r)sensors, deployed in k rows r

19. Question ? • If sensors are deployed randomly • How manysensors are needed to achieve k-barrier coverage with high probability (whp)? • Desired are • A sufficient condition to achieve barrier coverage whp • A sufficient condition for non-barrier coverage whp • Gap between the two conditions should be as small as possible

20. L(p) = all crossing paths congruent to p p p

21. Weak Barrier Coverage • A belt region is k-barrier covered whp if lim Pr(all crossing paths are k-covered) = 1 or lim Pr( crossing paths p, L(p) is k-covered ) = 1 • A belt region is weakly k-barrier coveredwhp if crossing paths p, lim Pr( L(p) is k-covered ) = 1

22. Conjecture: critical condition for k-barrier coverage whp • Grid distribution with independent failures, Shakkottai03 (Infocom 2003) • c’(n) = npπr2/log(n) • If , then k-barrier covered whp • If , not k-barrier covered whp Expected # of sensors in the r-neighborhood of path s r 1/s

23. What if the limitequals 1? • Given: • Length (l), Width (w), Sensing Range (R), and Coverage Degree (k), • To determine # sensors (n) to deploy, compute • s2 = l/w • r = (R/w)*(1/s) • Compute the minimum value of n such that 2nr/s ≥ log(n) + (k-1) log log(n) + √log log(n) s

24. Simulations • Region of dimension 10km * 100m • Sensing radius 10m • P =0.1

25. Simulations • Using this formula to determine n, • The n randomly deployed sensors provide weakk-barrier coverage with probability ≥0.99. • They also provide k-barrier coverage with probability close to 0.99.

26. Simulations

27. Conclusions • Barrier coverage • Basic results • Open problems • Blanket coverage: extensively studied • Barrier coverage: still at its infantry

28. Thank you!