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

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

Introduction Wireless sensor networks can replace such barriers

Introduction : Barrier Coverage USA Intruder

Introduction : Belt Region

The network model: Crossing Paths A crossing path is a path that crosses the complete width of the belt region. Crossing paths Not crossing paths

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

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

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

Barrier coverage vs. Blanket coverage A belt region is k-barrier covered 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

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

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

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

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.

Open Belt Region R L

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

Closed Belt Region

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? k x S / (2r) sensors, deployed in k rows r

Question ? If sensors are deployed randomly Desired are How many sensors 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

L(p) = all crossing paths congruent to p

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 covered whp if crossing paths p, lim Pr( L(p) is k-covered ) = 1

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

What if the limit equals 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

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

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

Simulations

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

Thank you!