barrier coverage with wireless sensors santosh kumar, ten h. lai and anish arora department of...

Barrier Coverage With Wireless Sensors

Santosh Kumar, Ten H. Lai and Anish AroraDepartment 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.

1-barrier covered

Not 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.

L R

Open Belt Region

Closed Belt Region

Coverage graph G k-barrier covered iff G has k essential cycl

es (that loop around the entire belt region).

Closed Belt Region

Optimal Configuration for deterministic deployments Assuming sensors can be placed at

desired locationsWhat 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 How many sensors are needed to achieve k-barrier c

overage 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 a

s possible

L(p) = all crossing paths congruent to p

p

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

If , then k-barrier covered whp

If , not k-barrier covered whp

s1/s

Expected # of sensors in the r-neighborhood of path

r

Grid distribution with independent failures, Shakkottai03 (InGrid distribution with independent failures, Shakkottai03 (Infocom 2003)focom 2003)

c’(n) = npc’(n) = npππr2/log(n)r2/log(n)

What if the limit equals 1?

Given: Length (l), Width (w), Sensing Range (R), and Coverage De

gree (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 problemsBlanket coverage: extensively studiedBarrier coverage: still at its infantry

Thank you!