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!