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Barrier Coverage With Wireless Sensors
Santosh Kumar, Ten H. Lai, Anish Arora
The Ohio State University
Presented at Mobicom 2005
Barrier Coverage
USA
Belt Region
Two special belt regions
Rectangular:
Donut-shaped:
How to define a belt region?
Parallel curves Region between two parallel curves
Crossing Paths
A crossing path is a path that crosses the complete width of the belt region.
Crossing paths Not crossing paths
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 vs. Blanket Coverage
Barrier coverage Every crossing path is k-covered
Blanket coverage Every point is covered (or k-covered)
Blanket coverage Barrier coverage
1-barrier covered but not 1-blanket covered
Question 1
Given a belt region deployed with sensors Is it k-barrier covered?
Is it 4-barrier covered?
Reduced to k-connectivity problem Given a sensor network over a belt region Construct a coverage graph G(V, E)
V: sensor nodes, plus two dummy nodes L, RE: edge (u,v) if their sensing disks overlap
Region is k-barrier covered iff L and R are k-connected in G.
L R
Be Careful!
Assumption:
If D1 ∩ D2 ≠ Φ, then
(D1 U D2) ∩ B is connected.
Global algorithm for testing k-barrier coverage
Given a sensor network Construct a coverage graph Using existing algorithms
To test k-connectivity between two nodes
Question: what about donut-shaped regions? Question: can it be done locally?
Is it k-barrier covered? Still an open problem for donut-shaped
regions.
Is it k-barrier covered? Cannot be determined locally k-barrier covered iff k red sensors exist
In contrast, it can be locally determined if a region is not k-blanket covered.
Question 2
Assuming sensors can be placed at desired locationsWhat is the minimum number of sensors to
achieve k-barrier coverage?k x L / (2R) sensors, deployed in k rows
Question 3
If sensors are deployed randomly 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
Conjecture: critical condition for k-barrier coverage whp
If , then k-barrier covered whp
If , non-k-barrier covered whp
s1/s
Expected # of sensors in the r-neighborhood of path
r r
k-barrier covered whp
k-barrier covered whp lim Pr( belt region is k-barrier covered ) = 1
not (k-barrier covered whp) lim Pr( belt region is k-barrier covered ) < 1
non-k-barrier covered whp lim Pr( belt region is not k-barrier covered ) = 1 lim Pr( belt region is k-barrier covered ) = 0
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
If , then k-barrier covered whp
If , not k-barrier covered whp
What if the limit equals 1?
weakly
weakly
weak
Determining #Sensors to Deploy
Given: Length (l), Width (w), Sensing Range (R), and
Coverage Degree (k), To determine # sensors (n) to deploy, compute
s2 = l/wr = (R/w)*(1/s)Compute the minimum value of n such that
2nr/s ≥ log(n) + (k-1) log log(n) + √log log(n)
s1/s
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.
Summary
Barrier coverage
Basic results
Open problemsBlanket coverage: extensively studiedBarrier coverage: further research needed