barrier coverage with wireless sensors
DESCRIPTION
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 - PowerPoint PPT PresentationTRANSCRIPT
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Barrier Coverage With Wireless Sensors
Santosh Kumar, Ten H. Lai, Anish Arora
The Ohio State University
Presented at Mobicom 2005
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Barrier Coverage
USA
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Belt Region
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Two special belt regions
Rectangular:
Donut-shaped:
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How to define a belt region?
Parallel curves Region between two parallel curves
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Crossing Paths
A crossing path is a path that crosses the complete width of the belt region.
Crossing paths Not crossing paths
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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
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k-Barrier Covered
A belt region is k-barrier covered if all crossing paths are k-covered.
1-barrier covered
Not barrier covered
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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
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Question 1
Given a belt region deployed with sensors Is it k-barrier covered?
Is it 4-barrier covered?
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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
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Be Careful!
Assumption:
If D1 ∩ D2 ≠ Φ, then (D1 U D2) ∩ B is connected.
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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?
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Is it k-barrier covered? Still an open problem for donut-shaped
regions.
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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.
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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
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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
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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
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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
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L(p) = all crossing paths congruent to p
p
p
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Weak Barrier Coverage
A belt region is k-barrier covered whp if
lim Pr(all crossing paths are k-covered) = 1or 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
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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
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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
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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.
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Summary Barrier coverage
Basic results
Open problemsBlanket coverage: extensively studiedBarrier coverage: further research needed