Barrier Coverage With Wireless Sensors Santosh Kumar, Ten H. Lai and Anish Arora Department of...
-
Upload
camron-atkins -
Category
Documents
-
view
216 -
download
0
Transcript of Barrier Coverage With Wireless Sensors Santosh Kumar, Ten H. Lai and Anish Arora Department of...
![Page 1: Barrier Coverage With Wireless Sensors Santosh Kumar, Ten H. Lai and Anish Arora Department of Computer Science and Engineering The Ohio State University.](https://reader030.fdocuments.in/reader030/viewer/2022033106/56649f465503460f94c68a34/html5/thumbnails/1.jpg)
Barrier Coverage With Wireless Sensors
Santosh Kumar, Ten H. Lai and Anish AroraDepartment of Computer Science and Engineering The Ohio State University
MobiCom 2005
![Page 2: Barrier Coverage With Wireless Sensors Santosh Kumar, Ten H. Lai and Anish Arora Department of Computer Science and Engineering The Ohio State University.](https://reader030.fdocuments.in/reader030/viewer/2022033106/56649f465503460f94c68a34/html5/thumbnails/2.jpg)
Outline
Introduction The network Model Algorithm for k-Barrier coverage Simulation Conclusions
![Page 3: Barrier Coverage With Wireless Sensors Santosh Kumar, Ten H. Lai and Anish Arora Department of Computer Science and Engineering The Ohio State University.](https://reader030.fdocuments.in/reader030/viewer/2022033106/56649f465503460f94c68a34/html5/thumbnails/3.jpg)
Introduction
Wireless sensor networks can replace such barriers
![Page 4: Barrier Coverage With Wireless Sensors Santosh Kumar, Ten H. Lai and Anish Arora Department of Computer Science and Engineering The Ohio State University.](https://reader030.fdocuments.in/reader030/viewer/2022033106/56649f465503460f94c68a34/html5/thumbnails/4.jpg)
Introduction : Barrier Coverage
USA
Intruder
![Page 5: Barrier Coverage With Wireless Sensors Santosh Kumar, Ten H. Lai and Anish Arora Department of Computer Science and Engineering The Ohio State University.](https://reader030.fdocuments.in/reader030/viewer/2022033106/56649f465503460f94c68a34/html5/thumbnails/5.jpg)
Introduction : Belt Region
![Page 6: Barrier Coverage With Wireless Sensors Santosh Kumar, Ten H. Lai and Anish Arora Department of Computer Science and Engineering The Ohio State University.](https://reader030.fdocuments.in/reader030/viewer/2022033106/56649f465503460f94c68a34/html5/thumbnails/6.jpg)
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
![Page 7: Barrier Coverage With Wireless Sensors Santosh Kumar, Ten H. Lai and Anish Arora Department of Computer Science and Engineering The Ohio State University.](https://reader030.fdocuments.in/reader030/viewer/2022033106/56649f465503460f94c68a34/html5/thumbnails/7.jpg)
The network model: Two special belt regions
Rectangular:
Donut-shaped:
![Page 8: Barrier Coverage With Wireless Sensors Santosh Kumar, Ten H. Lai and Anish Arora Department of Computer Science and Engineering The Ohio State University.](https://reader030.fdocuments.in/reader030/viewer/2022033106/56649f465503460f94c68a34/html5/thumbnails/8.jpg)
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
![Page 9: Barrier Coverage With Wireless Sensors Santosh Kumar, Ten H. Lai and Anish Arora Department of Computer Science and Engineering The Ohio State University.](https://reader030.fdocuments.in/reader030/viewer/2022033106/56649f465503460f94c68a34/html5/thumbnails/9.jpg)
k-Barrier Covered
A belt region is k-barrier covered if all crossing paths are k-covered.
1-barrier covered
Not barrier covered
![Page 10: Barrier Coverage With Wireless Sensors Santosh Kumar, Ten H. Lai and Anish Arora Department of Computer Science and Engineering The Ohio State University.](https://reader030.fdocuments.in/reader030/viewer/2022033106/56649f465503460f94c68a34/html5/thumbnails/10.jpg)
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
![Page 11: Barrier Coverage With Wireless Sensors Santosh Kumar, Ten H. Lai and Anish Arora Department of Computer Science and Engineering The Ohio State University.](https://reader030.fdocuments.in/reader030/viewer/2022033106/56649f465503460f94c68a34/html5/thumbnails/11.jpg)
Algorithm for k-Barrier coverage:
Local? Global ? Open Belt Region Closed Belt Region Optimal configuration for deterministic
deployments Min # sensors in random deployment
![Page 12: Barrier Coverage With Wireless Sensors Santosh Kumar, Ten H. Lai and Anish Arora Department of Computer Science and Engineering The Ohio State University.](https://reader030.fdocuments.in/reader030/viewer/2022033106/56649f465503460f94c68a34/html5/thumbnails/12.jpg)
Algorithm for k-Barrier coverage:Non-locality of k-barrier Coverage
![Page 13: Barrier Coverage With Wireless Sensors Santosh Kumar, Ten H. Lai and Anish Arora Department of Computer Science and Engineering The Ohio State University.](https://reader030.fdocuments.in/reader030/viewer/2022033106/56649f465503460f94c68a34/html5/thumbnails/13.jpg)
Algorithm for k-Barrier coverage:Non-locality of k-barrier Coverage
![Page 14: Barrier Coverage With Wireless Sensors Santosh Kumar, Ten H. Lai and Anish Arora Department of Computer Science and Engineering The Ohio State University.](https://reader030.fdocuments.in/reader030/viewer/2022033106/56649f465503460f94c68a34/html5/thumbnails/14.jpg)
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.
![Page 15: Barrier Coverage With Wireless Sensors Santosh Kumar, Ten H. Lai and Anish Arora Department of Computer Science and Engineering The Ohio State University.](https://reader030.fdocuments.in/reader030/viewer/2022033106/56649f465503460f94c68a34/html5/thumbnails/15.jpg)
L R
Open Belt Region
![Page 16: Barrier Coverage With Wireless Sensors Santosh Kumar, Ten H. Lai and Anish Arora Department of Computer Science and Engineering The Ohio State University.](https://reader030.fdocuments.in/reader030/viewer/2022033106/56649f465503460f94c68a34/html5/thumbnails/16.jpg)
Closed Belt Region
Coverage graph G k-barrier covered iff G has k essential cycl
es (that loop around the entire belt region).
![Page 17: Barrier Coverage With Wireless Sensors Santosh Kumar, Ten H. Lai and Anish Arora Department of Computer Science and Engineering The Ohio State University.](https://reader030.fdocuments.in/reader030/viewer/2022033106/56649f465503460f94c68a34/html5/thumbnails/17.jpg)
Closed Belt Region
![Page 18: Barrier Coverage With Wireless Sensors Santosh Kumar, Ten H. Lai and Anish Arora Department of Computer Science and Engineering The Ohio State University.](https://reader030.fdocuments.in/reader030/viewer/2022033106/56649f465503460f94c68a34/html5/thumbnails/18.jpg)
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
![Page 19: Barrier Coverage With Wireless Sensors Santosh Kumar, Ten H. Lai and Anish Arora Department of Computer Science and Engineering The Ohio State University.](https://reader030.fdocuments.in/reader030/viewer/2022033106/56649f465503460f94c68a34/html5/thumbnails/19.jpg)
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
![Page 20: Barrier Coverage With Wireless Sensors Santosh Kumar, Ten H. Lai and Anish Arora Department of Computer Science and Engineering The Ohio State University.](https://reader030.fdocuments.in/reader030/viewer/2022033106/56649f465503460f94c68a34/html5/thumbnails/20.jpg)
L(p) = all crossing paths congruent to p
p
p
![Page 21: Barrier Coverage With Wireless Sensors Santosh Kumar, Ten H. Lai and Anish Arora Department of Computer Science and Engineering The Ohio State University.](https://reader030.fdocuments.in/reader030/viewer/2022033106/56649f465503460f94c68a34/html5/thumbnails/21.jpg)
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
![Page 22: Barrier Coverage With Wireless Sensors Santosh Kumar, Ten H. Lai and Anish Arora Department of Computer Science and Engineering The Ohio State University.](https://reader030.fdocuments.in/reader030/viewer/2022033106/56649f465503460f94c68a34/html5/thumbnails/22.jpg)
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)
![Page 23: Barrier Coverage With Wireless Sensors Santosh Kumar, Ten H. Lai and Anish Arora Department of Computer Science and Engineering The Ohio State University.](https://reader030.fdocuments.in/reader030/viewer/2022033106/56649f465503460f94c68a34/html5/thumbnails/23.jpg)
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
![Page 24: Barrier Coverage With Wireless Sensors Santosh Kumar, Ten H. Lai and Anish Arora Department of Computer Science and Engineering The Ohio State University.](https://reader030.fdocuments.in/reader030/viewer/2022033106/56649f465503460f94c68a34/html5/thumbnails/24.jpg)
Simulations
Region of dimension 10km * 100m Sensing radius 10m P =0.1
![Page 25: Barrier Coverage With Wireless Sensors Santosh Kumar, Ten H. Lai and Anish Arora Department of Computer Science and Engineering The Ohio State University.](https://reader030.fdocuments.in/reader030/viewer/2022033106/56649f465503460f94c68a34/html5/thumbnails/25.jpg)
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.
![Page 26: Barrier Coverage With Wireless Sensors Santosh Kumar, Ten H. Lai and Anish Arora Department of Computer Science and Engineering The Ohio State University.](https://reader030.fdocuments.in/reader030/viewer/2022033106/56649f465503460f94c68a34/html5/thumbnails/26.jpg)
Simulations
![Page 27: Barrier Coverage With Wireless Sensors Santosh Kumar, Ten H. Lai and Anish Arora Department of Computer Science and Engineering The Ohio State University.](https://reader030.fdocuments.in/reader030/viewer/2022033106/56649f465503460f94c68a34/html5/thumbnails/27.jpg)
Conclusions Barrier coverage
Basic results
Open problemsBlanket coverage: extensively studiedBarrier coverage: still at its infantry
![Page 28: Barrier Coverage With Wireless Sensors Santosh Kumar, Ten H. Lai and Anish Arora Department of Computer Science and Engineering The Ohio State University.](https://reader030.fdocuments.in/reader030/viewer/2022033106/56649f465503460f94c68a34/html5/thumbnails/28.jpg)
Thank you!