High-Speed Networking Lab.
Efficient Placement and Dispatch of Sensors in
a Wireless Sensor Network
High-Speed Networking Lab.
Dept. of CSIE, Fu-Jen Catholic University
Adviser: Jonathan C. Lu, Ph.D.
Speaker: Yen-Fong Wang
11/08/08
High-Speed Networking Lab.
Outline
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Abstract
Introduction
The sensor placement
The sensor dispatch
Experimental results
Conclusion
Reference
11/08/08
High-Speed Networking Lab.
I. Abstract
• To solve deployment problem:
– Sensor placement
– Sensor dispatch
• Solution to the placement:
– Allows an arbitrary-shaped polygon sensing field possibly with
arbitrary-shaped obstacles
– an arbitrary relationship between the communication distance and
sensing distance of sensors
• Solution to the dispatch:
– Minimize the total energy consumption to move sensors
– Maximize the average remaining energy of sensors which move to
satisfied the coverage and connective
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High-Speed Networking Lab.
Outline
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Abstract
Introduction
The sensor placement
The sensor dispatch
Experimental results
Conclusion
Reference
11/08/08
High-Speed Networking Lab.
II. Introduction
• Wireless sensor networks (WSN)
– Tiny, low-power devices
– Sensing units, transceiver, actuators, and even mobilizers
– Gather and process environmental information
• WSN applications
– Surveillance
– Biological detection
– Monitoring
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High-Speed Networking Lab.
II. Introduction (con.)
• Sensor deployment is a critical issue because it
affects the cost and detection capability of a wireless
sensor network
• A good sensor deployment should consider both
coverage and connectivity
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Coverage
Connectivity
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High-Speed Networking Lab.
Outline
•
•
•
•
•
•
•
Abstract
Introduction
The sensor placement
The sensor dispatch
Experimental results
Conclusion
Reference
11/08/08
High-Speed Networking Lab.
III. The sensor placement
• The sensor placement problem
– Sensing field A is modeled by an arbitrary 2D polygon
– Obstacle do not partition the sensing field
– Communication distance:  c
– Sensing distance:  s
– Assume  c =  s
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High-Speed Networking Lab.
III. The sensor placement (con.)
• Reduce the number of sensors by minimizing the
overlapping coverage.
• Two intuitive placements:
Consider coverage first
Need to add extra sensors
to maintain connectivity
when rc  3rs
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High-Speed Networking Lab.
III. The sensor placement (con.)
Consider connectivity first
Need to add extra sensors
to maintain coverage
when r  3r
c
s
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High-Speed Networking Lab.
III. The sensor placement (con.)
• Partitioning the sensing field A into two types
of sub-regions:
– Single-row regions
3rmin
» A belt-like area between obstacles whose width is not larger than
, where r
rs,rc
min
min
» Can deploy a sequence of sensors to satisfy both coverage and connectivity
– Multi-row regions
» Need multi-rows sensors to cover such areas
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High-Speed Networking Lab.
III. The sensor placement (con.)
• Step 1: Partition the sensing field
– Expand the perimeters of obstacles outwardly and A's
boundaries inwardly by a distance of rmin
– If the expansion overlaps with other obstacles, then we can
take a projection to obtain single-row regions
– The remaining regions are multi-row regions
Obstacle
3rmin
Obstacle
3rmin
Obstacle
Expansions
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High-Speed Networking Lab.
III. The sensor placement (con.)
1
2
7
3
6
Obstacle
Obstacle
Obstacle
4
5
Obstacle
3
2
1
4
5
Obstacle
3rmin
6
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High-Speed Networking Lab.
III. The sensor placement (con.)
• Step 2: Place sensors in a single-row region
– Deploy sensors along the bisector of region
Case
Small Regions
Bisectors
Sensor Deployment
Obstacle
(a)
width < 3rmin
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Obstacle
Obstacle
width < 3rmin
(b)
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Obstacle
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High-Speed Networking Lab.
III. The sensor placement problem (con.)
• Step 3: Place sensor in a multi-row region
– Consider a 2D plane without boundaries & obstacles
» Deploy sensor row by row
» A row of sensors needs to guarantee coverage and connectivity
» Adjacent rows need to guarantee continuous coverage
– Case 1: rc  3rs
» Sensors on each row are separated by rc
2
» Adjacent rows are separated by rs 
– Case 2: rc  3rs
rs
2
r
 c
4
» Each sensors separated by 3rs
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High-Speed Networking Lab.
III. The sensor placement (con.)
• Case 1:
rc  3rs
rs
rc
rs/rc
rc
rs
rs
2
rs2 - r4c
rs
rs
rs
3
2
rs
rs
rs
rs
2
2
rs2 - r4c
rc
2
rc
2
rs > rc
rs = rc
rs < rc < 3rs
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High-Speed Networking Lab.
III. The sensor placement (con.)
• Case 2:
rc  3rs
rc
rs
rs
rs
rs
2
3 rs
2
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High-Speed Networking Lab.
Step 4:
• Three unsolved problems
connectivity
– Some areas near the boundaries are
uncovered
– Need extra sensors between adjacent rows
to maintain connectivity when
– Connectivity to neighboring regions
needs to be maintained rc  3rs
• Solutions
Obstacle
Obstacle
– Sequentially place sensors along the
boundaries of the regions and obstacles
uncovered areas
11/08/08
High-Speed Networking Lab.
Outline
•
•
•
•
•
•
•
Abstract
Introduction
The sensor placement
The sensor dispatch
Experimental results
Conclusion
Reference
11/08/08
High-Speed Networking Lab.
IV. The sensor dispatch
• The sensor dispatch problem
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–
–
–
Sensing field A
An area of interest I inside A
A set of mobile sensors S resident in A
A subset S’ S of sensors to be moved to I such that
after the deployment
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High-Speed Networking Lab.
IV. The sensor dispatch (con.)
• The Sensor dispatch problem asks how to find a
subset of sensors S’ in S to be moved to I such that
after the deployment, I satisfies coverage and
connectivity requirements and the movement cost
satisfies some object functions
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High-Speed Networking Lab.
IV. The sensor dispatch (con.)
• Minimize the total energy consumption to
move sensors
min

di

m
i
S'
 m : unit energy cost to move a sensor in one step
d i : the distance that sensor i is to be moved
• Maximize the average remaining energy of
sensors after the movement


e


d

max
i

S
' i
m
i
S
'
ei : initial energy of sensor i
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High-Speed Networking Lab.
Example
A
I
Mobile sensor
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High-Speed Networking Lab.
Example
A
I
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High-Speed Networking Lab.
Example
A
I
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High-Speed Networking Lab.
IV. The sensor dispatch (con.)
• A centralized dispatch solution:
– Step1: Run the sensor placement algorithm on I and get
target the locations L  x1 , y1 , x2 , y2 ,, xm , ym 
– Step2: Determine the energy cost csi , xi , yi  to move si to
each location x j , y j , j  1 m (Use the Dijkstra’s algorithm)
– Step3: Construct a weighted complete bipartite graph
– G  ( S  L, S  L) , such that the weight of each edge
• w(si, (xj, yj)) = - c(si, (xj, yj)) , if objective function (1) is used; or as
• w(si, (xj, yj)) = ei - c(si, (xj, yj)), if objective function (2) is used
– Step4: Solve the maximum-weight maximum-matching
problem on graph G (Use the Hungarian method)
11/08/08
High-Speed Networking Lab.
An Example of Dijkstra’s algorithm
1
2
a
0
0
b
2
2
c
2
2
d e
∞ ∞ a
∞ 8 b
3
4
5
0
0
0
2
2
2
2
2
2
5
5
5
8
8
8
c
d
e
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High-Speed Networking Lab.
An Example of Dispatch
• Initially, there are five mobile sensors A, B,
C, D, and E
I
C
A
D
B
E
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High-Speed Networking Lab.
An Example of Dispatch
I
1
2
3
4
C
• Run sensor placement algorithm on I to get
the target locations
L={(x1, y1), (x2, y2), (x3, y3), (x4, y4)}
A
D
B
E
11/08/08
High-Speed Networking Lab.
An Example of Dispatch
• Compute energy cost (assume  m=1)
I
1
2
3
4
C
c( A,( x3 , y3 ))  8 c( A,( x4 , y4 ))  11
c( B,( x1 , y1 ))  11 c( B,( x2 , y2 ))  11
A
D
B
c( A,( x1 , y1 ))  9 c( A,( x2 , y2 ))  12
c( B,( x3 , y3 ))  9 c( B,( x4 , y4 ))  9
c(C ,( x1 , y1 ))  10 c(C ,( x2 , y2 ))  6
c(C ,( x3 , y3 ))  11 c(C ,( x4 , y4 ))  8
c( D,( x1 , y1 ))  14 c( D,( x2 , y2 ))  13
c( D,( x3 , y3 ))  12 c( D,( x4 , y4 ))  10
c( E ,( x1 , y1 ))  33 c( E ,( x2 , y2 ))  35
c( E ,( x3 , y3 ))  30 c( E ,( x4 , y4 ))  31
E
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High-Speed Networking Lab.
An Example of Dispatch
• Construct the weighted complete bipartite graph G and assign weight on each edge
A
1
B
2
C
D
3
4
Weights of edges (assume that all sensors have
the same initial energy 40 & 1st objective
function is used)
A
B
C
D
E
1
31 29 30 26
7
2
28 29 36 27
5
3
32 31 29 38 10
4
29 31 32 30
9
E
S
L
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High-Speed Networking Lab.
An Example of Dispatch
• Use the Hungarian method ^to find a maximum-weighted perfect-matching M
Weights of edges
A
B
C
A
D
E
1
31 29 30 26
7
2
28 29 34 27
5
3
32 31 29 28 10
4
29 31 32 30
9
5
4
4
1
2
3
D
4
E
5
S
L
B
4
C
4
4
Min.
Virtual location
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High-Speed Networking Lab.
An Example of Dispatch
• Use the Hungarian method to find a maximum-weighted perfect-matching M
Weights of edges
A
A
D
E
1
24 22 23 19
0
2
23 24 29 22
0
3
22 21 19 18
0
4
20 22 23 21
0
5
0
0
1
B
2
C
3
D
4
E
5
S
L
B
0
C
0
0
Virtual location
11/08/08
High-Speed Networking Lab.
An Example of Dispatch
• Use the Hungarian method to find a maximum-weighted perfect-matching M
Weights of edges
A
A
B
C
D
E
1
6
4
5
1
0
2
5
6
11
4
0
3
4
3
1
0
0
4
2
4
5
3
0
5
0
0
0
0
18
1
B
2
C
3
D
4
E
5
S
L
Virtual location
11/08/08
High-Speed Networking Lab.
An Example of Dispatch
• Use the Hungarian method ^to find a maximum-weighted perfect-matching M
Weights of edges
A
A
B
C
D
E
1
5
3
4
0
0
2
4
5
10
3
0
3
4
3
0
0
1
4
1
3
4
2
0
5
0
0
0
0
19
1
B
2
C
3
D
4
E
5
S
L
Virtual location
11/08/08
High-Speed Networking Lab.
An Example of Dispatch
• Use the Hungarian method to find a maximum-weighted perfect-matching M
Weights of edges
A
A
B
C
D
E
1
4
2
3
0
0
2
3
4
9
3
0
3
4
3
0
1
2
4
0
2
3
2
0
5
0
0
0
1
20
1
B
2
C
3
D
4
E
5
S
L
Virtual location
11/08/08
High-Speed Networking Lab.
An Example of Dispatch
• Use the Hungarian method to find a maximum-weighted perfect-matching M
Weights of edges
A
A
D
E
1
31 29 30 26
7
2
28 29 34 27
5
3
32 31 29 28 10
4
29 31 32 30
9
5
4
4
1
B
2
C
3
D
4
E
5
S
L
B
4
C
4
4
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High-Speed Networking Lab.
An Example of Dispatch
• Move sensors to the target locations
I
A
1
C
2
3
B
4
D
C
A
A
1
B
2
C
3
D
4
E
5
S
L
D
B
E Do not move
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High-Speed Networking Lab.
Time complexity
• The time complexity of our sensor dispatch
algorithm is O(mnk2 + n3)
– O(mnk2 ): compute the energy cost of each si , xi , yi  and
Dijkstra’s algorithm to find shortest path
– O(n3): running Hungarian method on G^
– m: number of target locations in I
– n: number of mobile sensors
– k: number of vertices of the polygons of all obstacles and I
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High-Speed Networking Lab.
IV. The sensor dispatch (con.)
• A Distributed dispatch solution
– Step1: The sink runs the placement to get the location L to be
occupied by sensors (the sink broadcast L to all sensors)
– Step2: On receiving the table L, a sensor will keep a copy of
L and mark each location x j , y j , j  1 m as unoccupied
– Step3: Each sensor si then chooses an unoccupied location
from L as its destination
» The objective function (1) by minimized moving distance
» The objective function (2) by maximized remaining energy
– Step4: On si ‘s way moving toward its destination, it will
periodically broadcast the status of its table L
» If both si and sk are moving toward the same destination, they will
compete by their cost
11/08/08
High-Speed Networking Lab.
Outline
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Abstract
Introduction
The sensor placement
The sensor dispatch
Experimental results
Conclusion
Reference
11/08/08
High-Speed Networking Lab.
V. Experimental results
• Use rs , rc  = (7,5), (5,5), (3.5,5), (2,5) to reflect
the four cases r  r , r  r , r  r  3r , 3r  r
• Comparison metric
s
c
s
c
s
c
s
s
c
– Average number of sensors used to deploy
– Compare with two deployment methods
3rs
3rs
rc
rc
3rs
rs
Coverage-first
Connectivity-first
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High-Speed Networking Lab.
V. Experimental results (con.)
Sensing Fields
75
40
48
28
89
(a) Rectangle
(b) Circle
(c) Non-convex polygon
37
89
89
4
17
75
87
19
41
(d) H-shape
57
35
(e) Office 1
40
75
28
12
3
20
28
9
6
4
4
3
(f) Office 2
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High-Speed Networking Lab.
V. Experimental results (con.)
(a) Rectangle
470
400
300
275
253
201
193
148
100
0
rs > r c
rs = rc
Ours
Cov.-first
Conn.-first
300
273
273
220
159
126
100
rs > rc
rs = rc
(d) H-shape
353
252
210
174
200
265
253
225
171
141
100
Number of Deployed Sensors
Ours
Cov.-first
Conn.-first
300
Conn.-first
284
215
200
142
rs = rc
rs < rc < 3rs
215
178
135
111
100
0
rs > rc
rs = rc
rs < rc < 3rs
(f) Office 2
Ours
Cov.-first
Conn.-first
500
400
300
215
168
800
600
470
341
341
217
253
298
323
363
254
200
100
0
rs > r c
Cov.-first
300
rs < rc < 3rs
700
400
Ours
400
(e) Office 1
500
0
273
206
169
200
0
rs < rc < 3rs
367
rs > rc
rs = rc
rs < rc < 3rs
Number of Deployed Sensors
200
340
328
328
400
Number of Deployed Sensors
Ours
Cov.-first
Conn.-first
Number of Deployed Sensors
Number of Deployed Sensors
500
500
500
Number of Deployed Sensors
(c) Non-convex polygon
(b) Circle
600
700
600
Ours
Cov.-first
Conn.-first
500
500
300
361
360
400
227
267
268
315
341
386
200
100
0
rs > rc
rs = rc
rs < rc < 3rs
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High-Speed Networking Lab.
V. Experimental results (con.)
• Greedy: sensors select the closest locations
• Random: sensors randomly select locations
12000
Average Remaining Energy of Sensors
Total Energy for Movement
14000
Ours
Greedy
Random
10000
8000
6000
4000
2000
0
20
40
60
80
100
Number of Sensors in I
120
660
640
620
600
580
560
Ours
Greedy
Random
540
520
500
20
40
60
80
100
Number of Sensors in I
120
11/08/08
High-Speed Networking Lab.
Outline
•
•
•
•
•
•
•
Abstract
Introduction
The sensor placement
The sensor dispatch
Experimental results
Conclusion
Reference
11/08/08
High-Speed Networking Lab.
VII. Conclusion
• Propose a systematical solution for sensor
deployment
– Sensing field is modeled as an arbitrary polygon
with obstacles
– Allow arbitrary relationship between rc and rs
– Fewer Sensor are required to ensure coverage and
connectivity
11/08/08
High-Speed Networking Lab.
Outline
•
•
•
•
•
•
•
Abstract
Introduction
The sensor placement
The sensor dispatch
Experimental results
Conclusion
Reference
11/08/08
High-Speed Networking Lab.
IX. Reference
• Efficient Placement and Dispatch of Sensors in a
Wireless Sensor Network
You-Chiun Wang; Chun-Chi Hu; Yu-Chee Tseng;
IEEE Transactions on Mobile Computing
Volume 7, Issue 2, Feb. 2008
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