exposure in wireless ad-hoc sensor networks s. megerian, f. koushanfar, g. qu, g. veltri, m....
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Exposure In Wireless Ad-Hoc Sensor Networks
S. Megerian, F. Koushanfar, G. Qu, G. Veltri, M. Potkonjak
ACM SIG MOBILE 2001(Mobicom)
Journal version:S. Megerian, F. Koushanfar, G. Qu, G. Veltri, M. Potkonjak. “Exposure In Wireless Sensor Networks: Theory And Practical Solutions.” ACM Journal of Wireless Networks, 8 (5): pp. 443-454, September 2002.
Outline
Introduction Preliminaries Minimal Exposure Path General Exposure Computations Experimental Results
Introduction(1/4)
Coverage in sensor networks How well do the sensors observe physica
l space?” A measure of quality of service (surveillance)
that can be provided by a particular sensor network.
Introduction(2/4)
Coverage Types Area coverage
The main objective is to cover (monitor) an area Such as Node self-scheduling algorithm, Probing-
based density control algorithm and Disjoint dominating sets heuristic, etc.
Ref. [http://vc.cs.nthu.edu.tw/home/paper/list.php]
Introduction(3/4)
Point coverage The objective is to cover a set of targets (poin
ts) Such as Disjoint set cover heuristics (Linear progra
mming-based approaches)
Ref. [http://vc.cs.nthu.edu.tw/ezLMS/show.php?id=376&1155473386]
target
Introduction(4/4)
Barrier Coverage The goal is to minimize the probability of und
etected penetration through the barrier (sensor network)
Maximal breach path, maximal support path, minimal exposure path.
Maximal breach pathRef. [http://vc.cs.nthu.edu.tw/ezLMS/show.php?id=326&1155473548]
Preliminaries
Sensor Models Sensing ability diminishes as distance increases Sensing ability improves as the allotted sensing time (exposure) increases
Sensor field intensity All-sensor field intensity
Sensing measure at point p from all sensors in F
Closest-sensor field intensity Sensing measure at point p from the closest sensor in F
n
iA psSpFI1
),(),(
kpsdpsS
),(),(
),(),(
),(),(
min
min
psSpFI
SspsdpsdSss
C
mm
Exposure
Exposure Expected average ability of observing a target in the sen
sor field
The exposure of an object moving in the sensor field during the interval [t1, t2] along the path p(t) is defined as
dtdt
tdptpFItttpE
t
t2
1
)())(,(),),(( 21
))(),(()( tytxtp
))(,())(,( tpFIortpFI CA
22)()()(
dt
tdy
dt
tdx
dt
tdp
r
r
Minimal Exposure Path
Given: Sensor Field A N sensors Initial and final points I and F
Problem: Find the Minimal Exposure Path PminE in A, starti
ng in I and ending in F. PminE is the path in A, along which the exposure i
s the smallest among all paths from I to F.
Examples(1/3)
Square field One sensor is at position (0,0) Minimum exposure path from point p(1, 0) to
point q(0, 1)
4 exposure minimalThen
1
),(
1)),(),0,0(( Assume
22
E
yxpsdyxpsS
s
y
p=(1, 0)
q=(0, 1)
/42
2
2
2
Examples(2/3)
Square field (cont’) Minimum exposure path from point p(1, -1) to
point q(-1, 1)
Proof:
Examples(3/3)
Convex polygon field Sensor is at the center of the inscribed circle The minimum exposure path from vertices v2
vertices to vn
General Exposure Computations (1/3)
Finding the minimum exposure path under arbitrary sensor and intensity model is extremely difficult
Need Efficient and scalable methods To approximate exposure integrals To search for minimum exposure path
Algorithm
1. Use grid-based approach
2. Transform the grid into a weighted graph
3. Use Djikstra’s Single-Source-Shortest-Path algorithm
General Exposure Computations (2/3) Step 1
Divide the sensor network region using an n×n grid The path is restricted to line segments connecting
any two vertices. Example: 2×2 gird
First-order (m=1) Second-order (m=2) Third-order (m=3)
General Exposure Computations (3/3)
Step2 Transform F to the edge-weighted graph G
Each edge is assigned a weight equal to the exposure along its corresponding edge in F
Exposure is calculated using numerical integration techniques
Step3 Find the minimal exposure path from source ps to the pd
Use Djikstra’s Single-Source-Shortest-Path algorithm Can use Floyd-Warshal’s All-Pair-Shortest-Path algorithm to find
minimal exposure path between any arbitrary starting and ending points.
Experimental Results (1/4)
Simulation platform C++ package Sensor field is 1000×1000 square Assume a constant speed 3232 grid with 8 divisions per grid-
square edge (n=32, m=8)
(1/d2)
(1/d4)
1. As n is small, there are a wide range of minimal exposure paths.
2. As n increases, the exposure and the minimal path tend to stabilize.
The minimal exposure path gets closer to bounding edges of the field
The path length approaches the half field perimeter.
average median standard deviation
Experimental Results (2/4)
Uniformly distributed random sensor deployment As sensor density increases, the minimal exposure value and
path lengths tends to stabilize As number of sensor increases, relative standard deviation of
exposure diminishes
Experimental Results (3/4) Uniformly distributed random sensor deployment (cont’)
Path calculated by 8×8 grid is close to the accurate path obtained by the higher resolution grids
n = 32, m = 8n=16, m = 2n = 8, m =1
All sensor intensity IA
Closest sensor intensity IC
Experimental Results (4/4) Deterministic sensor placement
Higher exposure than the randomly generated network topology
Conclusion
This paper introduced the exposure-based model to provide valuable information about the worst case coverage.
This paper presented an grid-based approach to identify a minimal exposure path for a given distribution of sensor networks.
The proposed Algorithm consists of three parts: 1. Use grid-based approach2. Apply graph-theoretic abstraction3. Use Djikstra’s Single-Source-Shortest-Path algorithm
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