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