Strong Barrier Coverage of Strong Barrier Coverage of Wireless Sensor NetworksWireless Sensor Networks

Benyuan Liu, Olivier Dousse, Jie Wang and Benyuan Liu, Olivier Dousse, Jie Wang and Anwar SaipullaAnwar Saipulla

University of Massachusetts Lowell and DeutUniversity of Massachusetts Lowell and Deutsche Telekom Laboratories (Germany)sche Telekom Laboratories (Germany)

MobiHoc 2008, Hong KongMobiHoc 2008, Hong Kong

OutlineOutline

IntroductionIntroduction Network ModelNetwork Model Critical Conditions for Strong Barrier Critical Conditions for Strong Barrier

CoverageCoverage Constructing BarriersConstructing Barriers Performance EvaluationPerformance Evaluation ConclusionsConclusions

IntroductionIntroduction

Sensor Barriers is used to detect intruders Sensor Barriers is used to detect intruders crossing a randomly-deployed sensor crossing a randomly-deployed sensor networknetwork

1-Barrier Coverage1-Barrier Coverage

IntruderIntruder

IntroductionIntroduction

Strong Coverage and Weak CoverageStrong Coverage and Weak Coverage

IntroductionIntroduction

Sensor Network FuturesSensor Network Futures Random DeploymentRandom Deployment Power supply by BatteryPower supply by Battery

GoalGoal Constructing Strong Barrier CoverageConstructing Strong Barrier Coverage Finding Multiple Barriers Finding Multiple Barriers

Network ModelNetwork Model

Two-dimensional strip area of size Two-dimensional strip area of size AA2-dim strip2-dim strip= [= [00, , nn] × [] × [00, , ww((nn))]]

Poisson point process of density λPoisson point process of density λ The expected number of nodes in the netwThe expected number of nodes in the netw

ork is ork is λλnwnw((nn)) Boolean sensing modelBoolean sensing model The communication range is 2 times of the The communication range is 2 times of the

sensing rangesensing range

Network ModelNetwork Model

A path is said to be A path is said to be kk-covered if it intercept-covered if it intercepts at least s at least kk distinct sensors. distinct sensors.

We say an event occurs We say an event occurs with high probabiliwith high probability (w.h.p.)ty (w.h.p.) if its probability tends to 1 as if its probability tends to 1 as nn →∞→∞

Critical Condition for Strong Barrier Critical Condition for Strong Barrier Coverage Coverage

Theorem1. Theorem1. Consider a sensor network deployConsider a sensor network deployed on a two-dimensional rectangular area ed on a two-dimensional rectangular area AA2-dim 2-dim

stripstrip=[0,=[0,nn] ] × × [0, [0, ww((nn)], where sensors are distrib)], where sensors are distributed according to a Poisson point process with uted according to a Poisson point process with density density λλ

n

w(n)

The density :λ

Critical Conditions for Strong Barrier Critical Conditions for Strong Barrier CoverageCoverage

If If ww((nn) = ) = ΩΩ( log ( log nn), the network is strongly bar), the network is strongly barrier covered w.h.p. when the sensor density rearier covered w.h.p. when the sensor density reaches a certain value. There exists a positive coches a certain value. There exists a positive constant nstant ββ such that w.h.p. there exist such that w.h.p. there exist ββw(nw(n) disj) disjoint horizontal sensor barriers crossing the strioint horizontal sensor barriers crossing the strip.p.

Critical Conditions for Strong Critical Conditions for Strong Barrier CoverageBarrier Coverage

If If ww((nn) = ) = oo(log (log nn), the network has no strong b), the network has no strong barrier coverage w.h.p. regardless what the sensarrier coverage w.h.p. regardless what the sensor density is in the underlying sensor network. or density is in the underlying sensor network. That is, w.h.p. there exist crossing paths that aThat is, w.h.p. there exist crossing paths that an intruder can cross the strip without being detn intruder can cross the strip without being detected.ected.

Constructing BarriersConstructing Barriers Typical wireless sensors are powered by Typical wireless sensors are powered by

conventional batteriesconventional batteries, and they are , and they are energy energy stringentstringent

Important IssueImportant Issue Scheduling sensors so that at Scheduling sensors so that at any given momentany given moment

there are just there are just enoughenough active sensors to active sensors to cover the cover the barrierbarrier

[6] shows that whether a sensor network is [6] shows that whether a sensor network is strongly k-barrier covered strongly k-barrier covered cannotcannot be determined be determined using using local algorithmslocal algorithms..

Constructing BarriersConstructing Barriers

Vertical Strip and SegmentVertical Strip and Segment

Constructing BarriersConstructing Barriers

Selecting a sensor to be Selecting a sensor to be delegatedelegate Collecting the location information of the Collecting the location information of the

strip or segment by broadcastingstrip or segment by broadcasting Convert sensor network to flow networkConvert sensor network to flow network

For any two vertices For any two vertices uu and and vv in V, if their in V, if their sensing area overlap, connect them with an sensing area overlap, connect them with an edge capacity of 1.edge capacity of 1.

Add node Add node ss and and dd to the flow network to the flow network

Constructing BarriersConstructing Barriers

The Flow NetworkThe Flow Network

Constructing BarriersConstructing Barriers

Constructing BarriersConstructing Barriers Divide-and Conquer AlgorithmDivide-and Conquer Algorithm

1.1. Divide the given strip into small segments interleaveDivide the given strip into small segments interleaved by thin vertical stripsd by thin vertical strips

2.2. In each vertical strip, sensor nodes use In each vertical strip, sensor nodes use ComputeBarrComputeBarrierier to find al of the disjoint vertical barriers and the h to find al of the disjoint vertical barriers and the horizontal barriers that connect the vertical barrier togorizontal barriers that connect the vertical barrier together.ether.

3.3. For each strip segment, use For each strip segment, use ComputeBarriersComputeBarriers to find to find disjoint horizontal barriers intersecting the vertical bdisjoint horizontal barriers intersecting the vertical barriers on both ends of the segmentarriers on both ends of the segment

ComputeBarriersComputeBarriers Contributions Contributions

Lower Communication Overhead and Lower Communication Overhead and computation costscomputation costs

Improved robustness of the barrier Improved robustness of the barrier coveragecoverage

Strengthened local barrier coverageStrengthened local barrier coverage

Performance EvaluationPerformance Evaluation

The network of size The network of size ll × × ww according to a tw according to a two-dimensional Poisson point process of deo-dimensional Poisson point process of densityλ.nsityλ.

The simulation is repeated 500 times.The simulation is repeated 500 times. l l =10,000 meters =10,000 meters Sensing range r = 10 metersSensing range r = 10 meters

Condition for Strong Barrier CoverageCondition for Strong Barrier Coverage

Strengthened Local Barrier CoverageStrengthened Local Barrier Coverage• Ten segments

•20m to 350m

•Three kinds of density

•Barrier improvement ratio: the number of horizontal barriers in each segment / the number of global barriers for the whole strip

Strengthened Local Barrier CoverageStrengthened Local Barrier Coverage

ConclusionsConclusions

Theoretical foundations and practical Theoretical foundations and practical algorithmalgorithm

Below the critical width to length ration, Below the critical width to length ration, there is n strong barrier coveragethere is n strong barrier coverage

Based on this result, they further devise an Based on this result, they further devise an distributed algorithm to construct disjoint distributed algorithm to construct disjoint barriers with low delay, communication barriers with low delay, communication overhead, and computation cost.overhead, and computation cost.

The End The End