impact of mobility and heterogeneity on coverage and energy consumption in wireless sensor networks...

Impact of Mobility and Heterogeneity on Impact of Mobility and Heterogeneity on Coverage and Energy Consumption in Coverage and Energy Consumption in

Wireless Sensor NetworksWireless Sensor Networks

Xiao Wang, Xinbing Wang, Jun ZhaoDepartment of Electronic Engineering

Shanghai Jiao Tong University, Shanghai, China

Impact of Mobility and Heterogeneity on Coverage and Energy Consumption in Wireless Sensor Networks 2

OutlineOutline IntroductionIntroduction

BackgroundBackground Related worksRelated works MotivationsMotivations

System Model and Performance MeasuresSystem Model and Performance Measures

Main Results and Brief ExplanationMain Results and Brief Explanation

The Impact of Mobility and Heterogeneity The Impact of Mobility and Heterogeneity

Concluding RemarksConcluding Remarks

3

BackgroundBackground

Coverage is a basic concern in designing and implemen- Coverage is a basic concern in designing and implemen- ting wireless sensor networks. ting wireless sensor networks. Security surveillanceSecurity surveillance Intrusion detectionIntrusion detection Environment monitoring, etcEnvironment monitoring, etc

Efforts made for addressing coverage problems fall into Efforts made for addressing coverage problems fall into three main categories.three main categories. Blanket coverageBlanket coverage Barrier coverageBarrier coverage Sweep coverageSweep coverage

Impact of Mobility and Heterogeneity on Coverage and Energy Consumption in Wireless Sensor Networks

4

Related Works--IRelated Works--I

An unreliable wireless sensor grid network with An unreliable wireless sensor grid network with nn nodes: nodes:

The network remains covered if The network remains covered if

[1][1]

A random network in which the locations of nodes can be A random network in which the locations of nodes can be modeled as a stationary 2-dimensional Poisson point modeled as a stationary 2-dimensional Poisson point process:process:

The area coverage of the sensor network is The area coverage of the sensor network is

[2][2]


[1] S. Shakkottai, R. Srikant and N. Shroff, “Unreliable Sensor Grid: Coverage, Connectivity and[1] S. Shakkottai, R. Srikant and N. Shroff, “Unreliable Sensor Grid: Coverage, Connectivity and

Diameter,” INFOCOM, 2003.Diameter,” INFOCOM, 2003.

[2] B. Liu and D. Towsley, “A Study on the Coverage of Large-Scale Sensor Networks,” International[2] B. Liu and D. Towsley, “A Study on the Coverage of Large-Scale Sensor Networks,” International

Conference on Mobile Ad-hoc and Sensor Systems, 2004.Conference on Mobile Ad-hoc and Sensor Systems, 2004.

2 log( )( ) ( ) ~

np n r n

n

2

1 raf e

Related Works--IIRelated Works--II

K-coverage in a mostly sleeping wireless sensor networks:

For random uniform deployment, all points in the operational For random uniform deployment, all points in the operational

region are almost region are almost kk-covered if-covered if

for some .( goes to infinity as and for some .( goes to infinity as and

) [3]) [3]

[3] S. Kumar, T. H. Lai and J. Balogh, “On K-coverage in a Mostly Sleeping Sensor Networks,” [3] S. Kumar, T. H. Lai and J. Balogh, “On K-coverage in a Mostly Sleeping Sensor Networks,”

MobiCom, 2008.MobiCom, 2008.


2 log log( ) ( )1

log( ) log( )

np r k np np

np np

( )np ( )np n

( ) (log log( ))np o np

Related Works--IIIRelated Works--III

Dynamic coverage in mobile wireless sensor networks:

Consider a sensor network at time Consider a sensor network at time t=0t=0, with sensors moving , with sensors moving

according to random mobility model:according to random mobility model:

1. At any time instant 1. At any time instant tt, the fraction of area being covered is, the fraction of area being covered is

2. The fraction of are that has been covered at least once during 2. The fraction of are that has been covered at least once during

time interval time interval [0, t) [0, t) isis

[4][4] [4] B. Liu, P. Brass, O. Dousse, P. Nain and D. Towsley, “Mobility Improves Coverage of Sensor [4] B. Liu, P. Brass, O. Dousse, P. Nain and D. Towsley, “Mobility Improves Coverage of Sensor

Networks,” MobiHoc, 2005.Networks,” MobiHoc, 2005.


2

( ) 1 raf t e

2( 2 [ ] )( ) 1 ar rE V taf t e

7

MotivationMotivation

WSNs can achieve better balance between cove- WSNs can achieve better balance between coverage performance and the cost of sensors if opp- rage performance and the cost of sensors if opp- ortune degree of heterogeneity is incorporated in- ortune degree of heterogeneity is incorporated in- to the network.to the network.

Many applied WSNs are inherently mobile. Mobil- Many applied WSNs are inherently mobile. Mobil- ity is found to improve various aspects of network ity is found to improve various aspects of network performance.performance.

In previous works, usually the sufficient condition In previous works, usually the sufficient condition is obtained instead of the critical condition.is obtained instead of the critical condition.


8


System Models and Performance MeasuresSystem Models and Performance Measures Deployment SchemeDeployment Scheme Sensing StrategySensing Strategy Mobility PatternMobility Pattern Performance MeasuresPerformance Measures


The Impact of Mobility and HeterogeneityThe Impact of Mobility and Heterogeneity



9

Deployment SchemeDeployment Scheme

Let the operational region of the WSN be an unit square Let the operational region of the WSN be an unit square and the square is assumed to be a torus.and the square is assumed to be a torus.

Uniform Deployment Model --- Uniform Deployment Model --- nn sensors are randomly and unifor- sensors are randomly and uniformly deployed in the operational region, independent of each other.mly deployed in the operational region, independent of each other.

Poisson Deployment Model --- the locations of sensors are model- Poisson Deployment Model --- the locations of sensors are model-

ed as the ed as the 22-dimensional Poisson point process with density para- -dimensional Poisson point process with density para- meter meter nn..


10

Sensing StrategySensing Strategy

Basically, the binary disc sensing model is em- Basically, the binary disc sensing model is em- ployed in the study. Let ployed in the study. Let r denote the sensing r denote the sensing radius.radius.

There are There are uu groups in this heterog- groups in this heterogeneous network, eneous network, uu is a positive number invariant is a positive number invariant of of nn. Group consists of sensors with . Group consists of sensors with sensing radius .sensing radius .


1 2, , , uG G G

yG y yn c nyr

11

Mobility PatternMobility Pattern

I.I.D. Mobility ModelI.I.D. Mobility Model Reshuffle at the beginning of each time slot.Reshuffle at the beginning of each time slot.

1-Dimensional Random Walk 1-Dimensional Random Walk

Mobility ModelMobility Model Classified into Classified into HH-nodes and -nodes and VV-nodes;-nodes; Travel distance Travel distance DD along its dimension, along its dimension,

DD is a random variable uniformly is a random variable uniformly

distributed from distributed from 00 to to 11;;

2-Dimensional Random Walk Mobility Model2-Dimensional Random Walk Mobility Model Randomly and independently choose a direction ;Randomly and independently choose a direction ; Randomly and independently select a velocity .Randomly and independently select a velocity .


[0,2 )

max[0, ]v v

12

Performance Measures -- IPerformance Measures -- I

Asymptotic CoverageAsymptotic Coverage Equivalent Sensing Radius (ESR) under i.i.d. mobility model:Equivalent Sensing Radius (ESR) under i.i.d. mobility model:

ESR under 1-dimensional random walk mobility model:ESR under 1-dimensional random walk mobility model:

IfIf

then is the critical ESR under the i.i.d. model.then is the critical ESR under the i.i.d. model.


lim ( ) 1,if cr (n) for any c>1;

lim ( ) 1,if r (n) for any 0<c<1.n

n

P C r

P C r c

2

1( )

u

y yyr n c r

1( )

u

y yyr n c r

( )r n

13

Performance Measures -- IIPerformance Measures -- II

K-Coverage at an InstantK-Coverage at an Instant A point is said to be A point is said to be kk-covered at an instant -covered at an instant tt if it is sensed by at if it is sensed by at

least least kk sensors. sensors. Let denote the fraction of the whole region that is Let denote the fraction of the whole region that is kk-covered -covered

at instant at instant tt..

K-Coverage over a Time IntervalK-Coverage over a Time Interval A point is said to be A point is said to be kk-covered over a time interval -covered over a time interval TT if it has been if it has been

sensed by more than sensed by more than k k sensors at the end of that interval.sensors at the end of that interval. Let be the fraction of the whole region that is Let be the fraction of the whole region that is kk-covered -covered

during time interval during time interval TT..


( )t

( )T

14


System Models and Performance System Models and Performance

MeasuresMeasures

Main Results and Brief ExplanationMain Results and Brief Explanation Main resultsMain results Brief explanationBrief explanation

The Impact of Mobility and HeterogeneityThe Impact of Mobility and Heterogeneity



15

Main ResultsMain Results

Under the uniform deployment scheme:Under the uniform deployment scheme: With i.i.d. mobility model, the critical ESR is With i.i.d. mobility model, the critical ESR is With 1-dimensional random walk mobility model, the critical ESR isWith 1-dimensional random walk mobility model, the critical ESR is

Under the Poisson deployment scheme with the Under the Poisson deployment scheme with the 2-dimensional random walk mobility model:2-dimensional random walk mobility model: , is the upper incomplete , is the upper incomplete

gamma function, defined asgamma function, defined as , where denotes the , where denotes the

expected area covered by a sensor.expected area covered by a sensor.


log log log( )

n nr n

n

3(log log log )( )

4

n nr n

n

2

1( )

( , ){ } 1

( 1)!

u

y yyt

k n c rE

k

( , )1( )

( , { }){ } 1

( 1)!

u

y T yyT

k n c E SE

k

( , )a b

1( , ) a t

ba b t e dt

( , ){ }T yE S

16

Brief Explanation – Dense GridBrief Explanation – Dense Grid

Dense grid:Dense grid:

Transform the coverage of all points within the operational Transform the coverage of all points within the operational

region to the coverage of certain set of points.region to the coverage of certain set of points.


log

m m

m n n

17

Brief Explanation – Necessary PartBrief Explanation – Necessary Part

Proposition 1: In the WSNs with i.i.d. mobility model, if Proposition 1: In the WSNs with i.i.d. mobility model, if

and the density of the dense grid is and the density of the dense grid is

, then, then

where .where .

proofproof: :

Therefore, is necessary for the WSN to Therefore, is necessary for the WSN to achieve full coverage of the dense grid. achieve full coverage of the dense grid.


log log log ( )( )

n n nr n

n

logm n n2liminf ( )n P G e e

lim ( )n n

log log log( )

n nr n

n

i,

( ) ({P is not covered}) ({ and are not covered})i i j

i jP M P P M

P G P P P P

18

Brief Explanation – Sufficient PartBrief Explanation – Sufficient Part

If where , thenIf where , then

is sufficient to guarantee the full is sufficient to guarantee the full coverage of the dense grid. coverage of the dense grid.


( )r cr n 1c

log log log( )

n nr n

n

19

Brief Explanation – Failure PrBrief Explanation – Failure Pr

Under the 1-dimensional random walk mobility model:Under the 1-dimensional random walk mobility model:


20



MeasuresMeasures


The Impact of Mobility and Heterogeneity The Impact of Mobility and Heterogeneity Impact of MobilityImpact of Mobility Impact of HeterogeneityImpact of Heterogeneity



21

Impact of MobilityImpact of Mobility

We use the sensing energy model as .We use the sensing energy model as .

The average energy consumption of the mobile The average energy consumption of the mobile heterogeneous WSN is . heterogeneous WSN is .

Assume the network to be homogeneous and evaluate the Assume the network to be homogeneous and evaluate the impact of mobility:impact of mobility: Under i.i.d. mobility model or the network is stationary:Under i.i.d. mobility model or the network is stationary:

Under 1-dimensional random walk mobility model:Under 1-dimensional random walk mobility model:

Impact Impact


2y yE r

. . .

log log logi i d

n nE

n

2

. .

log log logr w

n nE

n

2

1

u

y yyE c r

. .log log log

r w statn n

E En

22

Impact of HeterogeneityImpact of Heterogeneity

Sensing Energy ConsumptionSensing Energy Consumption Under Under i.i.d. i.i.d. mobility model:mobility model:

Under Under 1-dimensional random walk 1-dimensional random walk mobility model:mobility model:

( , )( , )


. . .log log log

i i dn n

En

2

. .log log log

r wn n

En

3/2

. . 2

log log logr w

n nE

n

2

2

1 1 1

u u u

y y y y yy y y

c c r c r

0

3/21/2

2

1 1

1u u

y y y y dy y

c r c rn

23



MeasuresMeasures


The Impact of Mobility and The Impact of Mobility and

HeterogeneityHeterogeneity

Concluding RemarksConcluding RemarksImpact of Mobility and Heterogeneity on Coverage and Energy Consumption in Wireless Sensor Networks

24


Asymptotic coverage under uniform deployment scheme Asymptotic coverage under uniform deployment scheme with i.i.d. and 1-dimensional random walk mobility model.with i.i.d. and 1-dimensional random walk mobility model.

Impact of mobility and heterogeneity on sensing energy Impact of mobility and heterogeneity on sensing energy consumption.consumption.

The k-coverage under Poisson deployment scheme with 2-The k-coverage under Poisson deployment scheme with 2-dimensional random walk mobility model.dimensional random walk mobility model.


Questions?Questions?

Thanks for listening !Thanks for listening !

impact of mobility and heterogeneity on coverage and energy consumption in wireless sensor networks...

Documents

coverage of sensor networks

coverage impact of mobility

background coverage

area coverage

sensor systems

dynamic coverage

coverage problems

unreliable sensor grid