Impact of Mobility and Heterogeneity on
Coverage and Energy Consumption in
Wireless Sensor Networks
Xiao Wang, Xinbing Wang, Jun Zhao
Department of Electronic Engineering
Shanghai Jiao Tong University, Shanghai, China
Outline
 Introduction
 Background
 Related works
 Motivations
 System Model and Performance Measures
 Main Results and Brief Explanation
 The Impact of Mobility and Heterogeneity
 Concluding Remarks
Impact of Mobility and Heterogeneity on Coverage and Energy Consumption in Wireless Sensor Networks
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Background
 Coverage is a basic concern in designing and implementing wireless sensor networks.
 Security surveillance
 Intrusion detection
 Environment monitoring, etc
 Efforts made for addressing coverage problems fall into
three main categories.
 Blanket coverage
 Barrier coverage
 Sweep coverage
Impact of Mobility and Heterogeneity on Coverage and Energy Consumption in Wireless Sensor Networks
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Related Works--I
 An unreliable wireless sensor grid network with n nodes:
 The network remains covered if
p ( n) r 2 ( n) ~
log( n)
n
[1]
 A random network in which the locations of nodes can be
modeled as a stationary 2-dimensional Poisson point
process:
 The area coverage of the sensor network is
fa  1  e
  r 2
[2]
[1] S. Shakkottai, R. Srikant and N. Shroff, “Unreliable Sensor Grid: Coverage, Connectivity and
Diameter,” INFOCOM, 2003.
[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.
Impact of Mobility and Heterogeneity on Coverage and Energy Consumption in Wireless Sensor Networks
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Related Works--II
K-coverage in a mostly sleeping wireless sensor
networks:
 For random uniform deployment, all points in the operational
region are almost k-covered if
np r 2
k log log(np)   (np)
 1
log(np)
log(np)
for some
 (np) .(  (np) goes to infinity as n  and
 (np)  o(log log(np))
)
[3]
[3] S. Kumar, T. H. Lai and J. Balogh, “On K-coverage in a Mostly Sleeping Sensor Networks,”
MobiCom, 2008.
Impact of Mobility and Heterogeneity on Coverage and Energy Consumption in Wireless Sensor Networks
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Related Works--III
Dynamic coverage in mobile wireless sensor
networks:
 Consider a sensor network at time t=0, with sensors moving
according to random mobility model:
1. At any time instant t, the fraction of area being covered is
f a (t )  1  e
  r 2
2. The fraction of are that has been covered at least once during
time interval [0, t) is
f a (t )  1  e
  ( r 2  2 rE [Va ]t )
[4]
[4] B. Liu, P. Brass, O. Dousse, P. Nain and D. Towsley, “Mobility Improves Coverage of Sensor
Networks,” MobiHoc, 2005.
Impact of Mobility and Heterogeneity on Coverage and Energy Consumption in Wireless Sensor Networks
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Motivation
WSNs can achieve better balance between coverage performance and the cost of sensors if opportune degree of heterogeneity is incorporated into the network.
Many applied WSNs are inherently mobile. Mobility is found to improve various aspects of network
performance.
In previous works, usually the sufficient condition
is obtained instead of the critical condition.
Impact of Mobility and Heterogeneity on Coverage and Energy Consumption in Wireless Sensor Networks
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Outline
Introduction
System Models and Performance Measures
 Deployment Scheme
 Sensing Strategy
 Mobility Pattern
 Performance Measures
Main Results and Brief Explanation
The Impact of Mobility and Heterogeneity
Concluding Remarks
Impact of Mobility and Heterogeneity on Coverage and Energy Consumption in Wireless Sensor Networks
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Deployment Scheme
 Let the operational region of the WSN be an unit square
and the square is assumed to be a torus.
 Uniform Deployment Model --- n sensors are randomly and uniformly deployed in the operational region, independent of each other.
 Poisson Deployment Model --- the locations of sensors are modeled as the 2-dimensional Poisson point process with density parameter n.
Impact of Mobility and Heterogeneity on Coverage and Energy Consumption in Wireless Sensor Networks
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Sensing Strategy
Basically, the binary disc sensing model is employed in the study. Let r denote the sensing
radius.
There are u groups G1, G2 , , Gu in this heterogeneous network, u is a positive number invariant
of n. Group Gy consists of ny  cy n sensors with
sensing radius ry .
Impact of Mobility and Heterogeneity on Coverage and Energy Consumption in Wireless Sensor Networks
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Mobility Pattern
 I.I.D. Mobility Model
 Reshuffle at the beginning of each time slot.
 1-Dimensional Random Walk
Mobility Model
 Classified into H-nodes and V-nodes;
 Travel distance D along its dimension,
D is a random variable uniformly
distributed from 0 to 1;
 2-Dimensional Random Walk Mobility Model
 Randomly and independently choose a direction   [0, 2 ) ;
 Randomly and independently select a velocity v [0, vmax ] .
Impact of Mobility and Heterogeneity on Coverage and Energy Consumption in Wireless Sensor Networks
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Performance Measures -- I
 Asymptotic Coverage
 Equivalent Sensing Radius (ESR) under i.i.d. mobility model:
r (n) 

u
y 1
c y ry2
 ESR under 1-dimensional random walk mobility model:
u
r (n) 
cr
y 1 y y
 If

limn P(C )  1,if r  cr (n) for any c>1;
limn P(C )  1,if r  cr (n) for any 0<c<1.
then r (n) is the critical ESR under the i.i.d. model.
Impact of Mobility and Heterogeneity on Coverage and Energy Consumption in Wireless Sensor Networks
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Performance Measures -- II
K-Coverage at an Instant
 A point is said to be k-covered at an instant t if it is sensed by at
least k sensors.
 Let (t ) denote the fraction of the whole region that is k-covered
at instant t.
K-Coverage over a Time Interval
 A point is said to be k-covered over a time interval T if it has been
sensed by more than k sensors at the end of that interval.
 Let (T ) be the fraction of the whole region that is k-covered
during time interval T.
Impact of Mobility and Heterogeneity on Coverage and Energy Consumption in Wireless Sensor Networks
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Outline
Introduction
System Models and Performance Measures
Main Results and Brief Explanation
 Main results
 Brief explanation
The Impact of Mobility and Heterogeneity
Concluding Remarks
Impact of Mobility and Heterogeneity on Coverage and Energy Consumption in Wireless Sensor Networks
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Main Results
 Under the uniform deployment scheme:
r (n) 
log n  log log n
n
 With i.i.d. mobility model, the critical ESR is
 With 1-dimensional random walk mobility model, the critical ESR is
3(log n  log log n)
r (n) 
4n
 Under the Poisson deployment scheme with the
2-dimensional randomu walk mobility model:
2

(
k
,

n
c
r
) ,(a, b) is the upper incomplete


y 1 y y
E{(t ) }  1 
(k  1)!

a 1  t
gamma function, defined as (a, b)  b t e dt

(k , n y 1 c y E{S(T , y ) }) , where E{S(T , y ) }denotes the
u
E{(T ) }  1 
(k  1)!
expected area covered by a sensor.
Impact of Mobility and Heterogeneity on Coverage and Energy Consumption in Wireless Sensor Networks
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Brief Explanation – Dense Grid
 Dense grid:
Transform the coverage of all points within the operational
region to the coverage of certain set of points.
m m
m  n log n
Impact of Mobility and Heterogeneity on Coverage and Energy Consumption in Wireless Sensor Networks
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Brief Explanation – Necessary Part
 Proposition 1: In the WSNs with i.i.d. mobility model, if
log n  log log n   (n)
r (n) 
and the density of the dense grid is
n
m  n log n , then
liminfn P(G)  e  e2
where   limn  (n) .
proof:
P(G) 
 P({P is not covered})  
i
Pi M

Therefore, r (n) 
P({Pi and Pj are not covered})
Pi , Pj M
log n  log log n
n
is necessary for the WSN to
achieve full coverage of the dense grid.
Impact of Mobility and Heterogeneity on Coverage and Energy Consumption in Wireless Sensor Networks
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Brief Explanation – Sufficient Part
 If r  cr (n) where c  1

r (n) 
, then
log n  log log n
n
is sufficient to guarantee the full
coverage of the dense grid.
Impact of Mobility and Heterogeneity on Coverage and Energy Consumption in Wireless Sensor Networks
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Brief Explanation – Failure Pr
 Under the 1-dimensional random walk mobility model:
Impact of Mobility and Heterogeneity on Coverage and Energy Consumption in Wireless Sensor Networks
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Outline
Introduction
System Models and Performance Measures
Main Results and Brief Explanation
The Impact of Mobility and Heterogeneity
 Impact of Mobility
 Impact of Heterogeneity
Concluding Remarks
Impact of Mobility and Heterogeneity on Coverage and Energy Consumption in Wireless Sensor Networks
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Impact of Mobility
 We use the sensing energy model as Ey  ry2 .
The average energy consumption of the mobile
u
heterogeneous WSN is E   y 1 c y ry2 .
 Assume the network to be homogeneous and evaluate the
impact of mobility:
 Under i.i.d. mobility model or the network is stationary:
Ei.i.d .
 log n  log log n 
 

n


 Under 1-dimensional random walk mobility model:
Er .w.
 Impact
  log n  log log n 2 
 
 

n
 

 log n  log log n 
Er .w.   
  Estat
n


Impact of Mobility and Heterogeneity on Coverage and Energy Consumption in Wireless Sensor Networks
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Impact of Heterogeneity
 Sensing Energy Consumption
 Under i.i.d. mobility model:
 log n  log log n 
Ei.i.d .   

n


 Under 1-dimensional random walk mobility model:
  log n  log log n 2 
Er .w.    
 

n
 

  log n  log log n 3/2 

Er .w.   
2


n




 
(  c  c r 2   
 y 1 y  y 1 y y  


 
u

u

2
 
  u
2
cy ry  ,  cy ry   
 
  y 1
y 1
 
 
u


3/2

c y ry 

y 1

u

1/2
 1 
 d0 
n 
Impact of Mobility and Heterogeneity on Coverage and Energy Consumption in Wireless Sensor Networks
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Outline
Introduction
System Models and Performance Measures
Main Results and Brief Explanation
The Impact of Mobility and Heterogeneity
Concluding Remarks
Impact of Mobility and Heterogeneity on Coverage and Energy Consumption in Wireless Sensor Networks
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Concluding Remarks
 Asymptotic coverage under uniform deployment scheme
with i.i.d. and 1-dimensional random walk mobility model.
 Impact of mobility and heterogeneity on sensing energy
consumption.
 The k-coverage under Poisson deployment scheme with 2dimensional random walk mobility model.
Impact of Mobility and Heterogeneity on Coverage and Energy Consumption in Wireless Sensor Networks
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Questions?
Thanks for listening !