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A novel approach for finding optimal number of
cluster head in wireless sensor network
Ravi RanjanBharti School of Telecommunication Technology
and Management
Indian Institute of Technology Delhi
Hauz Khas, New Delhi 110016 INDIA
Email: [email protected]
Subrat KarBharti School of Telecommunication Technology
and Management
Indian Institute of Technology Delhi
Hauz Khas, New Delhi 110016 INDIA
Email: [email protected]
AbstractProlonging life time is the most important
designingobjectives in wireless sensor networks (WSN). In WSN the
totalamount of energy is limited, how to make best use of the
limitedresource energy is a very important aspect in research of
WSN. Inthis paper we provide a method for determining the optimal
num-ber of cluster head for homogeneous sensor networks deployed
in
different scenario using a reasonable energy consumption
model.In the first scenario nodes are thrown randomly, which canbe
modeled using two-dimensional homogeneous spatial Poissonpoint
process. In the second scenario, nodes are deterministicallyplaced
along the grid. For these two scenario we calculate theaverage
energy spend in the network in each round according toLEACH
protocol for both single and multi-hop between clusterhead and sink
(base station) as a function of the probability of thenode to
become a cluster head. Then we find optimal probabilityof becoming
a cluster head hence the optimal number of clusterhead that would
lead to minimize the average energy spendsin the network for each
round. Simulation results shows thatoptimal probability of becoming
a cluster heads that leads tominimize energy dissipation in the
network is not only dependon the total number of nodes, but also
depends on area of thenetwork A, packet length L and processing
energy of nodes.
Index TermsWireless sensor networks (WSN), Cluster num-ber,
Stochastic geometry, Voronoi cell .
I. INTRODUCTION
Wireless Sensor Networks are dense networks of low cost,
wireless nodes with limited ability for signal processing
that
sense certain phenomena in the area of interest and report
their observations to certain base station for further
analysis.
Distributed sensor networks enable a variety of application
in
both civilian as well as military domains [1]. An important
application of sensor networks is surveillance of
battle-field
or sensitive borders of countries. A simple way to monitor
such areas is to deploy sensors. Deployment could either
bedeterministic, i.e., placing a node along grid points, or the
nodes could be deploying randomly. Because of sensor nodes
self-constraints (generally tiny size, low-energy supply,
weak
computation ability, etc.), it is challenging to develop a
scal-
able,robust, and long-lived sensor networks. Much research
effort has focused on this area which results in many new
technologies and methods to address these problems in recent
years. The combination of clustering and data-fusion is one
of the most effective approaches to construct the
large-scale
and energy-efficient data gathering sensor networks [2] [3].
Clustering topology is an important technology to prolong
the life-time of the network. LEACH [4] which is the first
clustering protocol has motivated the design of many other
protocols. It is a distributed algorithm for homogeneous
sensor
networks where each sensor elects itself as a cluster-headwith
some probability and cluster reconfiguration scheme is
used to balance the energy load. Cluster heads aggregate the
packets from there cluster members before forwarding them
to sink. By rotating the cluster head role uniformly among
all nodes, each node tends to expend the same energy over
the time. The LEACH allows only single hop cluster and
direct communication between CH to BS considering energy
consumption only in data collection and transmission. In our
proposed algorithm, the energy consumption is considered at
all phases - in the CH election, aggregation,data routing
and
maintenance. Further we consider two type of deployement
scenarios one is random deployment and other is grid de-
ployment and obtain optimal probability of node becominga
cluster head using resonable energy model.We obtained
numerical result for optimal cluster probability which shows
that optimal values for these scenario will not only depend
on total number of node that was cosidered by leach but also
depends on trasmission range, packet length, circuit
dissipation
energy, etc.
I I . SYSTEM MODEL
In this paper we study the WSN scenario for homogeneous
sensor network. We have considered sensor nodes deployed in
two ways. In the first scenario (which is more realistic)
nodes
located randomly on the plane according to a homogeneous
spatial Poisson point process. In the second scenario
nodesplaced deterministically along grid points. We consider that
all
nodes are quasi stationary and dispersed into an 2-D square
area of sizeA = a2. Hence, the total number of nodes in sucharea
is also a Poisson random variableNwith meanA, whereA= a2. Let us
consider that p is the probability that a sensornode becomes a
cluster head. Therefore, average number of
CH isnp, wherep is the total number of nodes in that area. Soin
case of random deployment 0=p and 1 = (1 p) arethe intensity of the
corresponding(independent) Poisson point
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process. In this case clustering leads to formation of
Voronoi
cells with CH being the nuclei of these cells. In the case
of
grid, 0 and 1 are simply the number of cluster heads andbasic
nodes. In this paper we use the same approach as given
in LEACH protocol, in which any node may become a cluster
head with some random probability and the node (not itself a
CH) join the cluster of the closest CH. After the network
will
form, CH aggregate all data collected from the member and
transmit the aggregated data to the base station (BS).
A. Node architectures and energy models
A wireless sensor node typically consists of the following
three parts: (a) Sensor component (b) Transceiver component
(c) Signal processing component. The following assumptions
have been made for each of these components:
For the sensor component: Sensor nodes are assumedto sense a
constant amount of information every round.
Energy consumed in sensing is Esense(L) = L, where is the power
consumed for sensing a bit of data and Lis length of information in
bits. In general, the value of
L is constant.
For transceiver component: A simple model for the radiohardware
energy consumption is used.
Etra(L, d) = L Eelec+
L fs d2; d < doL mp d4; ddo (1)
Erec(L, d) = L Eelec (2)wheredo =
(fs/mp)
For signal processing component: This component con-ducts data
fusion. The energy spent in aggregating ksteams of L bits row
information into a single streamis determined by
E{Aggr
}(k, L) = kL (3)
The main energy dissipation of each node includes
transmitter
(receiver) electronics and transmit amplifier. WSN
application
is extensive which leads to complicated network environment.
Many uncertain factors are possible which will affect the
energy dissipation of the network. So we will use reasonable
energy consumption model to balance the energy load of the
network.
From the Eq.1 the energy dissipation is depend upon size of
each cluster. If the area of the region is fixed, then the size
of
each cluster is determined by the number of CH.In our case
npis the number of CH so energy dissipation dependsp hencewe
have to find optimal value ofp that minimize total energy
dissipation in the network.
B. Connectivity and coverage
To provide sensing coverage of region and successful use
of multihop communication for sensor network the condition
for the network connectivity and the area coverage must be
ensured[6]. Let be the intensity of poisson process and pbe the
reliability probability of each node. The connectedness
probability of nodes and coverage of area is given as
follows:
Pconnected and region is covered1 (1/r)2 e2pr2 (4)
We assume that all nodes are reliable i.e. p=1 and that the
sensing range of nodes is r. In a network dimensioningproblem a
parameter() is provided such that the connectivityand coverage
probability be at least (1). Therefore, werequire
12pr2
log
1
r2
(5)
for all , >0 :+ 2= 1, We consider r2
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each CH as nuclei. We first find the expected number of
member nodes in a typical Voronoi cell associated with a
particular CH. We then find expected number of member
outside circle of radius r around a CH for the purpose offinding
average relaying load on a critical node. We follow the
approach used in to determine the expected number of member
associated with CH nodes. Let (1) denotes the sigmaalgebra
generated by the point process corresponding to the
CH nodes. Since member as well as CH nodes deployed using
a homogeneous point process, we can shift the origin to one
of the CH point and use Campbells theorem and Slivnyaks
theorem to compute the expected number of member node
in a typical Voronoi cell. Let 0 denotes the Voronoi
cellassociated with CH node located at origin , and {xi 0}denotes
the set of all the member points. Then, 1{xi0} isthe indicator
function which is one when a member node ilies in a cell 0. Let
E[Nv] be the expected member in cell0 where
E[Nv|N=n]E[N] =E[
{xi0
}
1{xi0}]
=E
E
{xi0}
1{xi0}|(1)
=
20
0
e1x2
0xdxd
The event that member point located at (x, ) belongs to
theVoronoi cell 0 is equivalent to the event that there is amember
point in a small area xdxd located at (x, ), andthere is no other
CH point in a circle of radius r around thatmember point. From
this, we get
E[Nv] =01
(9)
Using similar approach, we can find the expected number of
member node located within a distance ofr from CH node
asfollows:
E[Nv(r) = E[
{xi0}1{xi0,|xi|
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2) Multihop communication: For multi hop communication
the aggregated data will be relayed by the other CH. Now for
the connectivity of the inter-cluster overlay, the
transmission
range of the CHs should be at least two or more cluster
diameters. Here we have consider the homogeneous sensor
network hence the same radio range R = 4r [7]. Hence theaverage
distance between CHs and BS is h=
Di4r
.The total
amount of energy sent in the network can be calculated as:
E[c] = Ap + B (1 p) + C (1p)p + Dp(1 p)+Ep 12 + Fp(0.765np 1) +
G
(20)
whereA = Lctr(2nEelec+ 49mpna
4), B = Lctr(5nEelec) +Ldata(2Eelec), C = Lctr(
13fsa
2) + Ldata(16fsa
2),D = Lctr(n
2(Eelec + EDA)), E = (Lctr +Ldata)(
n(0.1.743fsa
2)), F = (Lctr+ Ldata)(nEelec) andG= Lctr(2nEDA+
13
fsa2) + Ldata(nEDA)
B. Grid deployed network
Now we consider network in which nodes are placed along
grid point with distance r between them. If all nodes
arereliable, this grid will trivially provide connectivity and
take
the following form:
= 1
r2 (21)
1) Direct communication: For this case we calculate the
total energy spent in the nework as
E[c] = Ap+B (1p)+C(1 p)p
+Dp(1p)+E (22)
where A = Lctr(n(3Eelec + 89
mpa4)) + Ldata(n(Eelec +
49
mpa4)), B = Lctr(5nEelec + Ldata(2nEelec), C =
Lctr(13
fsa2)+ Ldata(
16
fsa2),D = Lctr(n
2(Eelec+ EDA)))
and E= Lctr(2nEDA+ 13fsa2) + Ldata(nEDA)2) Multihop
communication: To calculate the energy dissi-
pation in multihop case we can consider the network as
spatial
coherence region called basic observation area[7].In[7], the
average number of hop counts is given as h =np2 with np
is even, andh=
np
2 (np1)+1np otherwise. So the total amount
of energy spent can be calculated as:
E[c] = Ap + B (1 p) + C (1p)p + Dp(1 p)+Ep 12 + Fp(np 1) + G
(23)
whereA = Lctr(2nEelec+ 49mpna
4), B = Lctr(5nEelec) +Ldata(2Eelec), C = Lctr(
1
3
fsa2) + Ldata(
1
6
fsa2), D =
Lctr(n2(Eelec+ EDA)), E = (Lctr+ Ldata)(n( 43fsa2)),F = (Lctr +
Ldata)(nEelec) and G = Lctr(2nEDA +13
fsa2) + Ldata(nEDA)
IV. SIMULATION RESULTS AND DISCUSSION
In this section, we verify the optimal probability obtained
by
stochastic geometry, for direct and multihop communication
in the random and grid scenario in section III into a square
area of length 100 m with 100 node. We found that at the
optimal probabilitypopt is the value at which the energy
costs
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.450.089
0.09
0.091
0.092
0.093
0.094
0.095
0.096
0.097
0.098
Probabilty of becoming a CH
Totalen
ergy
spentin
a
round
Fig. 1. Total energy spent versus the probability of becoming CH
for directcommunication for random deployement
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.40.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.1
0.11
Probability of becoming CH
Totalenergy
spentin
a
round
Fig. 2. Total energy spent versus the probability of becoming CH
for multi-hop communication for random deployement
in the system is minimum via simulation.The value ofp
cancomputed by numerical analysis. The simulation results shows
the total energy spent in a round is minimized at
probability
p= 0.5, 0.46for direct communication and p = 0.36, 0.32
formulti-hop communication for same area. We also observed
options value
Lctr 20bytesLdata 1000bytesEelec 50nj/bitEDA 50nj/bit/signalfs
10pj/bit/m
2
mp 0.0013pj/bit/m4
TABLE ISIMULATIONPARAMETER
that for same n if area will increase then it leads to
increaseinpopt which is constant for LEACH.
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0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.450.09
0.095
0.1
0.105
0.11
0.115
Probability of becoming a CH
Totalen
ergy
spentin
a
round
Fig. 3. Total energy spent versus the probability of becoming CH
for directcommunication for grid deployement
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.450
0.02
0.04
0.06
0.08
0.1
0.12
Probability of becoming CH
Totalenergy
spentin
a
round
Fig. 4. Total energy spent versus the probability of becoming CH
for multi-
hop communication for grid deployment
V. CONCLUSIONS
In this paper we try to find optimal probability of a node
to becoming a cluster head that leads to minimize the
overall
energy spent in the network for a more complex and general
scenario. We formulate the optimal way for determining
number of CH for different scenario with the objective of
guaranteed connectivity and minimizing the total energy
spent
in the system. We found that the optimal parameter values
for
these scenario and complex model will not only depend on nthat
was cosidered by leach but also depends on trasmission
range, packet length, circuit dissipation energy, etc.
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