Optimizing the Number of Clusters in a Wireless ... - Semantic Scholar
Optimizing the Number of Clusters in a Wireless Sensor Network Using Cross-layer Analysis Li-Chun Wang∗ , Chuan-Ming Liu+ , and Chung-Wei Wang∗ ∗ +
National Chiao Tung University, Taiwan
National Taipei University of Technology (NTUT), Taiwan Email : [email protected]
its required transmission power when optimizing the
Abstract— This paper aims to determine the optimal number of clusters in an observation area for
number of clusters.
a wireless sensor network. We demonstrate that
In this paper, we apply a cross-layer analysis [3] to
this goal can be achieved by a cross-layer approach
determine the optimal number of clusters for a wireless
from both perspectives of the power efficiency in the medium access control (MAC) layer and the
sensor network. We first provide a scheduling policy
coverage performance in the physical (PHY) layer.
to select the cluster head. Then, we determine the optimal number of clusters from the cross-layer view point that integrates the physical, MAC, and network
Index Terms— Wireless Sensor Networks, Cluster, Cross-Layer Design, Energy Saving.
layers. II. P OW ER2 MAC Scheduling Policy and
I. Introduction
Problem Formulation One key parameter in designing a sensor network is the number of clusters [1], [2]. Intuitively, fewer
We provide a P OW ER2 (Power On With Elected
clusters lower the probability of each sensor node being
Representative node in a Round-robin fashion) scheduling policy to select the cluster representative
the cluster representative and result in less power
node based on the sensing resolution. The goal of
consumption. By contrast, more clusters decrease the
the P OW ER2 scheduling policy is to select a repre-
required transmission power for each cluster head due
sentative node in each cluster to sense the coverage
to a smaller coverage area. Hence, there exists a trade-
area of the cluster. The sensor nodes other than the
off between the frequency of being a cluster head and
representative node will enter the OFF-state in order The work was supported jointly by the National Science Coun-
to save energy. Fig. 1 illustrates the difference of
cil and the MOE program for promoting university excellence
the conventional non-scheduling and the P OW ER2
under the contracts EX-91-E-FA06-4-4, 93-2219-E009-012, and
scheduling cases.
93-2213-E009-097.
1
0-7803-8815-1/04/$20.00 ©2004 IEEE
585
ON-state
#1
ON-state
ON-state
ON-state ON-state 1 2
ON-state
ON-state ON-state N 1 N sensor
cluster
#2
ON-state ON-state 1 2
ON-state N sensor
N cluster
t
ON-state 1 t
OA(2,3) #
Nsensor ON-state ON-state Ncluster 1 2
K=4
ON-state ON-state N 1 sensor
N cluster
t
OA(1,1)
OA(1,2)
OA(1,3)
OA(1,4)
OA(2,1)
OA(2,2)
OA(2,3)
OA(2,4)
OA(3,1)
OA(3,2)
OA(3,3)
OA(3,4)
OA(4,2)
OA(4,3)
(a)
Listen-window
#1
#2
ON-state 1
ON-state 2
OFF-state
#
ON-state 1
OFF-state
Nsensor Ncluster OFF-state
t
OFF-state
sRP
OA(4,1)
d OA
t
OA(4,4)
ON-state OFF-state
N sensor N cluster
OFF-state
Fig. 2.
t
Sensor network topology. (K = 4)
sRP
of clusters, G the constant related to the antenna
(b) Fig. 1.
gain and antenna height, Preq the required received
The timing diagram of (a) non-scheduling policy and
signal power level to the next hop, and n the path loss
(b) P OW ER2 scheduling policy in each cluster in each sRP.
exponent. Suppose there are Nsensor sensor nodes in a re-
As seen in (1), the value of K can impact the energy
gion which is partitioned into NOA observation areas.
consumption in two different manners. Consider K is
Assume that the number of sensor nodes is higher
decreasing. On one hand, the energy consumption is
than NOA . The energy minimization problem is
reduced because the frequency of being the represen-
to determine the optimal number of clusters, Kopt , in
tative node becomes lower for a large-sized cluster. On
an observation area. The topology of a sensor network
the other hand, the energy consumption is also in-
with clusters is shown in Fig. 2
creasing because the transmission distance is enlarged for a large-sized cluster. Thus the optimal number of hop clusters in an observation area Kopt can be written as
III. Physical Layer Aspect The consumed energy in a sensor node using the
hop =[ Kopt
P OW ER2 scheduling policy can be expressed as NOA × K × TRx ] Nsensor 1 dOA + [Pelec + × ( √ )n ] Preq /G K NOA × K ×[ × TT x ] , Nsensor
( n2 − 1) × γ ( 2 ) ] n , α+β
(2)
where α = Pelec × TRx , β = Pelec × TT x , and γ =
Ehop (K) = Pelec × [
Pamp × TT x =
(dOA )n C
× TT x .
Figure 3 illustrates the impact of the number of hop clusters within an observation area (denoted as Kopt )
(1)
on the energy consumption for a sensor network using
where Pelec is the transmit power, TRx the receiving
the P OW ER2 scheduling policy (denoted as Ehop ). As
interval, TT x is the transmission interval, dOA the
shown in the figure, when the value of K is small, the
distance between two observation areas, K the number
transmission mode dominates the energy consumption. 2
586
0.1
The energy consumption per sensor node of multiple hop routing in different K and n without shadowing
0.06
Energy consumption per sensor node using the POWER schedule (unit:mJoule)
0.05 n=3 n=4 n=5
0.04
0.03
0.02
0.01
0.09
0.08 n=3 n=4 n=5
0.07
0.06
0.05
0.04
0.03
0.02
Kopt−flow K
0.01
opt−flow
K 0
0
5
10
15
20
25
30
35
0
40
opt−flow
0
5
10
K (the number of cluster in an OA)
15
20
25
30
35
40
K (the number of cluster in an OA)
Fig. 3. Energy consumption per sensor node in different K and
Fig. 4.
n without shadowing where TT x = TRx = 1 second, Pelec =
hop routing in different K and n without shadowing where
The energy consumption per sensor node of multiple
−8.67dBm, C = 2300 metern /mW , and dOA = 10 meter.
TT X−P LS = TRX−P LS = 1 second, Pelec = −8.67dBm, C = 2300 metern /mW , and dOA = 10 meter.
Thus one can see that Ehop decreases as the value account the tradeoff of energy consumption and hop
hop , the of K increases. When K is larger than Kopt
counts. Figure 4 illustrates the impact of the number
receiving mode dominates Ehop . Thus, Ehop increases
of clusters within an observation area on the energy
hop , a sensor as the value of K increases. When K > Kopt
consumption using the P OW ER2 scheduling policy.
network with clusters in an observation area can collect more information at the cost of consuming more power.
V. Conclusions Hence, it is important to choose a suitable value for In this paper, we have provided a cross-layer ap-
K according to different applications. For example, to
proach to determine the optimal number of clusters in
get better quality, it had better choose a large value
an observation area from the perspectives of physical
of K to enhance the sensing resolution, whereas if the
layer, medium access control sub-layer, cluster sub-
energy is the major concern, one may select a smaller
layer, and network layer.
value of K.
References IV. Network Layer Aspect [1] W.
Now we express the energy consumption considering
Heinzelman
application-specific
h(K)-hop routing for each sensor node as
and
H.
B.
protocol
A.
Chandrakasan,
architecture
for
“An
wireless
microsensor networks,” IEEE Transactions on Wireless
Communications, vol. 1, no. 4, pp. 660–670, October 2002. NOA × K × TRx ]+ [2] E. J. Duarte-Melo and M. Liu, “Analysis of energy consumpNsensor tion and lifetime of heterogeneous wireless sensor networks,” 1 NOA × K dOA [Pelec + × ( √ )n ] × [ × TT x ]} Proceedings of IEEE Global Telecommunications Conference C Nsensor K NOA × K , November 2002. × TT x ] . (3) − Pelec × [ Nsensor [3] S. Shakkottai, T. Rappaport, and P. Karlsson, “Cross layer
Eroute (K) = h(K) × {Pelec × [
design for wireless networks,” IEEE Communications Mag-
A small value of K yields fewer hop counts and larger
azine, pp. 74–80, October 2003.
energy consumption, and vice versa. Hence, an optimal number of clusters can also be obtained by taking into 3
587
National Chiao Tung University, Taiwan
National Taipei University of Technology (NTUT), Taiwan Email : [email protected]
its required transmission power when optimizing the
Abstract— This paper aims to determine the optimal number of clusters in an observation area for
number of clusters.
a wireless sensor network. We demonstrate that
In this paper, we apply a cross-layer analysis [3] to
this goal can be achieved by a cross-layer approach
determine the optimal number of clusters for a wireless
from both perspectives of the power efficiency in the medium access control (MAC) layer and the
sensor network. We first provide a scheduling policy
coverage performance in the physical (PHY) layer.
to select the cluster head. Then, we determine the optimal number of clusters from the cross-layer view point that integrates the physical, MAC, and network
Index Terms— Wireless Sensor Networks, Cluster, Cross-Layer Design, Energy Saving.
layers. II. P OW ER2 MAC Scheduling Policy and
I. Introduction
Problem Formulation One key parameter in designing a sensor network is the number of clusters [1], [2]. Intuitively, fewer
We provide a P OW ER2 (Power On With Elected
clusters lower the probability of each sensor node being
Representative node in a Round-robin fashion) scheduling policy to select the cluster representative
the cluster representative and result in less power
node based on the sensing resolution. The goal of
consumption. By contrast, more clusters decrease the
the P OW ER2 scheduling policy is to select a repre-
required transmission power for each cluster head due
sentative node in each cluster to sense the coverage
to a smaller coverage area. Hence, there exists a trade-
area of the cluster. The sensor nodes other than the
off between the frequency of being a cluster head and
representative node will enter the OFF-state in order The work was supported jointly by the National Science Coun-
to save energy. Fig. 1 illustrates the difference of
cil and the MOE program for promoting university excellence
the conventional non-scheduling and the P OW ER2
under the contracts EX-91-E-FA06-4-4, 93-2219-E009-012, and
scheduling cases.
93-2213-E009-097.
1
0-7803-8815-1/04/$20.00 ©2004 IEEE
585
ON-state
#1
ON-state
ON-state
ON-state ON-state 1 2
ON-state
ON-state ON-state N 1 N sensor
cluster
#2
ON-state ON-state 1 2
ON-state N sensor
N cluster
t
ON-state 1 t
OA(2,3) #
Nsensor ON-state ON-state Ncluster 1 2
K=4
ON-state ON-state N 1 sensor
N cluster
t
OA(1,1)
OA(1,2)
OA(1,3)
OA(1,4)
OA(2,1)
OA(2,2)
OA(2,3)
OA(2,4)
OA(3,1)
OA(3,2)
OA(3,3)
OA(3,4)
OA(4,2)
OA(4,3)
(a)
Listen-window
#1
#2
ON-state 1
ON-state 2
OFF-state
#
ON-state 1
OFF-state
Nsensor Ncluster OFF-state
t
OFF-state
sRP
OA(4,1)
d OA
t
OA(4,4)
ON-state OFF-state
N sensor N cluster
OFF-state
Fig. 2.
t
Sensor network topology. (K = 4)
sRP
of clusters, G the constant related to the antenna
(b) Fig. 1.
gain and antenna height, Preq the required received
The timing diagram of (a) non-scheduling policy and
signal power level to the next hop, and n the path loss
(b) P OW ER2 scheduling policy in each cluster in each sRP.
exponent. Suppose there are Nsensor sensor nodes in a re-
As seen in (1), the value of K can impact the energy
gion which is partitioned into NOA observation areas.
consumption in two different manners. Consider K is
Assume that the number of sensor nodes is higher
decreasing. On one hand, the energy consumption is
than NOA . The energy minimization problem is
reduced because the frequency of being the represen-
to determine the optimal number of clusters, Kopt , in
tative node becomes lower for a large-sized cluster. On
an observation area. The topology of a sensor network
the other hand, the energy consumption is also in-
with clusters is shown in Fig. 2
creasing because the transmission distance is enlarged for a large-sized cluster. Thus the optimal number of hop clusters in an observation area Kopt can be written as
III. Physical Layer Aspect The consumed energy in a sensor node using the
hop =[ Kopt
P OW ER2 scheduling policy can be expressed as NOA × K × TRx ] Nsensor 1 dOA + [Pelec + × ( √ )n ] Preq /G K NOA × K ×[ × TT x ] , Nsensor
( n2 − 1) × γ ( 2 ) ] n , α+β
(2)
where α = Pelec × TRx , β = Pelec × TT x , and γ =
Ehop (K) = Pelec × [
Pamp × TT x =
(dOA )n C
× TT x .
Figure 3 illustrates the impact of the number of hop clusters within an observation area (denoted as Kopt )
(1)
on the energy consumption for a sensor network using
where Pelec is the transmit power, TRx the receiving
the P OW ER2 scheduling policy (denoted as Ehop ). As
interval, TT x is the transmission interval, dOA the
shown in the figure, when the value of K is small, the
distance between two observation areas, K the number
transmission mode dominates the energy consumption. 2
586
0.1
The energy consumption per sensor node of multiple hop routing in different K and n without shadowing
0.06
Energy consumption per sensor node using the POWER schedule (unit:mJoule)
0.05 n=3 n=4 n=5
0.04
0.03
0.02
0.01
0.09
0.08 n=3 n=4 n=5
0.07
0.06
0.05
0.04
0.03
0.02
Kopt−flow K
0.01
opt−flow
K 0
0
5
10
15
20
25
30
35
0
40
opt−flow
0
5
10
K (the number of cluster in an OA)
15
20
25
30
35
40
K (the number of cluster in an OA)
Fig. 3. Energy consumption per sensor node in different K and
Fig. 4.
n without shadowing where TT x = TRx = 1 second, Pelec =
hop routing in different K and n without shadowing where
The energy consumption per sensor node of multiple
−8.67dBm, C = 2300 metern /mW , and dOA = 10 meter.
TT X−P LS = TRX−P LS = 1 second, Pelec = −8.67dBm, C = 2300 metern /mW , and dOA = 10 meter.
Thus one can see that Ehop decreases as the value account the tradeoff of energy consumption and hop
hop , the of K increases. When K is larger than Kopt
counts. Figure 4 illustrates the impact of the number
receiving mode dominates Ehop . Thus, Ehop increases
of clusters within an observation area on the energy
hop , a sensor as the value of K increases. When K > Kopt
consumption using the P OW ER2 scheduling policy.
network with clusters in an observation area can collect more information at the cost of consuming more power.
V. Conclusions Hence, it is important to choose a suitable value for In this paper, we have provided a cross-layer ap-
K according to different applications. For example, to
proach to determine the optimal number of clusters in
get better quality, it had better choose a large value
an observation area from the perspectives of physical
of K to enhance the sensing resolution, whereas if the
layer, medium access control sub-layer, cluster sub-
energy is the major concern, one may select a smaller
layer, and network layer.
value of K.
References IV. Network Layer Aspect [1] W.
Now we express the energy consumption considering
Heinzelman
application-specific
h(K)-hop routing for each sensor node as
and
H.
B.
protocol
A.
Chandrakasan,
architecture
for
“An
wireless
microsensor networks,” IEEE Transactions on Wireless
Communications, vol. 1, no. 4, pp. 660–670, October 2002. NOA × K × TRx ]+ [2] E. J. Duarte-Melo and M. Liu, “Analysis of energy consumpNsensor tion and lifetime of heterogeneous wireless sensor networks,” 1 NOA × K dOA [Pelec + × ( √ )n ] × [ × TT x ]} Proceedings of IEEE Global Telecommunications Conference C Nsensor K NOA × K , November 2002. × TT x ] . (3) − Pelec × [ Nsensor [3] S. Shakkottai, T. Rappaport, and P. Karlsson, “Cross layer
Eroute (K) = h(K) × {Pelec × [
design for wireless networks,” IEEE Communications Mag-
A small value of K yields fewer hop counts and larger
azine, pp. 74–80, October 2003.
energy consumption, and vice versa. Hence, an optimal number of clusters can also be obtained by taking into 3
587
