Base Station Repositioning for Prolonging Wireless Sensor Networks Lifetime Nurul Adilah Abdul Latiff

R Badlishah Ahmad

Faculty of Science and Technology Universiti Malaysia Terengganu Kuala Terengganu, Malaysia [email protected]

School of Computer and Communication Engineering Universiti Malaysia Perlis Kuala Perlis, Malaysia [email protected]

Nurul Mu’azzah Abdul Latiff Faculty of Electrical Engineering Universiti Teknologi Malaysia Skudai, Malaysia [email protected]

Abstract—In wireless sensor networks, the major source of a sensor node failure is battery exhaustion and replacing this energy source in the field is usually not practical. Therefore, the use of energy efficient infrastructure, such as repositioning the base station in a clustered wireless sensor network, is able to prolong the lifetime of the network and improve the overall network data. In this paper, we proposed an energy-efficient protocol for the repositioning of mobile base station using particle swarm optimization (PSO) in wireless sensor networks. Simulation results demonstrate that the proposed protocol can improve the network lifetime, data delivery and energy consumption compared to existing energy-efficient protocols developed for this network. Keywords-base station; wireless sensor networks; particle swarm optimization; network lifetime

I.

INTRODUCTION

Wireless sensor networks are a family of networks in wireless communication system and have the potential to become significant subsystems of engineering applications. Sensor network is composed of a large number of low cost and low power sensor nodes that can be spread on a densely populated area and a base station in order to monitor and control various physical parameters [1]. These sensors are endowed with a small amount of computing and communication capability and can be deployed in situation that wired sensor systems couldn’t be deployed. The applications and benefits of equipping existing and new infrastructures with intelligent sensor strategies are wide ranging. Random deployment of sensor nodes in inaccessible terrain such as environment monitoring in [2], military application in [3] and [4] and even health monitoring in [5] and [6] can be set up. In environment monitoring for instance, wireless sensor network can be used to monitor the environment such as chemical pollutants or detecting early warning of disaster incident such as volcano eruptions and earthquakes. These sensor nodes can also be used to monitor

animals and plants in a wildlife habitat. Wireless sensor network can be deployed in a military battlefield to sense enemy targets and to track their movements in real-time. This application can be very critical as the area is almost impossible to approach and it has a very limited access of infrastructure. Another type of application is the health monitoring where sensor nodes can be directly attached to intensive care patients and doctors can closely monitor their health progress. In order to extend the network lifetime, some published work has exploited the flexibility in base station positioning. Several indicators such as the definition of a network life span, the network operation model, or the network state parameters that are included in the formulation were pursued by researcher in this area. In [7] the authors used the failure of a percentage of the deployed sensors as indicative of a network life span. In this work, hierarchical network topologies are introduced to support the scalability in large area of wireless sensor network. The most common hierarchical topology is based on grouping sensors into clusters with a selected cluster head. A computational geometry based algorithm is proposed in this research. Certain nodes, called application nodes (AN) are assigned as cluster heads and these application nodes interface the cluster with the base station. In this case, the scope of base station positioning problem is reduced to the inter-cluster head network. The approaches in this work does not consider data relay, and thus the problem becomes solvable in a polynomial time. On the other hand, authors in [8] have proven that the reposition of the base station while network is operational can improve the network performance. It has been understood that if sensor nodes within the base station area become dysfunctional due to various reasons, it is better for the base station to reposition itself to become easily and reliably reachable to data sources. This repositioning of the base station can improve the network longevity and reduce the effect of packet drops that is caused by link failure. In this dynamic base

station positioning, there are critical issues to be considered such as when should the base station relocate itself, where should the base station positioned and how should the data been routed while the base station is moving. For this reason, the paper has presented heuristics approach that can improve the network performance in terms of repositioning for increased network longevity, enhancing timeliness of delayconstrained traffic and protecting the base station. The main idea in improving the energy consumption of wireless sensor networks is to move the base station toward the sources of the greatest traffic.

B. Radio Energy Model Our energy model for the sensor nodes is based on the first order radio model as used in [9]. In this model, the transmitter dissipates energy to run the radio electronics and the power amplifier, and the receiver dissipates energy to run the radio electronics. The radios can perform power control and hence use the minimum energy required to reach the intended recipients. To achieve an acceptable Signal-to-Noise-Ratio (SNR) in transmitting an l-bit message over a distance d, the energy expended by the radio is given by:

Consequently, the repositioning of the base station can be valuable to spread the traffic by increasing hops and the feasibility for meeting the timeliness requirements. The work in this paper on the other hand concerns on repositioning the base station in a network with clustered sensor nodes. In particular, the proposed protocol used similar approach as in [7] where the scope of base station positioning problem is decreased to the inter-cluster head network. However, instead of using computational geometry based algorithm, the work in this paper applies a heuristic technique known as PSO in order to select the optimal position of the base station at certain time. The objective of this positioning algorithm is to improve the energy efficiency of a network and consequently, increase the data delivery in a network.

ETX (l,d) = l ∙ Eelec + l ∙ εFS d2 , if d < d0 = l ∙ Eelec + l ∙ εTR d4 , if d ≥ d0

The remainder of this paper is organized as follows: In section II we describe the system models used in the proposed protocol. In section III, we define the problem statement of mobile base station. The next section, a detailed description of the proposed method is presented. In section V, the simulation study of the proposed protocol as well as the results of network performance is discussed, before concluding the paper in the last section. II.

SYSTEM MODEL

A. Network Model The sensor network model that is used in this paper is similar with [9] and [10]. For this work, a sensor network incorporates the following specific features: 

Each sensor node generates equal amount of data per time unit and each data unit is of same length.



All sensor nodes are stationary and homogeneous.



All sensor nodes have limited energy and unlimited buffer size.



All sensor nodes have power control capabilities to vary their transmit power.



All sensor nodes are aware of their location information.



Base station initial location is at the middle of sensing area.



Base station can move to the predetermined sites at the starting of each round.



For simplicity, the time taken for base station movement is negligible.

(1)

where Eelec is the energy dissipated per bit to run the transmitter or the receiver circuit, εFS and εTR depends on the transmitter amplifier model we use, and d0 is the threshold transmission distance. To receive an l-bit message, the radio expends: ERX (l) = l ∙ Eelec

(2)

For the simulations described in this paper, the communication energy parameters are set as: Eelec = 50nJ/bit, εFS =10pJ/bit/m2 and εTR = 0.0013pJ/bit/m4. III.

PROBLEM DEFINITION

A network topology with N number of sensor nodes randomly distributed across the sensing area is considered in this problem. The set of sensor nodes, Z = {n1, …, nj, …, nN}, 1 ≤ j ≤ N are partitioned into K clusters {C1, …, Ck, …, CK}, where Ck is the set of sensor nodes in cluster k, 1 ≤ j ≤ N. The operation of the proposed protocol is based on a centralized control algorithm that is performed at the base station, which is assumed to have large amount of energy supply. The protocol is organized in rounds and each round is subdivided into a setup phase and a steady state phase, as shown in Fig. 1. The setup phase is the phase at which clusters are formed as well as the base station new location is determined. This is followed by a steady state phase where data transmission takes place. The clustering of the sensor nodes are determined by PSO algorithm such as the one proposed in [11]. Furthermore, the equations used for clustering process are similar to the work above which is weighted combination of two objective functions as follows:

F  w1 f1  w2 f 2

(3)

The parameters wi , i  1,2 are user-defined constants used to weight the contribution of each sub-objective. The first objective function, f1, aims to minimize the maximum average distance between cluster heads and their respective members of clusters are stated in the equation below:

  dm n  n j Ck f1  max  k 1, 2,...,K Ck   k

j

    

(4)

IV.

where d mk n j is the distance between cluster head mk and its cluster member node n j , and C k

is the number of sensor

nodes that belong to cluster C k . Meanwhile, the second objective function f2 is given as:

 E0 n j  N

f2 

j 1 K

(5)

 Et mk  k 1

where E0 n j  is the initial energy of sensor node n j , while

Et mk  is the current energy of cluster head mk . The initial energy of a sensor node corresponds to its maximum battery capacity before simulation begins. This objective function aims to minimize the ratio of total initial energy of all sensor nodes in the network with the total of current energy of cluster heads. Therefore, the first PSO minimizes (3) in order to find the optimal cluster heads in the network which is given as m  m1 ,, mk ,mK  , where mk = (mk,x, mk,y) is the coordinates of k-th cluster head. Data transmission Time slot Time slot 1 2

Time slot Time slot n 1

sensing area. The base station then performs PSO algorithm to determine the next cluster heads and the location it needs to move. This process is repeated until all sensor nodes have run out of energy.

BS moves to initial position

PROTOCOL DESCRIPTION

Since the first PSO algorithm performed by the base station has selected the optimal position of cluster heads, the second PSO algorithm is required to determine the optimal position of the base station based on the cluster heads’ locations. Ideally, the base station must be located at the middle point of all cluster heads’ locations where the distance between all cluster heads and the base station are the same. However, in practice, finding this position is considered NP-hard problem [8]. Therefore, approximation algorithm such as PSO is one of the approaches that can be used in order to solve this problem. Because the base station positions have been determined by the first PSO, the search space for second PSO is restricted to the boundary of cluster heads’ locations and consequently reduces the complexity of the algorithm. A. Particle Representation For base station positioning problem, only one location for base station will be selected at the beginning of each round. Each particle in PSO is formed by a set of real value numbers which denote the coordinates of the base station new location. Thus, each particle xi is constructed as follows: xi = [ bi,x , bi,y ]

(6)

where bi,x and bi,y refer to the x-coordinate and y-coordinate of ith particle, respectively. B. Initialization Initially, a starting point for each particle’s location is selected based on the equations below: (7)

Setup phase

Steady-state phase

(8) Fixed-length round

Nodes send Cluster setup and base station BS BS moves information to location computed by PSO broadcasts to new BS algorithm cluster info location

Figure 1: Organization of the protocol

A base station initial position is set up at the middle of sensing area. After the clustering process, the base station needs to determine its new location at the sensing area based on the position of the selected cluster heads. Hence, another PSO algorithm is performed by the base station to determine its new location. For simplicity, we do not take into account the period during the base station’s movement from the original location to the new predetermined location. The base station moves to a new location at the end of set up phase. Once it arrives at new location, all the cluster head nodes will send the collected data from their cluster members to the base station. At the end of each steady state phase, the base station moves back to its original position which is located at the centre of

where minX and minY are the lower bound of x and y coordinates among the cluster heads’ locations. Meanwhile, maxX and maxY are the upper bound of x and y coordinates for all cluster heads’ locations. These equations estimate the centre point of all locations of cluster heads. Using the parameters startX and startY, the particle’s location is initialized as below: (9) The parameter rand (1,10) generates any integer number between 1 and 10. (9) is then denotes the random perturbation of the initial starting point (startX, startY). The particle is constructed to form a swarm of real-coded particles X = [x1,…,xi,…,xP] where P is the swarm size and xi = [mi,1,…,,mi,K]. In order to ensure that the initial base station coordinate is considered in the computation, this coordinate is included as one of particle’s position. In other words, if the

initial location of base station is at the centre of sensing area with coordinate (50,50), the first particle is defined as:

However, when a particle flies outside the region of the search space, its velocity is initialized as given in the following equation:

(10) Next, the initial particle’s velocity is generated randomly for each dimension, d using the following formula:

(16)

(11) The velocity of the initial swarm is represented by V0 = [v1,…, vi, …, vP]. C. Fitness Function The aim is to find the centre among all coordinates of cluster heads in the network. The coordinates of these cluster heads may form a convex polygon or non-convex polygon. Hence it is difficult to find the centre location geometrically. The fitness function used for this purpose is defined below: (12) This equation aims to minimize the maximum distance between all cluster heads to the base station in order to distribute the energy utilization among the cluster heads more evenly. This is because the major source of energy dissipation of all sensor nodes is from the communication distance. Using PSO algorithm, the function defined above is minimized and the coordinate of the base station location that produces the minimum value of (12) is chosen as its new location. D. Velocity Update The gbest version of PSO is implemented for base station positioning problem. Once the evaluation of the fitness function in (12) has been performed, PSO determines the pbest and gbest of each particle. At every iteration, the velocity of each particle for both dimensions x and y is updated using the following equations: vi (t+1) = w × vi(t) + c1r1(pi – xi(t)) + c2r2(pg – xi(t)) (13) xi(t) = xi(t – 1) + vi(t)

(14)

For this work, the interval confinement method introduced in [12] is used where the position of the particle is forced to be within Xmin and Xmax as denoted by the equation below:

(15)

E. Setup Phase At the starting of each setup phase, all sensor nodes send information regarding their current energy level and locations to the base station. Based on this information, the base station first computes the median energy level of all nodes and then chooses a set of sensor nodes called eligible nodes, whose energy levels are above the average value. To ensure that only sensor nodes with sufficient energy are selected as the cluster head, the candidates for the cluster head of the current round will be chosen randomly from the set of eligible nodes. Next, the base station runs the PSO algorithm to determine the best K cluster heads that can minimize the fitness function defined in (3),(4) and (5). After the first PSO algorithm has been performed by the base station to find optimal cluster heads, second PSO algorithm is implemented to find the new base station position in the network. Fig. 2 illustrates the flowchart of PSO procedures for base station positioning problem in sensor networks. V.

SIMULATION AND ANALYSIS

A. Experimental Setup A series of simulations was run using NS2 version 2.34 in a scenario with 100 sensor nodes scattered randomly across the network. Two cases of simulations were performed, where the first case the simulation area was 100m x 100m. For second case, the protocol is tested in a scenario with dimensions 500m x 500m. Initially, the base station was placed in the middle of a network area and is assumed to have an unlimited amount of energy. In this work, it is assumed that the base station can move with constant speed, which is 20m/s. Once the base station reaches the intended destination, it will stop for a certain period, ttx for data collection. After the end of TDMA schedule in one cluster, the base station moves to the next cluster to collect more data. There are 81 base station feasible sites which are organized on a bi-dimensional square grid composed of same-size cells. The distance between each feasible site is 10 m. Once the base station has performed the proposed protocol to compute its next destination, it moved to the new coordinates located with the sensing area.

Start

result. The simulations continued until all the sensor nodes run out of energy and considered non functional. The network parameters are summarized in Table I. TABLE I.

Generate initial position and velocity for all particles

Iterations, t = 1 Particle, i = 1

NETWORK PARAMETERS AND VALUES Parameters

Value

Number of nodes

100

Base station speed

20 m/s

Area size

Case 1: 100 m x 100 m Case 2: 500 m x 500 m

Calculate the particle’s fitness

If particle’s fitness < pbest Update pbest

Set i = 1 Increment t

If particle’s pbest < gbest Update gbest

y

Base station initial location

(50,50)

Radio propagation speed

3 x 108 m/s

Processing delay

50 μs

Bandwidth

1 Mbps

Data size

500 bytes

Number of clusters

5

Length of each round

100 seconds

Initial energy

10 J

n i>S? Update particle’s velocity and position

B. PSO Setup The values for parameters used in PSO algorithm are problem specific and empirically determined by simulations. These values are listed in Table II. TABLE II.

Increment i

PSO PARAMETERS

Apply interval confinement method

n

Iterations = Maximum ?

PSO Parameters

Values

Swarm size

30

Maximum iterations

500

Xmin, Xmax (Case 1)

0, 100

Xmin, Xmax (Case 2)

0, 500

c1, c2

2.0, 2.0

w

0.70

y End: Output

Figure 2: PSO procedures for base station positioning problem

Meanwhile, the number of clusters is set to be 5. For the simulation in this work, all sensor nodes begin with equal energy of 10 J. The simulations consist of several rounds of time in which each round is set to last for 100 seconds. This value was chosen according to the analysis in [9], where tround ≈ (0.08s × Estart) / 9mJ, where Estart is the initial energy of a sensor node. Based on that analysis, within this time, each node has enough energy on average to act as a cluster head once and a non-cluster head several times throughout the simulation lifetime. Several random network topologies are considered throughout the simulations to get the average

In order to evaluate the capability and efficiency of the proposed algorithm, the performance of the proposed protocol is compared with another PSO-based energy efficient protocol proposed in [11]. The focus of this work is to measure the benefits of using the positioning technique on top of the existing algorithm. All the simulated protocols are described as below: 

PSO-C1: This is a clustering protocol using PSO algorithm as presented in [11]. In this protocol, all sensor nodes are clustered by PSO and one sensor node is selected as cluster head in each cluster. Member nodes send the data to their respective cluster head and cluster head performs data aggregation before it send the data to the base station using CSMA technique.



PSO-BSP: This is the proposed protocol as described in previous section.

C. Results and Analysis The performance of the PSO-BSP algorithm in terms of its capability to deliver data to the base station and energy efficiency is compared with PSO-C1, which does not utilize the repositioning of the base station. Fig. 3 shows the total data received by the base station for different network area. It shows that for both cases of different network area, PSO-BSP can achieve higher data delivery compared to PSO-C1. The improvement in data delivery for PSO-BSP over PSO-C1 is about 2 percent for case 1 with network area of 100m x 100m. Meanwhile, the benefit of using PSO-BSP is more significant when bigger network area is used, where the improvement in data delivery is about 16 percent. Thus, it is clearly shown that repositioning the base station before each steady state phase starts is a good approach to utilize the network energy efficiently. The efficiency of PSO-BSP is further exemplified through the graph shown in Fig. 4. This graph confirms that PSO-BSP delivers the most data messages per unit energy for both simulated network areas.

the network against the time until all sensor nodes run out of energy. This can be seen in Fig. 5. It can be observed that both PSO-BSP and PSO-C1 expend the energy more rapidly in the case with bigger network area. This is because, the larger the network area, the lower the density of the network. Consequently, the distance between sensor nodes and the cluster heads, as well as the distance between cluster heads and the base station become longer. Therefore, more energy is expanded for communication. However it can be seen that for both cases, PSO-BSP and PSO-C1 utilize the network energy at almost the same rate, although PSO-BSP can result with higher data delivery. Next, we want to show that PSO-BSP can deliver more data at the base station as a function of number of nodes alive. This is depicted in Fig. 6. By looking at this figure, we can see that the base station in PSO-BSP receives more data messages than PSO-C1 for the same number of node death in both cases of different network area. However, all algorithms deliver less data messages to the base station in the second case since bigger network area indicates higher energy consumption for communication.

5

1000

x 10

900

PSO-C1 PSO-BSP

3 2.5

800

Energy dissipted(J)

Total data delivered at the base station

3.5

2 1.5

600 500 400 PSO-C1 (Case 1) PSO-BSP (Case 1) PSO-C1 (Case 2) PSO-BSP (Case 2)

300

1 200

0.5

100 0

0

100m x 100 m

500m x 500m Area

Figure 3: Total data delivered at the base station for different network area

PSO-C1 (Case 1) PSO-BSP (Case 1) PSO-C1 (Case 2) PSO-BSP (Case 2)

2 1.5 1

1500 Time (s)

2000

2500

3000

60

40 PSO-C1 (Case 1) PSO-BSP (Case 1) PSO-C1 (Case 2)

20

PSO-BSP (Case 2)

0.5

0 0

1000

80

Number of nodes alive

2.5

500

100

x 10

3

0

Figure 5: Total energy dissipated in the network over simulation time

5

3.5

Number of received data at the base station

700

0

200

400 600 Energy dissipation (J)

800

1000

Figure 4: Total data delivered at the base station per given amount of energy

To investigate the energy consumption of the proposed algorithm, a graph was plotted showing energy dissipated in

0

0.5 1 1.5 2 2.5 3 Number of data received at the base station

3.5 5

x 10

Figure 6: Number of nodes alive per amount of data sent to the base station

The performance of PSO-BSP in terms of network lifetime, when we consider that the network is functional until certain percentage of sensor nodes die, is investigated below. Fig. 7 shows the network lifetime according to percentage of sensor

nodes die for network area 100m x 100m, while Fig. 8 shows the result when network area is 500m x 500m. When we observe Fig. 7, we can see that PSO-BSP makes an incremental improvement in terms of network lifetime over PSO-C1. However, this improvement is not obvious. This is because the proposed algorithm only repositions the location of base station at each round to increase energy efficiency in the network, while other arrangement regarding clustering problem remains the same as in PSO-C1. Despite the fact that the times until 1 percent, 25 percent, 50 percent and 100 percent of sensor nodes die in both algorithms do not show an apparent difference, PSO-BSP still manage to increase the data delivery at the base station compared to PSO-C1 as discussed in previous section. Nonetheless, the differences in functional network lifetime for both algorithms are more noticeable when larger network area is considered. The improvement of network lifetime made by PSO-BSP over PSO-C1 can be as high as a factor 0.2. Also, the time different between PSO-BSP and PSO-C1 when all sensor nodes die is about 90 seconds. Therefore, from this result we can conclude that the proposed base station repositioning algorithm can gives more benefit when bigger network area is considered.

VI.

In this paper we have described a new protocol for mobile base station problem in wireless sensor networks. A mechanism to reposition the base station in a clustered wireless sensor network is introduced. This mechanism, which is called PSO-BSP, is based on PSO algorithm that selects the optimal position based on distance function of cluster heads. The PSO-BSP algorithm is run where the objective is to improve the energy efficiency of a network and consequently, increase the data delivery in a network. Results from the simulations have shown that the proposed protocol showing gains in energy efficiency which leads to higher data delivery compared to the protocol in [11] that does not utilize base station repositioning. Nevertheless, it has been found from the simulations that only minor increment in network lifetime can be achieved when using PSO-BSP. This is because, the proposed algorithm does not intend to use different strategy when clustering, and hence the use of repositioning method is to improve the energy consumption in the network. Future works include simulations of the proposed protocols in different network density and study of effect of base station speed to the network performance. ACKNOWLEDGMENT (HEADING 5)

3000 PSO-C1 PSO-BSP

The authors would like to thank all those who contributed toward making this research successful. Also, we would like to thank to all the reviewers for their insightful comment. This work was sponsored by Universiti Malaysia Perlis in conjunction with Universiti Malaysia Terengganu.

2500

2000

Time (s)

CONCLUSION

1500

REFERENCES

1000

J. Yick, B. Mukherjee, and D. Ghosal, “Wireless Sensor Network Survey,” Computer Networks, Vol. 52, No. 12, (2008), pp. 2292-2330. [2] L. Mo, and L. Yunhao, “Underground Coal Mine Monitoring With Wireless Sensor Networks,” Journal ACM Transactions on Sensors Network, Vol. 5, No. 2, (2009). [3] E. T. Matson, A. Smith, and J. E. Dietz, “Application of Adaptive Wireless Sensor Organizations to Secure Spatial Domains,” IEEE Conference on Technologies for Homeland Securites, (2009), pp. 67-72. [4] L. Qiang, L. Yu-Hua, B. Wei-Hong, and L. Zhi-Jun, “Application of Wireless Sensor Network in Military Warehouse,” Journal of Academy of Armored Force Engineering, (2009), Vol. 23, No. 4, pp. 64-66. [5] L. Zhou, W. Bingwen, and Y. Wenjun, “Design and Deployment of Bridge Structural Health Monitoring System Based on Wireless Sensor Network,” 6th International Conference on Wireless Communications Networking and Mobile Computing (WiCOM), (2010), pp. 1-4. [6] N. S. Pakzad, L. G. Fenves, S. Kim, and E. D. Culler, “Design and Implementation of Scalable Wireless Sensor Network for Structural Monitoring,” Journal of Infrastucture Systems, (2008), Vol. 14, No. 1. [7] J. Pan, L. Cai, Y. T. Hou, Y. Shi, and S. X. Shen, “ Optimal Base Station Locations in Two-Tiered Wireless Sensor Networks,” IEEE Transactions on Mobile Computing, (2005), Vol. 4, No. 5, pp. 458-473. [8] K. Akkaya, M. Younis, and W. Youssef, “Positioning of Base Stations in Wireless Sensor Networks,” IEEE Communication Magazines, (2007), Vol. 45, No. 4, pp. 96-102. [9] W. R Heinzelman, A. P Chandarakasan, and H. Balakrishnan, “Energyefficient Communication Protocol for Wireless Microsensor Networks,” in Procs. of the 33rd Hawaii Int’l. Conf. on System Sciences, (2000). [10] N. A. Abdul Latiff, N. M. Abdul Latiff, R. B. Ahmad, “Prolonging Lifetime of Wireless Sensor Network with Mobile Base Station using Particle Swarm Optimization,” 4th International Conference on Modeling, Simulation and Applied Optimization (ICMSAO), (2011). [1]

500

0

1%

25 % 50 % Percentage of Sensor Node Death

100 %

Figure 7: Network lifetime according to percentage of sensor node dies for case 1 2000 PSO-C1 PSO-BSP

Time (s)

1500

1000

500

0

1%

25 % 50 % Percentage of Sensor Node Death

100 %

Figure 8: Network lifetime according to percentage of sensor node dies for case 2

[11] N. M. Abdul Latiff, C. C. Tsimenidis, and B. S. Sharif, “Energy-Aware Clustering for Wireless Sensor Networks using Particle Swarm Optimization,” in Procs. of PIMRC 2007, (2007), Athens. [12] Clerc, M. (2006). Particle Swarm Optimization. London: ISTE Publishing Company [13] The Network Simulator ns2. Available at: http://www.isi.edu/nsnam/ns/

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