Journal of Sensors

Volume 2016 (2016), Article ID 3831810, 8 pages

http://dx.doi.org/10.1155/2016/3831810

## Energy Efficient Wireless Sensor Network Modelling Based on Complex Networks

^{1}Information Engineering School, Nanchang University, Nanchang 330031, China^{2}International School, Beijing University of Posts and Telecommunications, Beijing 10083, China

Received 18 September 2014; Accepted 25 June 2015

Academic Editor: Chenzhong Li

Copyright © 2016 Lin Xiao et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

The power consumption and energy efficiency of wireless sensor network are the significant problems in Internet of Things network. In this paper, we consider the network topology optimization based on complex network theory to solve the energy efficiency problem of WSN. We propose the energy efficient model of WSN according to the basic principle of small world from complex networks. Small world network has clustering features that are similar to that of the rules of the network but also has similarity to random networks of small average path length. It can be utilized to optimize the energy efficiency of the whole network. Optimal number of multiple sink nodes of the WSN topology is proposed for optimizing energy efficiency. Then, the hierarchical clustering analysis is applied to implement this clustering of the sensor nodes and pick up the sink nodes from the sensor nodes as the clustering head. Meanwhile, the update method is proposed to determine the sink node when the death of certain sink node happened which can cause the paralysis of network. Simulation results verify the energy efficiency of the proposed model and validate the updating of the sink nodes to ensure the normal operation of the WSN.

#### 1. Introduction

Wireless sensor network (WSN), which combines the technology of sensors, embedded computing, and wireless communications, is the most important element in the Internet of Things.

In this paper, we consider the large scale WSN which consists of sensor nodes and sink nodes. The sink node among senor nodes will play the central control function; the control information and transmission signal will be passed through the sink node. Considering the work load and efficiency of the sink node, multiple sink nodes will be deployed in the network [1].

The power consumption and energy efficiency of WSN are the significant problem of the operation of the WSN. The network deployment (especially sink node placement) and topology control of the WSN have great effect on the energy efficiency of WSN [2].

When mentioning sink node placement, most researches consider the influence from the location of the sink node to the network lifetime. Reference [3] researched the sink node deployment strategy under the lattice structure. Reference [4] proposed two kinds of algorithms; one is a global algorithm based on the sink node placement for the general; the other is the one-hop algorithm based on the information of adjacent nodes. They are all able to prolong the network lifetime to some extent. References [5, 6] researched sink nodes with mobility that can distribute their positions according to the energy consumption of the network so as to extend network lifetime. Reference [7] proposed a kind of heuristic algorithm on the foundation of the simple structure that assuming the distance from sensor nodes to sink nodes is only one hop. Reference [8] proposed a general energy consumption model suited for common sensor nodes and heterogeneous nodes topology. Reference [9] improved the property of [8] and proposed the constraint conditions of the death for the model.

Recently, some works focus on wireless network topology modeling based on complex network theory. Reference [10] added shortcuts to the wireless mesh network taking into account practical constraints, such as radio transmission range of nodes, numbers of radios per mesh router, and available bandwidth of wireless links. Long range shortcuts can be created by either adding wired links [11] or directional beamforming [12]. The authors in [13] proposed a multicast reprogramming protocol for wireless sensor networks based on small world concepts. Reference [2] proposed energy efficiency small world ad hoc networks, which gave a tradeoff between energy consumption and network performance.

In this paper, we consider the network topology optimization based on complex network theory to solve the energy efficiency problem of WSN. In this paper, sensor nodes and sink nodes will be connected in accordance with the small world characteristic. Based on the features of small world network, nodes can be randomly added or rewired so as to contract the average path length and decline energy consumption. We use clustering analysis method to separate the large numbers of sensor nodes and select sink nodes from them and maximize the energy efficiency.

This paper is organized as follows. Section 2 gives the proposed energy efficient WSN topology. The performance is validated by simulation in Section 3. Finally, Section 4 gives the conclusion of this paper.

#### 2. Proposed Energy Efficient WSN Topology

In this energy efficient WSN model, firstly we discuss the optimization problem for the network topology by setting multiple sink nodes; then we obtain the energy efficiency of such WSN.

##### 2.1. Initialize the Small World Topology

Sensor nodes in the network are arranged randomly; the adjacency matrix for them will be constructed according to the distance between any two nodes. This distance will be calculated by the distance formula based on the coordinate of rectangular coordinate system, and the calculation formula is

After obtaining the adjacency matrix, the fundamental small world topology can be obtained by proposed method in [2].

##### 2.2. Determine the Optimal Number for Sink Nodes

Sink nodes of the WSN topology should be picked up from the sensor nodes network with the small world characteristic. Since multiple sink nodes will be applied in the network, clustering analysis is used since its categories for the cluster share the similarity of the central communication function of sink nodes. The hierarchical clustering analysis is selected to implement this clustering for a series of sensor nodes from the bottom to the top level with the comparison of nodes communication distance.

To start the analysis for clustering, the proper number for sink nodes should be identified at first. So as to display the energy saving and high efficiency feature of the proposed model, the number for sink nodes ought to be weighed among the network lifetime, sink node cost, and initial energy for the network. The used variables in this paper are given as follows.

*Variables Definition* : number of sink nodes; : total number of nodes in the network; : number of key nodes each sink node links with; : transmission energy for communication per nodes pair; : receiving energy for communication per nodes pair; : other energy consumption when nodes do not communicate; : initial energy per key node per sink node; : total energy cost per key node for one time of inter node communication; : lifetime for key node; : network cost for the whole; : cost per sink node; : cost per sensor node; CR: ratio of to .

During the process that sensor nodes communicate with sink nodes, data from sensor nodes will be delivered to key nodes firstly which linked directly with sink nodes. Key nodes have to pass the data from sensor nodes.

The total energy cost per key node for one time of inter node communication will be

Define the function of lifetime for key nodes as

It is easy to see that, with the increase of the number of sink nodes, the lifetime for key nodes increases as well. While sink nodes number keeps increasing, making the hop for any sensor nodes in the network be 1, just as , the more increase for sink nodes number will be meaningless to the lifetime.

Then we define the network cost function asFor fixed scale WSN, the value of is fixed, and the value of will get to change with the value of sink nodes number . The more the sink nodes in this network, the more the cost of the network.

The proper number of sink nodes can be obtained by

In order to gain the optimal number for sink nodes* n*, the derivation towards the ratio* L/C* is shown as follows:where represents

So do the second derivation towards :

Finally, the proper number can be worked out as

Take the result into the cluster analysis; the multiple sink nodes topology can identify the number of communication centres in the WSN.

##### 2.3. Identify the Multiple Sink Nodes

Take the optimal value of sink nodes into cluster category and go for hierarchical clustering. Since the hierarchical clustering is the cluster method based on distance, the process of it can be divided into the following steps.

At first, find the similarity among objects and define the distance that can represent the differentiation of them. In this paper, the Euclidean distance that is calculated above is selected to realize the dissimilarity of them. When the objects and have a close relation, the value of is rather small, even close to 0.

Next, produce the hierarchical cluster tree with the linkage function. In accordance with the hierarchical clustering analysis for nodes topology, the distribution for sink nodes can be marked out; this process is shown in Figure 1.