Mathematical Problems in Engineering

Volume 2015, Article ID 608121, 11 pages

http://dx.doi.org/10.1155/2015/608121

## Energy Balanced Redeployment Algorithm for Heterogeneous Wireless Sensor Networks

School of Automation, Beijing Institute of Technology, Beijing 100081, China

Received 15 August 2014; Accepted 1 September 2014

Academic Editor: Yun-Bo Zhao

Copyright © 2015 Guang Ye 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

Wireless sensor networks (WSNs) have gained worldwide attention in recent years. Since WSNs can be conveniently deployed to monitor a given field of interest, they have been considered as a great long-term economic potential for military, environmental, and scientific applications and so forth. One of the most active areas of research in WSNs is the coverage which is one of the most essential functions to guarantee quality of service (QoS) in WSNs. However, less attention is paid on the heterogeneity of the node and the energy balance of the whole network during the redeployment process. In this work, the energy balanced problems in mobile heterogeneous WSNs redeployment have been analyzed. The virtual force algorithm with extended virtual force model is used to improve the QoS of the deployment. Furthermore energy model is added to enhance or limit the movement of the nodes so that the energy of nodes in the whole WSNs can be balanced and the lifetime of the networks can be prolonged. The simulation results verify the effectiveness of this proposed algorithm.

#### 1. Introduction

WSNs consist of small-sized low cost sensor nodes which have several restrictions in energy supply, computing power, and bandwidth of the wireless communication [1]. The QoS of the network is highly related to the deployment performance of the nodes. However, in many working environments such as disaster areas, battlefields, and toxic gas regions, all sensor nodes are mainly deployed randomly by aircraft instead of human beings. In such case, the deployment result may not satisfy the requirement of the system. All the nodes may cluster in a small region or may even distribute sparsely without connectivity guarantee which would influence the QoS and reliability of the WSNs significantly.

Many researchers are currently engaged in coverage problem [2–4] and numerous algorithms are related to mobile WSNs.

Mobile WSNs are composed of a distributed collection of nodes, each of which has communication, sensing, computation, and locomotion capabilities. The mobility of sensor nodes allows more complex application scenarios. With locomotion capabilities, sensor nodes can adjust their positions after stochastic distribution; thus the whole networks could enhance the coverage performance and reach more precise placement. However, the movement of the node would expend the energy of the node. Some node may run out of power because of the long distance movement during redeployment.

Another actual problem in WSNs coverage is that the nodes in networks cannot be always the same in practice due to various reasons. The coverage analysis of heterogeneous WSNs is very useful for both academic and industrial fields. The concept of heterogeneous sensor network is proposed in [5]. The existence of heterogeneous WSNs is mainly due to the following aspects. (1) Nodes are different as physical devices, and the physical properties of the sensor node are very difficult to be completely homogenized. (2) The same type of sensor nodes may work differently due to work environment, regional terrain characteristics, and imbalanced workload or other reasons. All those could affect the behaviour of nodes in WSN.

In the literature, abundant work has been done in the redeployment of the mobile WSNs, and many effective algorithms have been put forward to obtain a required placement and improve the coverage rate. Pervious work on mobile WSNs redeployment algorithms can be classified into two main kinds: virtual force algorithms (VFA) and computational geometry-based approach. In VFA based algorithms [6], those models the mobile sensor nodes as electrons or molecules, and nodes move toward or away from each other by the virtual force (often related to the distance between nodes) or potential fields. However algorithms above do not consider some actuality problems such as connectivity maintenance and the energy cost [7]. References [8–10] are algorithms according to the computational geometry in which nodes update their positions to from a uniform Voronoi diagram or Delaunay triangulation. It can provide well performance but is hard to be used for the need of the global position information of the whole network which usually cannot be realized.

In this paper, the redeployment problem in mobile heterogeneous WSNs considering energy balanced is addressed. Delaunay triangulation is used in VFA to find the logic neighbors nodes in order to avoid nodes cluster in a small region. Furthermore according to the research fixed ideal distance is proposed to solve the serious coverage holes and redundant problem in traditional VFA. And the energy model of the nodes is proposed. In order to balance the energy of the whole networks, in this paper energy control function is added to the virtual force model.

Throughout the paper, it is assumed that the communication range is two times the sensing range. The rest of this paper is organized as follows. Section 2 gets over the past work that closely related to our work. Section 3 analyzes energy unbalanced problem in mobile WSNs redeployment and provides a solution. Section 4 gives the simulation results that illustrate the performance. Section 5 is the conclusion of the paper.

#### 2. Related Works

The prior work on redeployment of mobile WSNs in recent years which closely related to this subject is summarized below.

The concept of redeployment of mobile WSNs is derived from dealing with coordination in behavior control of many robots teams [11, 12]. Gage [11] has classified the use of robot swarms to provide blanket, barrier, or sweep coverage of area. According to this classification, the redeployment problem studied in this paper focuses on the blanket coverage. Reference [12] considers multirobot exploration and mapping for larger teams and gives an evaluation of different strategies for coordinating the efforts of a robot team during an exploration mission in an unknown environment. In [13], a potential-field-based approach (PFBA) is presented to deploy sensor nodes in a target environment. In order to obtain a uniform deployment in an unknown enclosed area, control force defined as negative gradient of potential (NGOP) is employed. However, some crucial problems had not been considered such as connectivity maintenance and topology control. In [14], the author introduced the concept of virtual force algorithm (VFA) to the WSNs deployment. The VFA adopts the similar strategy as PFBA, by considering the virtual attractive and repulsive forces exerted on each node by neighbor nodes and obstacles. The VFA can significantly increase sensor coverage. These works only consider homogeneous sensing models. Based on works in [14], a distributed self-spreading algorithm is developed in [15]. The virtual force in (distributed self-spreading algorithm) DSSA is modeled as internuclear repulsion and attraction between molecules. Computational geometry such as Voronoi diagram and Delaunay triangulation is commonly used in redeployment of WSNs, and the vector-based algorithm (VEC), the Voronoi-based algorithm (VOR), and MiniMax are presented in [8]. The algorithms above use Voronoi diagrams to divide the coverage field into many small areas and enhance the covered area by pushing or pulling nodes according to virtual force. Computational geometry-based algorithms can solve the stacking problem. However the Voronoi diagram is a global structure; it means that the diagram can be obtained only if the global location information of all nodes in the WSNs is known.

#### 3. Preliminaries

##### 3.1. Network Model and Assumptions

In this paper we focus on the redeployment problem of heterogeneous WSNs in 2-dimensional plane. The position of node is described as (). The distance between node and node is defined as Euclidean distance . The initial deployment is a random deployment in unknown distribution. We assume that every node can learn its own position by GPS or other localization technologies. is the communication range; if , node and node are neighbor nodes. Nodes can receive and send message to their neighbors without losing data. Meanwhile, nodes can also get relative distances and orientations between them. Nodes are aware of their remaining energy and can share this information with their neighbors. is the sensing range. The perceptual model is defined as follows ( is an arbitrary position in target area):

In general, is larger than .

All of the virtual physics algorithms for redeployment problem in WSNs are similar to the structure of virtual force, which include the ideas of potential field with circle packing that models the sensor node to be a particle in the potential field. And the potential field exerts forces on the nodes in its field. For a couple of neighbor nodes and , the potential function could be built. And the virtual force is shown as follows:

Nodes move toward the target area by the virtual forces. The force can be attractive force or repulsive force. Generally, there is an ideal distance . If the distance between nodes and is less than , repulsive force will act on nodes. Similarly, attractive force will act on nodes if the distance is larger than the ideal distance. The repulsive force is to insure the sensors are sparse enough without too much redundant area and the attractive force is to guarantee the coverage without coverage holes.

The control law for nodes is described inwhere is the acceleration of the node, is the velocity of the node, is damping coefficient, and is the neighbors of node .

In traditional VFA, the virtual force is defined as follows:where is the virtual force attractive coefficient, is the virtual force repulsive coefficient, is the Euclidean distance between node and node , and is the unit vector from node to node .

Nodes move to new positions according to (3). The total force exerted on node can be described as follows:

#### 4. Energy Balanced Redeployment Algorithm for Heterogeneous WSNs

The extended virtual force algorithm is a redeployment algorithm with some novel features which can overcome the limitations of traditional VFA. In practical networks the sensing range of nodes cannot be always the same due to various reasons; in that case coverage holes may appear which may influence the QoS of the WSNs seriously. Prior algorithm assumed that is two times larger than ; however as a matter of fact is much larger than . High may induce stacking problem in redeployment.

In order to solve the problem above, Energy Balanced Redeployment Algorithm (EBRA) is proposed.

Firstly we prove the stability of the algorithm.

##### 4.1. Stability Analysis

The stability of the algorithm can be proved with Lyapunov stability theory.

*Proof. *Assume is the position vector of node . The control input of node is the virtual force exerted on node by its neighbor . Then the virtual potential field can be known according to (2) and (5). The total force of the node can be summarized as follows:Then energy function which combines kinetic energy with potential energy is built as Lyapunov function:For the symmetry of and , on the orientation from node to node . The time derivative is described as follows:The energy function can be simplified as follows:Combining (9) and (3), we getwhere is the damping coefficient and is seminegative definite. According to Lyapunov stability theory, the redeployment algorithm is asymptotically stable.

##### 4.2. Redeployment Algorithm for Heterogeneous WSNs

As exponential force model can achieve fast convergence, the force model is shown in (11) and Figure 1:where is the unit vector from node to node , and are constants that may be changed in different situations, and is the ideal distance.