Energy efficiency is one of the basic requirements of wireless sensor networks (WSNs) yet this problem has not been sufficiently explored in the context of cluster-based sensor networks. Specifically, the interaction of different types of sensor nodes is one of the major factors of energy efficiency in large-scale heterogeneous networks. In this paper, we aim at improving the interactions among sensor nodes, and we present a heterogeneous local-world model to form large-scale wireless sensor networks based on complex network theory. Two types of nodes, normal nodes and cluster nodes, are added to the networks. The degree distribution for this model is obtained analytically by mean-field theory. This approach depicts the evolution of the network as having a topological feature that is not completely exponential and not completely power law; instead, it behaves between them. The experiment and simulation indicate that the control method has excellent robustness and a satisfactory control effect (interaction of different types of sensor nodes). Furthermore, the results also show that the higher the generation rate of the cluster nodes is, the closer the degree distribution follows the power-law distribution.
Wireless sensor networks (WSNs) are composed of a large number of sensor nodes. These nodes are deployed in a specific area to monitor physical phenomena. Wireless sensor networks are poised to revolutionize our abilities for sensing and controlling our environment. However, sensor nodes rely on batteries to provide energy in WSNs. As a result, the primary problem in WSNs is always energy savings for sending and receiving data. Consequently, power control must be performed in WSNs. In recent years, with the development of WSNs, advances in wireless communication and sensing technology have made it possible to produce a large number of individually cheap and small units. Usually, these small pieces of equipment are used in WSNs, as combinations of sensors and wireless network nodes. With the increasing scale of WSNs, some characteristics of complex networks have emerged. The problem of coefficient, error, and attack tolerance remains to be solved in large-scale networks. As a result, it is crucial to find out a good way to handle these problems.
In recent years, complex networks have received increasing attention for exhibiting the topological structure, function and dynamical properties of many real-world networks such as the World Wide Web, the Internet [
While the B-A scale-free network model captures the basic mechanism that is responsible for the power-law degree distribution, it is still a minimal model with several limitations. As stated in [
Because cluster structure networks can be modified to obey the property of scale-free, many people attempt to adjust the traditional structure of WSNs to a new structure of scale-free. Thus, sensor nodes can save energy even if there is a large-scale network in the monitoring area. They obtain a satisfactory result when forming WSNs that possess the scale-free character as well. It is shown that scale-free networks are robust against the random removal of nodes or node failures. Therefore, another advantage of this type of WSN is the robustness of the network, which is a groundbreaking result in this research field and provides good inspiration for this paper.
In 2007, Chen et al. [
In this paper, an evolving model for WSNs based on the B-A model and the Li-Chen model [
The remainder of this paper is organized as follows. In Section
A local world is a small community with a few nodes in a large-scale network. The model of the local-world is deduced from the B-A model. In the Li-Chen model, each node has only local connection information; nodes connect only in their local world based on local connection information. Then,
Starting from a small number
At each time step
After
In this section, we model a WSN as an inhomogeneous network with growth and preferential attachment. This model contains two types of nodes: normal nodes and cluster nodes. There is only one cluster node attached to a normal node; in other words, the normal node has only one edge, which means that the normal node cannot relay data from other nodes. A cluster node can integrate and transmit data from other nodes. Both of the two types of nodes can connect to a cluster node, and the number of edges is limited in every cluster node because of its energy efficiency. As every new cluster node joins the network, it is randomly assigned an initial energy
Then, the growing model is described as follows: starting with a small number of nodes,
At every time step, a new cluster node or a normal node with one edge enters into the existing network with a probability
The new incoming node links to an old cluster node that is selected randomly from the preexisting network. Nodes in WSNs have the constraint of energy and connectivity and only communicate data with the cluster nodes in their local area. First,
If the new incoming node is a cluster node, then the probability is set as follows: If the new incoming node is a normal node, then the probability is adapted as follows:
In [
After step
From
From the discussion above, the whole probability
In this section, using mean-field theory [
When
The denominator of the above equation is the number of cluster nodes in time
This case means that the local world
In a network, the degrees
Then, we can simplify (
To calculate
From (
When
In this case, a newly added node selects one of the cluster nodes in its local world
A comparison of (
We define
Then, we can obtain the following:
Combining the initial condition
Moreover, to find the degree distribution
Then,
Hence, the degree distribution
Next, inserting
To compare different ratios of cluster nodes to the whole network’s forming factor, in this case, we take two different ratios of
When we set
The scenario of forming WSNs over 500 times when
The scenario of forming WSNs over 500 times when
The degree distribution does not follow the power-law distribution but instead distributes between a power-law and an exponential distribution, and the frequency of the degree in the whole network is shown in Figure
We set our simulation parameters to be
The relationship between the degree and its ratio
Plot of the simulation result for
We set our simulation parameters to be
Figures
Because the distribution of the node degree could not uncover the internal complexity of the topological structure, it is worth investigating the connectivity correlation among the cluster nodes, which could lead to a more profound understanding of the structure. For the sake of depicting the relationship among the cluster nodes and normal nodes, we first discuss the property of the average nearest-neighbor connectivity. Because the cluster nodes play the role of a backbone in ensuring the data processing performance of the WSNs, we compute this performance here as in [
Degree distribution and its average frequency in neighboring nodes.
Degree distribution and its average frequency in neighboring nodes when
Second, to show our link mechanism’s property, Figures
We set our simulation parameters to be
We set our simulation parameters to be
We can draw a conclusion that, with an increase of
This paper presents an evolving model for improving the energy efficiency of WSNs. This model adapts and balances the interactions of different types of sensor nodes to reach the goal of energy efficiency with two different types of probability in the evolving network. Furthermore, the proportion of edges linking to a normal node is improved in every cluster node. Our numerical experiments above show that our new model reaches the requirements for and improves on the network robustness. A good model adapts the cluster structure when the number of nodes increases continuously. However, it ignores the dead sensor nodes with the growth of the network in our model. For the next step, we will pay more attention to the random deletion of sensor nodes that are too close to a real environment of WSNs.
This work is supported by National Natural Science Foundation of China under Grant nos. 61063037 and 61163056, by Key Projects in the Science & Technology Pillar Program of Jiangxi Province of China under Grant no. 20111BBG70031-2, and by Innovation Special Funds Projects for Graduate Students of Jiangxi Province under Grant no. YC2011-S079.