A Local Energy Consumption Prediction-Based Clustering Protocol for Wireless Sensor Networks

1. Introduction

A wireless sensor network (WSN) consists of plentiful low-power sensor nodes capable of sensing, processing and communicating. These sensor nodes observe the phenomenon at different points in the field, collaborate with each other and send the measured data to the base station (BS). Therefore, WSNs are extremely important in cyber-physical system (CPS) for observing and cognizing the complicated physical world at low cost [1]. However, sensor networks have limited and non-rechargeable energy resources; energy efficiency is a very important issue in designing the network topology, which affects the lifetime of sensor networks greatly. Thus, how to minimize energy consumption and maximize network lifetime are the central concerns when we design protocols for WSNs. Fortunately, these are the main goals of topology control [2,3]. Roughly speaking, topology control technology can be classified into two types. One is power control, and the other is hierarchical topology control. For the hierarchical topology control, generally, there exist about four methods, i.e., clustering methods (e.g., [4–6]), connected dominating set methods (e.g., [7–11]), spanning tree methods (e.g., [12–14]) and spanner methods (e.g., [15,16]). By topology control, we usually can obtain a simplified topology of a given WSN while reserving connectivity (e.g., [17,18]) and coverage (e.g., [19–21]). Moreover, the diameter of the obtained topology cannot be increased any more (e.g., [22]).

As a kind of effective topology control method, clustering has proven to be an important way to decrease the energy consumption and to extend the lifetime of WSNs. In a clustering scheme, sensor nodes are grouped into clusters; in each cluster, one node is selected as the leader, named the cluster head (CH), and the other nodes are called cluster members (CMs). Each CM measures physical parameters related to its environment and then sends them to their CHs. When the data from all CMs is arrived, CHs aggregate the data and send it to the BS.

On the one hand, since CHs are responsible for receiving and aggregating the data from their CMs and transmitting the aggregated data to the specified destination, the energy consumption is much higher than that of CMs. Thus, to solve the problem, choosing appropriate cluster heads is the key issue when designing a cluster protocol. On the other hand, if CHs send the aggregated data to the BS directly, long-distance transmission will consume a lot of energy and lead to the premature death of CHs. Thus, designing a suitable inter-cluster multi-hop routing tree to forward data is also an important object of a clustering protocol.

In this paper, aiming at some energy heterogeneous WSNs where nodes are deployed uniformly, we propose a novel clustering protocol: LECP-CP (local energy consumption prediction-based clustering protocol), in which a new cluster head election algorithm is designed, which uses the predicted local energy consumption ratio of nodes as the parameter to compete for the role of the CH. Thus, the global energy consumption can be optimized by the optimization of the local energy consumption. To further reduce the energy consumption of CHs, we also propose a new inter-cluster communication routing tree construction algorithm, based on the local energy consumption ratio of nodes, as well. In addition, we provide explicit numerical calculations for the optimal cluster radius to minimize the energy consumption of the entire network, which is proven to be more accurate and realistic by theoretical analysis and simulation experiments.

The rest of the paper is organized as follows. Section 2 introduces the related works in this field. Section 3 gives the network model. Section 4 presents the local energy consumption prediction-based clustering protocol in details. Section 5 describes the derivation process of the local energy consumption ratio of nodes in detail. Section 6 analyzes several properties of our algorithms. Section 7 exhibits and analyzes our simulation results. Finally, Section 8 concludes the paper.

2. Related Work

In the choice of CHs, the criteria of existing clustering algorithms are different. We summarize the previous work about the selection methods of CHs as follows.

Low energy adaptive clustering hierarchy (LEACH) [23,24] randomly rotates the CHs to distribute the energy load among all of the sensor nodes in the network. The CHs' selection of them uses a probability scheme by which each node determines whether it is selected to be the CH based on the random number generated by itself. Although LEACH is simple and does not require a large communication overhead, it does not consider the energy and the distribution of CHs, which makes the algorithm energy-inefficient. Different from LEACH, DCHSintroduces the residual energy of nodes into the probability threshold, which improves the energy efficiency of the entire network and can extend the network lifetime effectively. Some other similar cluster head election algorithms based on the residual energy of nodes are also proposed in [25–29].

The algorithms proposed in [26,30,31] are the centralization version of LEACH. They improve LEACH by using central control, that is the BS collects information, such as node energy and location, from all sensor nodes and selects the optimal CHs. The defects of these are that the clustering process may be very complex and can generate more overhead. Thus, the centralized clustering algorithm has poor scalability and is only suitable for small or medium-sized networks. For this reason, most of the effective clustering algorithms are all distributed.

Hybrid energy efficient distributed clustering (HEED) [32] is a distributed clustering algorithm, in which CHs are selected from the sensor nodes based on a certain probability related to a hybrid of energy and communication cost. Only sensor nodes with high residual energy and lower intra-communication costs can become CHs. Clusters generated by HEED are more well-distributed than LEACH. However, it cannot guarantee the optimal number of elected CHs and the network connectivity. A similar, but improved, clustering algorithm, EEDC, is proposed in [33], which can reduce the number of iterations and prolong the network lifetime efficiently.

An energy-aware data gathering protocol for wireless sensor networks ( EADEEG) [34] is a novel distributed clustering algorithm. It elects cluster heads based on the ratio between the average residual energy of neighbor nodes and the residual energy of the node itself, which can achieve a good CH distribution and prolong the network lifetime. However, in some cases, there are “isolate points” in EADEEG, which influence the monitoring performance and lifetime of networks. In addition, it chooses 2R_a as the inter-cluster communication radius, where R_a denotes the cluster radius, which cannot ensure the connectivity among CHs. Similar to EADEEG, but improved, cluster head election algorithms are adopted in the cluster setup phase of clustering algorithms [35–37], which can effectively solve the “isolate points” problem existing in EADEEG, and the CHs generated by them can cover all the nodes in the network. For the disconnected problem, two energy-efficient clustering algorithms, called a distributed algorithm of clustering technology based on parameters used for electing CHs (BPEC) [38] and energy-efficient cluster formation protocol (EECF) [39], can keep all of the CHs connected by choosing 3R_a as the inter-cluster communication radius.

Besides the node degree, location and energy, there still exist many other considerable influencing factors when designing clustering algorithms, such as coverage, connectivity, mobility, and so on. Soro et al. in [40] proposed some good cluster head election techniques. However, this paper focuses on coverage preservation, while the energy consumption and network lifetime is on the back burner. As a consequence, many hybrid control algorithms are also widely used in CHs selection. For instance, in [41], energy, concentration and centrality are combined to optimize the CH selection in order to extend the network lifetime efficiently. Energy and local distance are used in cluster head election mechanism using fuzzy logic (CHEF) [42] to compute the probability of being selected as CHs. The clustering algorithms proposed in [43,44] are similar to CHEF. The distance of the cluster centroid, the residual energy of nodes and network flow are selected to compute the selection probability of the CH. multi-weight based clustering (MWBC) [44] is a clustering algorithm based on multiple factors, such as the degree, current energy, transmission power, link quality and relative position of nodes when selecting CHs, aiming at maximizing the network lifetime. Simulation results demonstrate that these algorithms can make a good selection of CHs, and the network lifetime , to varying degrees, can be extended. However, in these algorithms, the weights of different factors can only be determined by experience instead of the precise calculations, which leads to the instability of these algorithms and, thereby, affects the performance of the entire network.

Generally, some algorithms mentioned above, such as [24,26–28], can take full advantage of the high energy of nodes. Selecting some high-energy nodes to take on the CH role ensures that the energy consumption of these CHs is balanced. However, there often exist the following cases. If the cluster size is not well-controlled, on the one hand, the energy consumption of some high-energy nodes may be also higher; after a round, the residual energy of these high-energy nodes is less than of these low-energy nodes, and on this occasion, the advantages of these nodes are not obvious. On the other hand, if the energy consumption of some high-energy nodes is lower, in this case, there will be much energy left while some other nodes have been dead, which cause the the network energy to be wasted. That is, in these cases, these algorithms cannot guarantee the local energy consumption optimization, let alone the global energy consumption optimization. Thus, to avoid these situations, we propose the concept of the local energy consumption ratio and then introduce it into the cluster head election phase. Some other algorithms, such as [41–44], also overlook this influencing factor in the choice of CHs. These hybrid algorithms consider the local energy consumption ratio as a parameter for nodes to compete for CHs, which is also helpful.

If CHs send their data to the BS directly, energy consumption increases if CHs are far away from the BS. Accordingly, for communication among CHs, searching for different communication routing paths among CHs to alleviate the loads of the CHs is also studied.

Applying the multi-hop communication method, each CH can find out the appropriate forwarding node, based on their distance to the BS, to relay data. The inter-cluster communication tree construction in energy-aware distributed unequal clustering (EADUC) [36] is based on the residual energy and relaying cost of forwarding nodes, while in EADC (energy aware distributed clustering) [37], the routing algorithm increases the forwarding tasks of the nodes in scarcely covered areas by forcing CHs to choose nodes with higher energy and fewer member nodes as their next hops, which can help EADC achieve load balance among CHs in non-uniform networks. For more results related to clustering protocols, one can refer to [5].

In this paper, to further reduce and balance the energy consumption of nodes, we construct a simple and energy-efficient inter-cluster communication tree based on the local energy consumption ratio of nodes in a distributed way.

3. Network Model

To simplify the network model, we adopt a few reasonable assumptions as follows.

(1)

There are N sensor nodes that are distributed in an M × M square field.

(2)

The BS and all of the nodes are stationary after deployment.

(3)

All of the sensor nodes can be heterogeneous.

(4)

All of the sensor nodes are location-unaware.

(5)

All of the nodes can use power control to adjust the amount of transmit power.

(6)

The BS is out of the sensor field. It has enough energy, and its location is known by each node.

(7)

Each node has a unique identity id.

To transmit l-bit data to a distance d, the radio expends energy as:

While receiving l-bit data, the radio expends energy as:

4. LECP-CP Details

In this section, we give the details of LECP-CP. The whole operation is divided into rounds, and each round includes a cluster setup phase and a data transmission phase. To form a clustering topology, the cluster setup phase is divided into three subphases: node local energy consumption prediction phase, cluster head competition phase and cluster formation phase. In the data transmission phase, CMs collect the local data from the environment and send the collected data to the CHs. CHs receive and aggregate the data from their CMs and then send the aggregated data to the next-hop CH node based on the routing tree that we have constructed. The data transmission phase should be longer than the setup phase to reduce the overhead of the algorithm and to prolong the lifetime of the network. The state message of each node is listed in Table 1. Several control messages are needed, and the description of these messages is shown in Table 2.

5. The Derivation Process of Ratio(s_i)

When selecting the CH, LECP-CP firstly predicts the local energy consumption ratio of a node, then determines whether it has the ability to act as a CH. In this section, we analyze the local energy consumption ratio of any node s_i.

In the cluster setup phase, a quantity of energy needs to be consumed. The energy expended on the clustering topology construction is called the additional energy cost, which includes the additional energy cost of a CH and many CMs in a cluster.

E_a–ch and E_a–cm are used to denote the additional energy cost of the CH and all CMs, respectively. In a round of the CH rotation process, a CH needs to broadcast one Head_Msg, one Schedule_Msg and one Router_Msg. It also needs to receive n Join_Msgs and one Router_Msg. The additional energy cost of the CH is as follows:

Thus, the total effective energy consumption E_e–total in a cluster is:

Here, we can obtain the total energy consumption in a cluster from Equations (9) and (14). We have:

By analyzing, we know:

Since $\mathit{\text{ratio}}\left(s_i\right)=\text{∑}_{i=1}^{n+1}{E}_{\mathit{\text{con}}}\left(s_i\right)/\text{∑}_{i=1}^{n+1}{E}_{\mathit{\text{cur}}}\left(s_i\right)$, which is introduced in Section 4.1.1, then we finally obtain Equation (3) when combining Formulas (15) and (16).

Obviously, for any s_i, its local energy consumption ratio can be calculated in advance, and the ratio(s_i) can be used to determine whether s_i will be selected as the CH; additionally, we can draw the conclusion from Equation (3) that the more the total current energy and the fewer the energy consumption of nodes within the cluster radius of s_i are, the smaller the ratio(s_i) is. Thus, it is more accurate and realistic to make ratio(s_i) the parameter of s_i to compete for the role of the CH.

6. LECP-CP Analysis

Theorem 1: The CH set generated by LECP-CP can cover all of the network nodes, and there is at most one CH within the cluster radius R_a of any CH.

Proof: t_i = ratio(s_i) · T₂ · V_r according to Formula (4). Thus, we can obtain t_i < T₂ since ratio(s_i) < 1 and V_r < 1. That is, the waiting time t_i of any node s_i is smaller than T₂. Thus, any expected CH will broadcast a Head_Msg and become a CH before T₂ expiring, which can avoid the generation of “isolate points”.

As we stated previously, Formula (4) ensures that different nodes have different waiting times. We assume that node s_i has a shorter waiting time than others and broadcasts the Head_Msg within radius R_a. Thus, all of the nodes within this range will give up the competition and become CMs. Therefore, there is no more than one CH within the radius R_a of any CH.

Lemma 1: Given a maximal independent set S of an undirected connected graph G(V,E), if the number of nodes in S is no less than two, then there must exist at least one node in S within three hops of every node υ in S.

Theorem 2: If the inter-cluster transmission range R_inter–CH and the intra-cluster transmission range R_intra–CH satisfy that R_inter–CH ≥ 3R_intra–CH, then the CH set generated by LECP-CP algorithm is a connected dominating set of the network.

Proof: Firstly, we prove that the CH set S generated by LECP-CP algorithm is a dominating set. According to Theorem 1, there is no more than one CH within a cluster, so the CH set S must be an independent set. After the execution of the LECP-CP algorithm, each node in the network either is the CH, or the member node of one cluster, and any plain node adding to the cluster head set will destroy its independence; so, the CH set S is the maximum independent set. Since the maximum independent set is also a dominating set, the CH set generated by the LECP-CP algorithm is a dominating set of the network.

Then, we prove that CHs in the dominating set S are connected if the inter-cluster transmission range R_inter–CH and the intra-cluster transmission range R_intra–CH satisfy that R_inter–CH ≥ 3R_intra–CH. According to Lemma 1, there must exist at least one cluster head node in S within three hops of any CH s_i of S. Figure 3 depicts a case exhibiting the longest distance between two adjacent CHs. In this worst-case configuration, it is clear that when the transmission range R_inter–CH of a CH is not less than three-times R_intra–CH, the overlay graph composed of CHs will be connected.

Lemma 2: Suppose that the network area is A and the cluster radius is R_a, then the expected number of CHs generated in the network is $M_{exp}=\lceil \frac{4A}{3\sqrt{3}{R}_a^2}\rceil$.

Proof: Clusters generated by the clustering algorithm need to cover all nodes in the network, that is they need to cover the whole network. Since there are overlaps among clusters and there is only one CH in any cluster, thus when the overlaps among clusters are the most, the number of CHs achieves the maximum; to the contrary, there is the least number of CHs in the network when the overlaps among clusters are the least. BPEC [16] shows the cases of minimum cluster area and maximum cluster area, depicted by Figure 4. On these occasions, we can correspondingly obtain the maximum number of CHs $M_{max}=\lceil \frac{2A}{\sqrt{3}{R}_a^2}\rceil$ and the minimum number of CHs $M_{min}=\lceil \frac{2A}{3\sqrt{3}{R}_a^2}\rceil$, respectively.

Since the maximum and minimum cluster area are both proportional to $R_a^2$, thus we can deduce that the cluster area in the practical network is also proportional to $R_a^2$. Take the condition where the heterogeneous nodes are randomly deployed in the network into consideration: the expected number of CHs in the practical network is taken as $M_{exp}=\lceil \frac{4A}{3\sqrt{3}{R}_a^2}\rceil$.

Theorem 3: If N nodes are randomly deployed over a square field, the area of which is A, then when the cluster radius is set as the optimal value $R_{\mathit{\text{opt}}}=\sqrt[4]{\frac{4\sqrt{3}A\left(6E_{\mathit{\text{elec}}}+E_{\mathit{\text{sen}}}+E_{\mathit{\text{com}}}\right)}{9N{\epsilon }_{fs}}}$, the energy consumption of the entire network can be minimized.

Proof: In Section 5, we have obtained that in a round of the CH rotation process, the total energy consumption in a cluster is:

Obviously, if the energy consumption in each cluster of one round is the minimum, then the total energy consumption in the network is the minimum. According to Lemma 2, the expected number of CHs in the practical network is taken as $M_{exp}=\lceil \frac{4A}{3\sqrt{3}{R}_a^2}\rceil$; thus, the energy consumption of all clusters in one round is:

Taking the derivative of Formula (18) over R_a and making the derivation result be zero, then we can obtain the optimal cluster radius R_opt:

Theorem 4: The overhead complexity of control messages in the network is O(N).

Proof: At the beginning of each round, each node broadcasts a Node_Msg. Thus, there are N Node_Msgs in the whole network. In each round, each cluster member broadcasts a Join_Msg, while each CH broadcasts a Head_Msg, a Schedule_Msg and a Route_Msg. Suppose the number of generated CHs is k; then, the total number of Join_Msgs is N − k, and the numbers of Head_Msgs, Schedule_Msgs and Route_Msgs messages are all k. Thus, the total number of control messages in the entire network is N + (N − k) + k + k + k = 2N + 2k. Therefore, the overhead complexity of control messages in the network is O(N).

Theorem 5: The time complexity of LECP-CP is O(1).

Proof: LECP-CP adopts a distributed clustering strategy. Thus, the time complexity of the entire network is equal to that of a single node O(1). In other words, the time complexity is a constant and has nothing to do with the network size.

7. Experimental Section

The simulation was performed in NS-2. Every simulation result shown in this section is the average result of 50 independent experiments, unless otherwise specified. Each experiment is done in different scenarios where the nodes are uniformly deployed over a 200 m × 200 m field, and four scenarios (100 nodes, 200 nodes, 300 nodes, 400 nodes) are chosen.

Figure 5 shows the initial network topology of the four scenarios.

The parameters of the simulations are listed in Table 3.

8. Conclusions

In this paper, aiming at energy heterogeneous WSNs where nodes are deployed uniformly, we propose a novel clustering protocol, LECP-CP, in which a new cluster head election algorithm is designed, which uses the predicted local energy consumption ratio of nodes as the parameter to compete for the role of the CH. Thus, the global energy consumption can be optimized by the optimization of the local energy consumption. To further reduce the energy consumption of CHs, we also propose a new inter-cluster communication routing tree construction algorithm, based on the local energy consumption ratio of nodes, as well. In addition, we provide explicit numerical calculations for the optimal cluster radius to minimize the energy consumption of the entire network, which is proven to be more accurate and realistic by theoretical analysis and simulation experiments.