Abstract
Improving the quality of monitoring and guaranteeing target coverage and connectivity in energy harvesting wireless sensor networks (EHWSNs) are important issues in nearperpetual environmental monitoring. Existing solutions only focus on the utility of coverage or energy efficient coverage by considering target connectivity for batterypowered WSNs. This paper focuses on optimizing the maximum monitoring frequency with guaranteed target coverage and connectivity in EHWSNs. We first analyzed the factors affecting monitoring quality and the energy harvesting model. Thereafter, we presented the problem formulation and proposed the algorithm for maximizing monitoring frequency and guaranteeing target coverage and connectivity (MFTCC) that is based on graph theory. Furthermore, we presented the corresponding distributed implementation approach. On the basis of the existing energy harvesting prediction model, expensive simulations show that the proposed MFTCC algorithm achieves high average maximum monitoring frequency and energy usage ratio. Moreover, it obtains a higher throughput than existing target monitoring methods.
1. Introduction
Wireless sensor network (WSN) is a multihop wireless network consisting of many sensor devices and is widely applied in environmental monitoring, precision agriculture, and natural disaster relief [1, 2]. A WSN generally coordinates sensor nodes to monitor, collect, and process the data of sensing targets. To overcome the effects of limited resources in WSNs (such as energy, transmission rate, and computation) and enhance the network performance, many studies have been conducted, such as energy efficient transmission and routing [3, 4], coverage [5], and topology control [6], to improve network utility. One of the most important research issues in WSNs is the coverage problem [5]. The coverage problem involves the effective monitoring of targets by the optimal deployment or activation scheduling of sensor nodes, that is, the coverage problem is a performance optimization problem of ensuring that the monitoring target is covered by one or multiple sensor nodes. In this context, numerous coverage optimization algorithms have been proposed [7–14]. For instance, the authors in [7] studied the area coverage problem in microgrids and proposed an iterative process method to solve the problem. Furthermore, the probabilistic sensing model was employed in [8] to characterize the sensing region, and an εfull area coverage optimization algorithm was proposed to solve the problem. In addition, the authors in [9] proposed a target coverage algorithm based on the multiobjective optimization of coverage, and their simulation results corroborated that the proposed algorithm not only improves the quality of network coverage but also prolongs the network lifetime. Similarly, Wei et al. [10] presented a kdegree target coverage algorithm with energy awareness. The authors in [11] analyzed the performance of four target coverage algorithms from an industrial perspective. For the target coverage in a surveillance environment, a cooperative scheduling scheme with guaranteed target coverage was proposed in [12] to solve the problem of scheduling sensors. Moreover, for the barrier coverage problem, Nguyen and SoIn and Silvestri and Goss [13, 14] proposed a distributed deployment algorithm and an autonomous deployment algorithm, respectively.
These studies mainly focused on three coverage types: area, point (target coverage), and barrier coverages. For the area coverage, the sensor nodes in a WSN must be deployed optimally to cover each point in a given area. In the point coverage, a set of point targets must be covered by sensor nodes in a given region. The barrier coverage mainly focuses on intruder detection in a given belt region and does not cover every point of a region. In the existing studies on the three coverage types above, most of the proposed coverage algorithms mainly focus on batterypowered WSNs. Batterypowered WSNs are failureprone due to their limited power supply. Therefore, the existing studies mainly concentrated on extending the network lifetime to address the coverage problem. Moreover, some studies did not consider the connectivity between the targets and the sink station and only aimed to maximize the coverage of targets.
The advent of energy harvesting technologies (such as solar, wind, and vibration) can be utilized to solve the power supply limitation in WSNs. A sensor node in an energy harvesting WSN (EHWSN) can be powered perpetually. Therefore, the coverage problems in EHWSNs tend to concentrate on qualityaware target coverage, but not the extension of network lifetime for the coverage problem [15–27]. In these algorithms, the optimization objective mainly focuses on coverage utility, including maximizing the number of covered targets or time slots of sensor nodes covering targets.
However, few algorithms consider the problem of target monitoring quality for guaranteeing target coverage and connectivity in EHWSNs. In this work, we are interested in developing an efficient algorithm for improving the quality of monitoring while ensuring the target coverage and connectivity of EHWSNs. The proposed algorithm aims to maximize the monitoring frequency of all targets covered by the sensor nodes and the requirement of connectivity between the target and the sink node. Maximum monitoring frequency is defined as the maximum number of monitoring each target receives in a monitoring cycle of an EHWSN. The two corresponding constraint conditions are as follows. The first constraint is the monitoring of each target by at least one sensor node for a given period. The second constraint is the need to construct a connected path between each target and sink node. To solve the optimization problem, we first divide the monitoring period into L monitoring cycles. The size of monitoring cycles L is determined on the basis of the prediction accuracy of energy harvesting. In this context, we initially describe the maximum monitoring frequency problem with guaranteed target coverage and connectivity. Thereafter, we formulate the optimization problem and propose an effective heuristic algorithm based on graph theory. The proposed algorithm not only considers the maximum monitoring frequency and the fairness of target monitoring but also ensures the connectivity between each target and sink node.
The main contributions of this paper are as follows:(1)We first integrated the monitoring frequency of a target with coverage and connectivity and presented the solution of maximizing monitoring frequency under guaranteed target coverage and connectivity in an EHWSN.(2)We proposed an efficient maximizing monitoring frequency algorithm with a guaranteed coverage and connectivity optimization algorithm (MFTCC) based on graph theory. The proposed algorithm not only achieves the maximum monitoring frequency with guaranteed target coverage and connectivity but also embodies the fairness of target monitoring. Moreover, we provided the distributed implementation and analysis of MFTCC.
The rest of this paper is organized as follows. Section 2 presents the related works; Section 3 describes the optimization problem and the problem formulation; Section 4 presents an efficient heuristic optimization algorithm for guaranteed target coverage and connectivity in EHWSNs; Section 5 evaluates the network performance; and Section 6 concludes this paper.
2. Related Works
The coverage problem in traditional WSNs is one of the fundamental problems for which many coverage algorithms have been proposed. These algorithms can be categorized as area, target (discrete point), and barrier coverages [5]. In traditional WSNs, the study on the coverage problem focuses on the maximum network lifetime under a limited energy supply. With the advent of energy harvesting technologies, the problem of limited energy supply can be solved. Therefore, the optimization objective becomes the maximum quality of coverage (QoC). Gaudette et al. [28] first proposed the maximum QoC problem in a solarpowered WSN. This problem involves increasing the minimum number of targets covered by adjusting the transmission range of sensor nodes over a 24hour period. However, this traffic overhead is assumed static, which is unsuitable for practical deployment. Liang et al. [15] proposed an adaptive rate allocation algorithm for monitoring quality maximization, but this algorithm is believed that all targets can be covered by sensor nodes. In [16], DeWitt and Shi focused on the kbarrier coverage in an EHWSH and proposed an algorithm for achieving maximum lifetime. Moreover, Li et al. [17] proposed an algorithm for satisfying a certain area coverage in an EHWSH, which extends to network lifetime by scheduling active sensor nodes. Similarly, Yang and Chin [18] proposed a MUA algorithm to minimize the activation time of sensor nodes and guarantee that all targets are covered. Cheng et al. [19] proposed an optimal scheduling algorithm in a wireless rechargeable sensor network for stochastic event capture. They considered three scenarios in the analysis of the performance of quality of monitoring. Ren et al. [20] presented an optimal algorithm for the coverage quality of targets, which also considers the connectivity between the sensors and the base station. Furthermore, Yang and Chin [21] proposed an efficient heuristic algorithm of scheduling sensor nodes to monitor targets and consider the connectivity between the sensor nodes and the sink node. In their algorithm, they also designed some constraint conditions, such as complete targets coverage, energy, and flow conservation. Xiong et al. [22] presented a novel prioritybased greedy scheduling algorithm to extend the network lifetime of a hybrid WSN consisting of common and rechargeable nodes. They mainly focused on maximizing the network lifetime by satisfying the required coverage. Yang and Gündüz [23] studied the perpetual target coverage problem in an EHWSN. They considered the maximum network lifetime by adjusting the sensor sensing range. In addition, Yang and Chin [24] proposed an optimal algorithm for the minimum number of relay nodes to achieve the target coverage and connectivity. In [25], they also presented a distributed maximum energy protection algorithm to address the maximum network lifetime coverage for EHWSNs. Chen et al. [26] proposed the reinforcement learningbased sleep scheduling for coverage (RLSSC) algorithm for solarpowered WSNs. The RLSSC composed of twostage scheduling algorithms can effectively prolong the network lifetime by adjusting the working modes of the sensor nodes. In [27], the limited sensing angle and the recharging ability of sensor nodes were considered. For this scenario, the author presented the maximum lifetime target coverage problem and proposed two heuristics to solve it.
However, these existing target coverage and connectivity algorithms mainly focus on the maximum network lifetime of batterypowered WSNs or the coverage utility in EHWSNs. Few studies have considered the maximum monitoring frequency of targets with guaranteed target coverage and connectivity.
3. Network and Energy Model
In this section, we first present the network model of target coverage in an EHWSN and the definition of energy consumption for monitoring, forwarding, and receiving information. Subsequently, the energy harvesting model based on the weighted movingaverage (EWMA) algorithm is introduced.
3.1. Network Model
We consider an EHWSN as an undirected topology graph G(V, E), where V = {S ∪ Z ∪ R}, S = {s_{1}, s_{2}, …, s_{i}, s_{i+1}, …, s_{n}} is the set of n sensor nodes, Z = {z_{1}, z_{2}, …, z_{i}, z_{i+1}, …, z_{m}} is the set of m targets, R is the sink node, and E = {e_{ij}} is the set of all links. Each sensor node s_{i}∈S is powered by a solar energy source and has fixed maximum transmission and monitoring ranges. In the deployment areas of EHWSNs, each target in Z can be covered by one or more sensor nodes, that is, all targets are in the sensing range of the sensor nodes. The monitoring information of each target is transmitted to sink node R by the sensor nodes. Moreover, we assume the total monitoring period (T) is divided into L monitoring cycles, that is, T = {l_{1}, l_{2}, l_{3}, …, l_{i}, l_{i+1}, …, l_{L}}.
Let EZ_{j}(s_{i}) be the energy consumption of monitoring a target (z_{j}) once by sensor node s_{i}, ER(s_{i}) be the energy consumption of receiving monitoring data once on sensor node s_{i}, and EF(s_{i}) be the energy consumption of forwarding monitoring data once on sensor node s_{i}. BE(s_{i}) denotes the battery capacity of sensor node s_{i}.
3.2. Energy Harvesting Model
In this work, we mainly consider the environmental monitoring for an EHWSN. We take solar power as the energy supply and use a widely adopted environmental energy harvesting assumption, that is, the harvesting energy of each sensor node in a future period is uncontrollable but predictable through its historic energy harvesting profile. Moreover, the consumption energy of each sensor node is less than the harvesting energy. For a longperiod monitoring task, the monitoring frequency for each target is determined by the usable energy of the sensor node. Furthermore, we assume that a monitoring period is divided into L monitoring cycles, and when one monitoring cycle ends, the next recharging pattern and monitoring cycles are repeated. In recent years, some prediction approaches to harvesting energy have been widely adopted [29, 30]. Here, we take the widely used energy prediction algorithm in [29], that is, the exponentially weighted movingaverage (EWMA) algorithm. The specific formulation of energy prediction is as follows [29]:where a denotes the given weight (0 < a < 1) and E_{h}(l_{i}) denotes the prediction value of the amount of harvested energy at monitoring cycle l_{i}. E_{h}(l_{i} − T) is the actual amount of energy harvested in the previous monitoring period. According to the above formulation of energy prediction, we define the amount of energy, SE(s_{i}, l_{i}), for sensor node s_{i} ∈ S in the next monitoring cycle as follows:where BE(s_{i}, l_{i}) is the battery capacity and RE(s_{i}, l_{i}) is the residual energy of sensor node s_{i} at current monitoring cycle l_{i}.
4. Problem Description and Formulation
In this section, we first describe the requirement of monitoring quality, coverage, and connectivity in EHWSNs. Thereafter, we present the problem formulation of maximizing the monitoring frequency with guaranteed target coverage and connectivity in an EHWSN.
Section 2 indicates that the traditional studies on the target coverage problem have mainly focused on maximizing the network lifetime while maintaining coverage and connectivity or kcoverage and kconnectivity. However, for an EHWSN, the network lifetime is no longer a major problem because the energy of a sensor node can be harvested from its environment (such as solar). Therefore, the key problem should be to improve the monitoring quality. Although the literature [20] considered the qualityaware target coverage algorithm, this monitoring quality refers to the number of sensor nodes covering a target and the number of time slots for a target covered in a monitoring period. Given that this metric in literature [20] cannot guarantee that each target is covered in the total monitoring period, this metric of qualityaware target coverage does not effectively reflect the monitoring quality.
For the target coverage and monitoring for the EHWSN, the following factors must be considered into monitoring quality, such as the monitoring frequency and fairness of monitoring frequency for targets. Furthermore, target coverage and connectivity should also be fundamental requirements for target monitoring in an EHWSN. To understand the monitoring quality, we explain the influencing monitoring quality and present some fundamental requirements, which are shown in Figure 1.
Figure 1 indicates that the following problems must be considered to improve the quality of monitoring under guaranteed target coverage and connectivity in EHWSNs. First, in addition to maximizing the monitoring frequency for each sensor node, fairness must be considered. Second, each target must be covered by at least one sensor node at each monitoring period. Third, according to the transmission range of a sensor node, a connected path between each target and sink node should be established.
Therefore, we aim to maximize the monitoring frequency based on fairness under guaranteed target coverage and connectivity in EHWSNs. Specifically, we consider the maximizing monitoring frequency as the quality of monitoring and take it as the optimization objective. The constraints mainly include the monitoring fairness, target coverage, and connectivity. The problem is defined as follows:
In the above formulation, FM_{t}(z_{i}) denotes the monitoring frequency for the target (z_{i}) covered by a sensor node at monitoring cycle t. d denotes the difference in monitoring frequency for sensor nodes covering any two targets. N_{t}(z_{i}) denotes the number of sensor nodes covering target z_{i} at monitoring cycle t. C(z_{i}) denotes the set of sensor nodes covering target z_{i}. P(C(z_{i}), R) denotes the connectivity between the sink node and any sensor node covering target z_{i}. If target z_{i} is connected to the sink node, then P(C(z_{i}), R) = 1; otherwise, P(C(z_{i}), R) = 0. In formula (3), the optimization objective is to maximize the monitoring frequency of sensor nodes covering all targets. Formulas (4)–(7) are the main constraints. In (4), the constraint mainly reflects the fairness of monitoring frequency for each target, that is, the difference in monitoring frequency between any two targets is less than d. In (5), to guarantee that each target is covered by at least a sensor node, more than one sensor node is required to cover target z_{i}. In (6), all sensor nodes covering targets must be connected to the sink node, that is, connectivity must be guaranteed.
In literature [20], Ren et al. considered the problem of the coverage utility with connectivity and proved that the problem is NPhard. Furthermore, Gaudette et al. [28] believed that maximizing the quality of coverage under connectivity is a nonlinear optimal control problem. In the problem defined above, in addition to coverage and connectivity, maximizing monitoring frequency and fairness are considered. In this context, we know that the above optimization problem is also NPhard. Therefore, we provide an efficient heuristic algorithm based on graph theory to effectively solve the problem (Section 5).
5. Description of Proposed Algorithm (MFTCC)
In this section, we present a heuristic algorithm for solving the proposed optimization problem, that is, the optimization algorithm for maximizing monitoring frequency with guaranteed target coverage and connectivity (MFTCC). First, the idea of the proposed MFTCC algorithm is introduced. Thereafter, a detailed description of the MFTCC algorithm is presented.
The proposed MFTCC algorithm guarantees that each target is covered by a sensor node and the connectivity between the target and sink nodes. Moreover, it reflects the fairness of the monitoring frequency of sensor nodes covered targets. Before presenting the MFTCC algorithm, we present the idea of achieving the MFTCC. The MFTCC algorithm utilizes graph theory to solve the problem presented in Section 4. To solve this problem, we define link weight and the energy consumption for monitoring once based on the transmission path. Figure 2 shows the definition of link weight. The value of each link weight is equal to the minimum energy between two sensor nodes. The energy of each node is equal to the residual battery plus the harvested energy of each sensor node. Subsequently, we define the energy consumption for once monitoring based on the transmission path, as is shown in Figure 3.
Figure 3 indicates that the information on the monitoring target must be transmitted to the sink node, that is, the transmission paths must be established between the sensor nodes and the sink node. Therefore, we must define the energy consumption for the monitoring and relay nodes. Figure 3 shows that the energy consumption of monitoring node s_{1} is equal to EZ_{1}(s_{1}) + EZ(s_{1}) and that relay node s_{i} is equal to ER(s_{i}) + EF(s_{i}). Section 4 indicates that the target coverage and connectivity between the sensor nodes and the sink node in an EHWSN are important. However, guaranteeing that each target is covered by sensor nodes under the connectivity requirement is difficult to achieve. To achieve the condition, we first establish the virtual connection between targets and sensor nodes. Specifically, in the sensing range of each sensor node, each target establishes a connection with the sensor node. For instance, as shown in Figure 4, the dotted line is the connection between each target and sensor nodes in the sensing range.
In Figure 4, if the path between each target and sink nodes exists, then the target coverage and connectivity are solved. In this work, we must maximize the monitoring frequency. Moreover, in monitoring targets, each sensor on the path will consume communication energy. Therefore, according to the optimization objective in Section 4, the maximization of the monitoring frequency based on the energy consumption of communication must be solved. In this context, we add a virtual source node (Sr) into the EHWSN, and the source node connects with each target node z_{i}. Figure 5 shows such final network.
In Figure 5, we further define the link weight between the virtual source and sensor nodes as s_{i} ∈ S. We know that the energy consumption of monitoring target z_{j} once by sensor node s_{i} is EZ_{j}(s_{i}). Thus, these link weights between the virtual source and sensor nodes are defined as follows:where (Sr, z_{i}) indicates that the value of the link weight is equal to the energy of monitoring target z_{j} once by sensor node s_{i}. It is the minimum consumption energy of monitoring a target once for each sensor node on the path between the target and sink nodes.
According to the definition of link weight, we can transform the optimization problem in Section 4 into the maximum monitoring energy flow problem between virtual source node Sr and the sink node. On the basis of definition (8) and the maximum monitoring energy flow, the number of covering targets can be calculated. Moreover, solving the maximum monitoring energy flow can guarantee the connection between the targets and the sink node. Therefore, the detailed procedure of the proposed MFTCC is described in Algorithm 1.

In Algorithm 1, the weights for all link are calculated on the basis of (Sr, z_{i}) = (z_{i}, s_{i}) = EZ_{j}(s_{i}), (s_{i}, s_{j}) = min(SE(s_{i}, l_{t}), SE(s_{j}, l_{t})) in line 1, and some variables are initialized (line 2). Node decomposition is implemented in line 3 (as shown in Figure 6). Node decomposition aims to ensure that the energy of each node can be updated timely by calculating the feasible path.
In lines 4–29 (as shown in Figure 7), the objective is to seek m feasible paths based on the maximum monitoring energy flow. m feasible paths indicate that m target nodes are monitored simultaneously. If the feasible path does not exist or m target nodes are not monitored simultaneously, then the calculation of feasible path (lines 9–11) is skipped/exited. From lines 12 to 26, the link weights of feasible path are updated on the basis of the different types of node. The update of link weights is based on the maximum flow theory of an undirected graph; that is, the forward link is reduced by the corresponding energy value, and the weight of the reverse link is increased by the same energy value. When the feasible path, including node z_{i}, exists, the target node can be monitored once, and one is added to the number of monitoring (line 27). When m feasible paths exist and are calculated, each link in G_{d} (V′, E′) is reset according to the types of two nodes for each link (lines 28–32). Thereafter, the next m feasible paths are calculated until the number of feasible paths is less than m. That is, the residual energy in the network does not supply the monitoring for m target nodes simultaneously.
6. Distributed Implement Scheme of MFTCC
In this section, we propose and explain the distributed implement scheme of the proposed MFTCC algorithm.
The proposed distributed algorithm is more suitable for the practical deployment in WSNs. In this section, the distributed implementation of the proposed MFTCC is presented, and the distributed implementation is performed using the neighbor nodes’ information of each node. The central MFTCC algorithm in Section 5 indicates that the distributed algorithm must solve the following problems. First, the central MFTCC algorithm in Section 5 must add a virtual source node (Sr) into the EHWSN. However, the distributed approach is not achievable. Moreover, the distributed approach must solve the fairness of monitoring target for sensor nodes.
To solve the abovementioned problem, we first present the design idea of the distributed implementation of the MFTCC algorithm. The implementation procedure is mainly composed of the following three parts. In the first part, each sensor node exchanges residual energy with neighbor sensor nodes. Thereafter, each sensor establishes a connection relationship based on the node decomposition. In the second part, all sensor nodes covering the targets monitor a time in the beginning of a monitoring cycle and send the energy information of all nodes in the transmission path to the sink node. Subsequently, the frequency of monitoring in the next monitoring cycle is calculated on the basis of the collected energy information of the sink node. In the final part, the sink node sends feedback to all sensor nodes to update the target monitoring frequency of the next monitoring cycle.
The detailed steps of the distributed MFTCC algorithm are summarized in Algorithm 2.

7. Analysis of MFTCC Algorithm
In this section, we first present the analysis of the proposed MFTCC algorithm, which includes the lower and upper bounds of the maximum monitoring frequency calculated by the MFTCC algorithm, the coverage and connectivity of the target nodes, and the difference in monitoring frequency between any two target nodes. Subsequently, the complexity of the MFTCC algorithm is analyzed.
The proposed MFTCC algorithm focuses on solving the qualityaware target coverage problem while guaranteeing target coverage and connectivity in the EHWSN. We define the maximum monitoring frequency as the optimization objective of coverage quality, and the fairness of monitoring for each node is considered. Thus, we analyze the performance of the maximum monitoring frequency and the fairness of monitoring for the proposed MFTCC algorithm, which are as follows.
Theorem 1. Given the monitoring network G(V, E), if the number of target nodes is equal to m and the number of monitoring cycle is L, then the lower and upper bounds of the maximum monitoring frequency calculated by the MFTCC algorithm are as follows:where k is a constant and equal to the energy capacity of the minedgecut divided by the number of target nodes (m).
Proof. We know from Section 3 that the value of monitoring frequency for a target node depends on the energy of the sensor nodes in the monitoring network G(V, E). In Section 4, the MFTCC algorithm establishes all link weights ((s_{i}, s_{j})) in the monitoring network G(V, E) based on the energy of the sensor nodes. The problem of maximizing the monitoring frequency for the target nodes is converted into the maximum energy flow problem. In the monitoring network G(V, E), the added virtual source node (Sr) is connected to all target nodes. In the MFTCC algorithm, denotes the calculation result of maximum energy flow, which means that all target nodes are monitored once; that is, the total monitoring count is . In the MFTCC algorithm, when the maximum energy flow calculation is finished and the link weight is updated, the MFTCC algorithm continues to calculate the maximum energy flow until the number of augmented flows is less than m; that is, k and exist in L monitoring cycles, and when , the MFTCC algorithm will end. The maxflow mincut theorem indicates that the maximum flow between virtual source node Sr and the sink node is equal to the sum of the energy capacities of the minimum cut edge set. Therefore, the value of k is rounded down to the sum of the energy capacities of the minimum cut edge set divided by the number of target nodes (m).
Theorem 2. Given the monitoring network G(V, E), let the number of target nodes be equal to m. The MFTCC algorithm can guarantee the cover of target nodes and the connectivity to the sink node. Moreover, the difference in monitoring frequency between any two target nodes is less than or equal to 1, that is, , 1 < t < L.
Proof. Theorem 1 and Section 4 show that each target node is covered by at least one sensor node, and the monitoring information of each target node is transmitted to the sink node by a feasible path. Therefore, the MFTCC algorithm can guarantee the cover of target nodes and the connectivity to the sink node. We prove by contradiction that . Let , 1 < t < L and ; if , then , 1 < t < L. From the MFTCC algorithm, when all monitoring cycles are considered, and . According to Theorem 1, if m = 1, then . The result leads to a contradiction with Theorem 1.
7.1. Complexity Analysis
Given monitoring network G(V, E) with n sensor nodes to monitor m targets and l_{e} links, for the total monitoring period (T), including L monitoring cycles, let the sum harvested energy capacity of the minimum cut edge set in monitoring period T be EC_{T}. Assuming that the energy consumption of monitoring each target in the minimum cut edge set is ET, the loop count is l_{c} = EC_{T}/ET in lines 4 to 32 of the proposed MFTCC algorithm. In MFTCC, the node decomposition in lines 1 to 3 makes two nodes to convert to four nodes and add four links. Thus, the computational complexity is O(n + 4l_{e}). The computational complexity of finding feasible path P based on the minimum spanning tree algorithm in line 7 is O(4n^{2}). In lines 11 to 30, due to the node decomposition operation, the longest path is less that 2n − 1. Thus, the computational complexity is O(3 (2n − 1) + m). In line 32, the number of updating link weights is less than m, and the computational complexity is O(m). Therefore, the total time complexity of MFTCC is O(l_{c}(n + 4l_{e} + 4n^{2} + 3 (2n −1 ) + 2m).
8. Performance Evaluation
In this section, we evaluate the performance of the proposed MFTCC algorithm through the following experimental simulation. We first verify the performance of the proposed MFTCC algorithm in terms of the maximum monitoring frequency, energy usage ratio, and the fairness of targets monitoring for 50 sensor nodes and 10 target nodes. Thereafter, we also evaluate the above performance, the throughput, and the endtoend delay performance of networks with 50 nodes to 100 nodes and 10 targets to 35 targets.
8.1. Performance of Monitoring Frequency, Energy Usage Ratio, and Fairness
We establish an EHWSN with 50 sensor and 10 target nodes, which are uniformly distributed in 1000 × 1000 m^{2} regions. The transmission and monitoring ranges of all sensor nodes are 250 m and 200 m, respectively. The distribution of the sensor and target nodes is shown in Figure 8(a), and the communication network among the sensor nodes is based on the transmission range in Figure 8(b). The existing algorithms mainly focus on the quality of coveragebased target connectivity in EHWSNs. Few algorithms focus on solving the maximum monitoring frequency problem with guaranteeing targets coverage and connectivity in EHWSN. Therefore, we compare our proposed MFTCC with the target monitoring in random based on coverage utility (TMRCU) [17] and target monitoring in random based on the shortest hop path (TMRSHP). TMRCU presents a modification of the proposed algorithm in [17]. Given that the proposed algorithm mainly considers the coverage utility, they focused on constructing a utility forest consisting of L trees to transmit monitoring information. They did not consider the frequency of monitoring targets. Therefore, the TMRCU randomly monitors the targets covered by sensor nodes in constructing a utility forest. Moreover, for the current communication network, the transmission path of monitoring information is established on the basis of the routing algorithm. Usually, the shortest path is used for the information transmission [5]. TMRSHP constructs a shortest hop path to transmit the monitoring information from the target to sink nodes. Tables 1 and 2 show the performance comparison results.
(a)
(b)
In Table 1, the average maximum monitoring frequency and energy usage ratio of the proposed MFTCC algorithm are greater than those of other algorithms. Table 1 shows that the high energy usage ratio of our proposed MFTCC can make the best of the harvested energy. Moreover, the low energy usage ratio of other algorithms results in harvested energy waste on the sensor nodes. Table 1 also indicates that the monitoring frequency of proposed MFTCC in unit energy consumption is lower than that of other algorithms, indicating that the proposed MFTCC increases the maximum monitoring frequency at the cost of energy consumption. Given that the sum of energy consumption is smaller than the harvested energy, the proposed MFTCC could improve the monitoring frequency of the target nodes. Table 2 presents the comparison of the fairness of target monitoring for different algorithms. In Table 2, the maximum difference in monitoring frequency between any two target nodes of our proposed MFTCC algorithm is 1. However, TMRCU and TMRSHP are 8 and 10, respectively. The result corroborates that our proposed algorithm exhibits fairness in target monitoring.
To further validate our proposed MFTCC algorithm in terms of maximum monitoring frequency and energy usage ratio, we consider networks with 50 to 100 nodes and 10 to 35 targets randomly placed in a 1000 m × 1000 m field. Similarly, the transmission range of all sensor nodes is 250 m, and the monitoring range is 200 m. Moreover, we consider the energy consumption of monitoring and transmitting a monitoring task as an energy unit and assume that the harvesting energy of each sensor node is randomly generated in the range of 10 to 30 energy unit. Table 3 lists the specific simulation parameters. We compare our MFTCC with TMRCU and TMRSHP. Figures 9 and 10 present the comparison results of maximum monitoring frequency and energy usage ratio, whereas Figure 11 shows the comparison of the fairness of target monitoring.
Figures 9 and 10 indicate that the average maximum monitoring frequency and the energy usage ratio of the proposed MFTCC algorithm are smaller than those of the TMRCU and TMRSHP algorithms. In Figure 9, the average maximum monitoring frequency of the proposed MFTCC increases greatly with the increase in network node scales, and the proposed MFTCC obviously outperforms the TMRCU and TMRSHP algorithms. For the TMRSHP algorithm, the average maximum monitoring frequency remains the same from 50 sensor nodes to 100 sensor nodes, indicating that the increase in sensor nodes cannot improve the performance of monitoring for TMRSHP. Similarly, the energy usage ratio of the proposed MFTCC algorithm is apparently higher than that of the other algorithms. Moreover, Figure 10 shows that the energy usage ratio presents a decreasing trend with the increase in sensor nodes. In Figure 11, we present the comparison of the fairness of target monitoring. Figure 11 shows that the maximum differences in monitoring frequency between any two target nodes of our proposed MFTCC algorithm for 50 to 100 nodes are both 1. However, the maximum differences in the monitoring frequencies of the TMRCU and TMRSHP algorithms are higher than those of the proposed MFTCC algorithm, validating the proposed MFTCC algorithm in terms of the fairness of target monitoring.
8.2. Evaluation of Network Performance
To further verify the validation of the network performance of the MFTCC algorithm, we evaluate the performance of these different algorithms (including the proposed algorithm) by ns2 simulations. We consider networks of 50 to 100 sensor nodes and 10 + (S − 50)/2 target nodes randomly placed in a 1000 m × 1000 m field. The transmission and monitoring ranges use the settings in Table 2. Before the simulation, the routing is established by the transmission path, and the transmission between the sensor nodes and the sink node utilizes a UDP connection. CBR flow is used between each pair of nodes. The length of the monitoring packet is 128 bytes, and the sending rate of each CBR flow is fixed at 2 Mbps. We simulate four algorithms, including TMRCU, TMRSHP, the proposed MFTCC, and the distributed MFTCC algorithm. We compare the performance of these algorithms by measuring the throughput and average endtoend delay. Figures 12 and 13 exhibit the results.
Figure 12 shows that the throughput of the proposed MFTCC algorithm is higher than that of other algorithms, and the throughput increases with the number of sensor nodes. For the design of our proposed algorithm, we consider the maximum monitoring frequency and therefore propose the MFTCC to have an obvious increasing effect on the throughput. In Figure 13, TMRSHP is based on the shortest hop path to transmit the information of monitoring, which has the lowest throughput and endtoend delay. The endtoend delay of our proposed MFTCC is higher than that of other algorithms, indicating that the average length of transmission paths may be increased, thereby increasing the endtoto delay. However, for the monitoring application of EHWSNs, the monitoring information mainly focuses on data monitoring but not video monitoring, which indicates that the monitoring application of EHWSNs is often focused on measuring the maximum data throughput rather than the endtoend delay. Figures 9 and 12 indicate that the proposed MFTCC algorithm achieves the maximum monitoring frequency and presents a good throughput performance. Thus, achieving maximum monitoring frequency and throughput is important for improving the monitoring performance in EHWSNs.
9. Discussion and Conclusion
The coverage problem is one of the most important research issues in WSNs. Related studies have mainly focused on area, target, and barrier coverages. Most of the works have concentrated on improving the coverage quality of batterypowered WSNs. Many energy efficient coverage algorithms have been proposed to extend the lifetime of WSNs. In recent years, energy harvesting technologies have been adopted to solve the problem of limited energy supply in WSNs. Given the continuous energy supply in EHWSNs, the traditional coverage algorithms for batterypowered WSNs are unsuitable for the qualityaware target coverage problem in EHWSNs. In this work, we investigated the problem of maximizing the monitoring frequency while guaranteeing target coverage and connectivity in EHWSNs. Unlike previous works, we not only consider the monitoring quality but also guarantee the target coverage and connectivity. More importantly, we also consider the fairness of each target monitoring. First, the factors affecting the maximum monitoring frequency in the monitoringcycle model of EHWSN are analyzed, and the problem formulation is presented. To solve this problem, we define the link weight on the basis of the residual battery and the harvested energy of each sensor node and construct the virtual connection between targets and sensor nodes. We then devise a centralized MFTCC algorithm on the basis of graph theory and a distributed approach. We also analyze the lower and upper bounds of the maximum monitoring frequency calculated by the MFTCC algorithm. By experimental simulations, our proposed MFTCC algorithm achieves the highest monitoring frequency and energy usage ratio in a given monitoring cycle. Given that the proposed MFTCC algorithm can dynamically select the relay nodes based on the harvested energy of the sensor nodes in transmission progress, the simulation results affirm that the proposed MFTCC algorithm can achieve higher monitoring quality and energy usage ratio than the TMRCU and TMRSHP algorithms. This scenario also indicates that the proposed MFTCC utilizes the harvested energy and improves the monitoring coverage quality. Furthermore, the proposed MFTCC algorithm presents a better performance than other algorithms in terms of the fairness of target monitoring. The maximum difference in monitoring frequency between any two target nodes in the proposed MFTCC algorithm is only 1, whereas those in the TMRCU, TMRSHP algorithms exceed 8. In terms of network performance, the ns2 simulations also demonstrated that although the proposed MFTCC algorithm has a high average endtoend delay, it can effectively increase the throughput, also validating the maximum monitoring frequency. Thus, in data monitoring using EHWSNs, the proposed MFTCC algorithm is more promising for qualityaware monitoring with guaranteed target coverage and connectivity than the traditional coverage algorithms.
In future work, we will continue to study the target coverage problem by considering the randomness of energy harvesting. Owing to the random dynamics of harvested energy, the longterm coverage performance must be considered to take full advantage of the harvested energy. Therefore, the target coverage problem, considering the longterm coverage quality, for EHWSNs is the direction of future research. Moreover, the longterm performance of the video target coverage in EHWSNs is also a future research plan.
Data Availability
The related simulation data used to support the findings of this study are available from the corresponding author upon request.
Conflicts of Interest
The authors declare no conflicts of interest.
Acknowledgments
This research was supported by the Jiangxi Provincial Department of the Education Science and Technology Project (GJJ171013), the National Natural Science Foundation of China (grant no. 61401189), the Natural Science Foundation of Jiangxi Province, China (grant no. 20161BAB212036), and the Open Research Fund of the Jiangxi Province Key Laboratory of Water Information Cooperative Sensing and Intelligent Processing (grant nos. 2016WICSIP023, 2016WICSIP028, and 2016WICSIP030).