MMQT: Maximizing the Monitoring Quality for Targets Based on Probabilistic Sensing Model in Rechargeable Wireless Sensor Networks

In wireless sensor networks (WSNs), target coverage is an important issue which aims at finding a set of sensors to monitor the targets for maximizing both the surveillance quality and network lifetime. However, most of them assumed that each sensor is battery powered and the Boolean Sensing Model (BSM) is applied. Sensors powered by battery have a limited lifetime while the BSM is difficult to reflect the physical features of sensing. This paper proposes target coverage mechanisms, called C-MMQT and D-MMQT, which consider the solar-powered sensors and allows the battery to be recharged for maintaining the perpetual lifetime of sensor networks. The proposed mechanisms apply the Probabilistic Sensing Model (PSM) and consider that different targets have different importance. Two challenges have been overcome in this paper. First, each sensor is well scheduled for switching between recharging and working states for maintaining its perpetual lifetime since its battery is solar powered. Second, the sensors that are able to monitor the common target are well scheduled for cooperative sensing to maximize the surveillance quality since PSM is applied. Two efficient sensor schedules are proposed to maximize the surveillance quality of the bottleneck target which has the lowest surveillance quality. Performance study shows that the proposed mechanisms outperform the existing mechanisms in terms of Quality of Monitoring, Average utility, Fairness and Efficiency index.


I. INTRODUCTION
Wireless sensor networks (WSNs) are composed of many sensor nodes that are randomly deployed in the monitoring area. These sensors are tiny devices that are embedded with microcontroller unit, sensing and communication hardware components for supporting functions including data processing, communication and sensing [1], [2].
In general, sensor devices have some resource limitations, including battery life cycle, computational power and memory. Therefore, during the network operation, the energy efficiency of nodes plays a major role because the replacement of the battery is not possible in most of the applications [3]. According to different applications, coverage problems are The associate editor coordinating the review of this manuscript and approving it for publication was Nabil Benamar .
classified into three categories. The first one is barrier coverage which aims to schedule a minimal number of sensors to detect the intruder crossing a boundary region. The second one is area coverage, which aims to schedule a set of sensors to monitor a given area such that the number of working sensors is minimal while the monitoring region contains no coverage hole. The last one is target coverage, which aims to monitor a given set of targets with the highest surveillance quality. In WSNs, the target coverage problem is one of the most important issues where sensors are responsible for monitoring the important targets and reporting if any suspicious event occurs near these targets.
Since sensors are generally powered with batteries that have limited energy, efficiently scheduling the sensors is an important concern for better energy management of a given WSN. Recent studies are divided into two categories for VOLUME 8, 2020 This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/ prolonging the network lifetime, the first category is energy conservation technologies [1]- [5] while the second category is energy transfer technologies [6]- [15]. Energy conservation techniques have been widely discussed in WSNs. In the past years, studies [1]- [5] proposed several sleep-awake scheduling mechanisms for energy conservation of the sensor nodes. By applying the scheduling mechanisms, sensors can periodically switch between sleep and awake modes. The sensor saves its energy consumption in the sleep mode while it performs the sensing and communication tasks in the awake mode. However, reducing the energy expenditure rate can only prolong the network lifetime. The sensors eventually exhaust their energy even when they apply the efficient sleep-awake mechanisms.
To achieve the perpetual lifetime of sensor networks, recent studies [6]- [15] proposed battery charging technologies. In literature, these studies can be further classified into two categories: wireless energy transferring and environmental energy harvesting technologies.
The wireless energy transferring technologies [6]- [10] mainly transmitted the electrical energy from a power transmitter to a power receiver without the interconnecting wires. The wireless power transmitter periodically moved towards the sensor and then recharge its battery when the sensor runs out of its battery. Studies [6]- [10] assumed that wireless power transmitters were mobile sinks and they can recharge the sensor to support its perpetual lifetime. However, the wireless power transmitter took a long time and consumed a large amount of energy to visit all the sensor nodes, especially for a large-scale monitoring region. On the other hand, environmental energy harvesting [11]- [15] is an efficient way to cope with the energy problem. There are lots of environmental energy resources, such as wind, solar, thermal and so on. Solar power is the most promising among all of the environmental energy resources [16]. Using solar power, the sensors can recharge its battery without mobile sink moving toward any sensor because the scale of sunlight is extensive. As a result, environmental energy harvesting can reduce the extra energy consumption.
To avoid the hardware cost for the replacement of battery and the energy consumption of wireless power transmitters, this paper investigates the target coverage issue for the solarpowered sensor networks. The challenge is that energy harvesting is usually insufficient to support the uninterrupted operations of sensors. In general, it is necessary to make a duty cycle for scheduling each sensor staying in charging or working states. It is a fact that the surveillance quality of each target for a given time slot highly depends on the cooperative sensing of those sensors staying in the working state in a certain time slot. Consequently, how to schedule the sensors such that the lowest surveillance quality can be maximized is still a big challenge and needs to be further investigated.
This paper assumes that the sensor nodes can recharge its battery while monitoring the point of interests (POIs) at the same time, which reflects the capability of the most practical sensors. The event detection probability for each POI depends on the distance between the sensor and the POI. The problem is how to design an activation schedule for the sensors to achieve the highest surveillance quality while maintaining the perpetual operation of the networks.
The key contributions of the proposed MMQT mechanisms are itemized as follows: A. MAINTAINING THE PERPETUAL NETWORK LIFETIME The proposed MMQT mechanisms consider the working and recharging schedules for maintaining their perpetual lifetime. This strategy further guarantees that the recharged energy of each sensor satisfies the required energy for working operations in each cycle.

B. CONSIDERING THAT POIs HAVE DIFFERENT IMPORTANCE
Different from existing studies [11]- [15], the proposed algorithm considered that different POIs might have different importance since they play different roles depending on the tasks. The proposed MMQT guarantees that the POIs with the higher importance would have a higher quality of monitoring (QoM).

C. THE PHYSICAL FEATURES OF THE SENSOR ARE TAKEN INTO CONSIDERATION
This paper applies the PSM to evaluate the surveillance quality which can reflect the physical features of sensing. Most of the existing works [12]- [15] applied BSM to develop the target coverage algorithms. Their estimations of coverage quality were not accurate and might result in coverage holes in the applications.

D. ACHIEVING HIGH SURVEILLANCE QUALITY FOR EACH POI
Study [14], [15] did not guarantee that all the POIs in the sensor network are covered at any given time. The proposed MMQT achieves high surveillance quality for each POI by allocating an unscheduled sensor to cooperatively monitor the bottleneck POI which has the lowest surveillance quality. As a result, the surveillance quality of the bottleneck POI can be improved and hence the minimal surveillance quality of the POIs is likely to be maximized.
The rest of the paper is organized as follows. Section II reviews the related work and compares them with the proposed MMQT. Section III presents the assumptions, network model and problem formulation. Section IV gives detailed descriptions of the activation scheduling algorithms. Section V investigates the performance improvements against the existing studies. Finally, section VI gives the conclusion and future work of this study.

II. RELATED WORK
This section presents the existing studies related to the target coverage issue in WSNs. In literature, these studies can be divided into two categories: energy conservation and the solar-powered categories. Related studies fall in the energy conservation category assumed that each sensor is battery powered. To extend the network lifetime, most of them scheduled the sensor nodes staying in sleep and the awake modes in turn. In studies [1]- [3], the sensors decided their activation schedule in a distributed manner according to the neighboring information. The sensors were partitioned into a number of subsets, and each of them would take turns to cover the POIs. Although the proposed approaches can prolong the network lifetime, the energy balance issue between different subsets of sensors did not be considered. Study [4] proposed an activation scheduling approach which further considered the density and the energy consumption of each subset of the sensors. Study [5] considered the communication of all sensors and proposed a topology control protocol which can separate the sensors into specific subsets, and maintain the communication of the network. Although studies [1]- [5] can increase the network lifetime of sensors, they did not consider that the sensors can recharge its battery by the environmental energy harvesting. As a result, the battery of the sensor will drain as time goes by.
To provide the perpetual operation of wireless sensor networks, some other studies [11]- [15] fall in the solar-powered category which assumed that the battery of each sensor can be recharged by solar power. Study [11] proposed a robust target coverage for energy harvesting wireless sensor networks. This study considered three novel robust coverage requirements. First, sensor nodes must not expend more than their total harvested energy over T time slots. Second, the energy expenditure of each sensor node should not exceed the energy harvested in each slot. Finally, the energy expenditure of sensor nodes should not exceed the energy accumulated in the current slot. Furthermore, they considered the random energy arrivals in the network and ensures all the targets are monitored continuously. However, it could not guarantee that all the POIs are covered at any given time.
Study [12] addressed the target coverage problem in a solar-powered sensor network where each sensor can control its sensing range. Study [13] investigated the target coverage problem and aimed at maximizing the network lifetime of rechargeable wireless sensor networks. It scheduled sensors in a way that one subset of sensors stayed in an active state while other sensors stayed in a sleep state to recharge their battery. It proposed a linear programming based solution to determine the activation schedule of sensor nodes. Although studies [12] and [13] considered the solar-powered sensors and provides the perpetual operation of wireless sensor networks, they did not consider that different POIs have different importance.
Study [14] considered the quality-aware target coverage problem in an energy harvesting sensor network. For a given monitoring period, the sensors were powered by renewable energy sources and operated in a duty cycle mode. It scheduled a different subset of sensors to be activated in each time slot. As a result, the coverage quality was increased with the number of time slots in which a target was covered. Although study [14] aimed to maximize the coverage quality of the entire network, they did not consider how to balance the QoM of each POIs at any given time and cooperative sensing among sensors.
Study [15] proposed a greedy hill climbing activation scheme which assumed that sensors can either recharge its battery or monitor POIs at the same time. The detection probability of a sensor to some POI depends on the distance between the sensor and POI. The proposed approach firstly calculated the ratio between the recharge and discharge time as its charging period to ensure a sensor can supply the energy which was consumed in the working period. Then it scheduled a sensor to be active in a time-slot aiming to maximize the incremental utility together with the sensor previously scheduled. Although it provided the perpetual operation of wireless sensor networks and maximize the QoM of the entire network, it cannot guarantee that all the POIs are covered at any given time. Furthermore, it did not consider the different importance of different POIs.
The studies [11]- [15] considered the schedule of sensors and the efficiency of solar power. However, they did not consider how to balance the QoM of each POIs at any given time. Furthermore, they did not consider the issue that POIs might have different importance. Table 1 summaries the comparisons between this paper and the existing studies which considered the solar-powered sensor networks. This paper investigates the target coverage problem by considering the PSM. The objective of this paper is to maximize the QoM of the target with minimal QoM. The cooperative sensing is taken into account. The proposed approaches schedule the sensors based on the two-dimensional space time points which consist of different targets and the time slots of each cycle. The cooperative sensing contribution of each sensor will be calculated for each space time point. In each run, one sensor that has the largest cooperative sensing contribution to the bottleneck space time point will be scheduled to be active at that point, aiming to maximize the QoM of the target with the minimal QoM. As a result, the weakest QoM among all targets will be maximized run by run while the perpetual network lifetime can be maintained.

III. NETWORK ENVIRONMENT AND PROBLEM FORMULATION
This section firstly introduces the network environment and assumptions of the considered solar-powered sensor networks. Then, the problem formulation of this study is presented.

A. NETWORK ENVIRONMENT
This paper assumes that a set of m POIs O = {o 1 , o 2 , . . . , o m } is distributed over a two-dimensional region R with size L x W , where L and W are the length and width of R, respectively. Assume that POIs have different importance since they play different roles depending on the executing tasks. Let w i be the weight of POI o i . The POI with higher importance would have a larger weight value. In region R, there are a set of n solar-powered homogeneous sensors, denoted by S = {s 1 , s 2 , . . . ,s n }, which are randomly deployed over the monitoring region. The sensing radius of each sensor is denoted by r s , which is the same for all the sensors and the clocks of all sensors have been synchronized. Fig. 1 gives a scenario of the considered network where the flag and node represent the POI and sensor, respectively.

B. SENSING MODEL
In this paper, the Probabilistic Sensing Model (PSM) [17] is applied. The following gives an example to illustrate the PSM. As shown in Fig. 2, the red point denotes the POI which is monitored by the sensor s j . The sensing range of any sensor s j is divided into two regions, including the guarantee zone which is marked with a light violet color and the uncertain zone which is marked with light green color. Let Z gutee and Z uncer denote the guarantee and uncertain regions of the sensing range of any sensor, respectively. Let r g s and r s denote the radiuses of Z gutee and Z uncer , respectively. When the event occurs in the region Z gutee , the detection probability of sensor s j is 100%. However, in case the event is occurred in Z uncer , the detection probability of an event by the sensor s j is decreased with the distance between the sensor s j and POI. Let where the parameters λ and γ are the path-loss exponents of the sensing signal strength and could be adjusted according to the physical properties of the sensor. In the recharging-only state, each sensor has to consume some energy to activate its solar-panel. Let e min be the energy reserved for solar-panel activation. Let e rec denote the energy that the sensor can obtain from the solar-power in the recharging-only state in one time slot. That is to say, in the recharging-only state, the sensors would gain e rec −e min energy in one time slot. The sensors would collect some information from the POIs which they covered in the sensingonly state and transmit the information to the sink node after the sensing-only state. Therefore, they have to reserve certain energy for transmission after the sensing-only state. Let e sen denote the energy consumption of sensors in one time slot in the sensing-only state, and e rpt denote the reserve energy for the transmission after the sensing-only state. Therefore, the entire energy consumption of the sensors in the sensingonly state in one time slot is e sen + e rpt and reserve at least e min for triggering the recharge circuit. The energy of sensors does not change in the sleeping state.
This work used a simple battery model with no energy loss or leakage. Although the sensor can recharge its battery by solar power, we assume that the battery capacity is limited. As a result, the sensors cannot unlimitedly store the energy in the battery capacity. Let e max be the upper bound of the battery capacity. Once the sensors remaining energy is less than e min , then the sensor is treated as dead. Fig. 3 depicts an example of residual energy of sensor s j at different time slots. It is assumed that the recharge and discharge ratio is 4:1. Therefore, each sensor can stay in a sensing & recharging state for one time slot and stay in recharging-only state for the remaining four slots. Let e j,k denote the remaining energy of sensor s j at the starting time point of the slot t k . As shown in Fig. 3, if the sensor s j was in the recharging-only state at time slot t k−1 , the e j,k is the smaller one between e j,k−1 plus the increased energy e rec and the upper bound of battery capacity e max . If the sensor s j was in the sensing-only state at time slot t k−1 , then e j,k is e j,k−1 minus the energy consumption e rpt + e sen at time slot t k−1 . The values of α rec j,k , α sen j,k and α slp j,k are defined in Exps. (5), (6) and (7). Therefore, the residual energy of the sensor s j at time slot t k is given in the Exp. (2).
Let τ denote the length of a time slot. There are three physical parameters which impact the energy of each sensor, including battery capacity, discharging rate and recharging rate denoted by e max , u sen and u rec . The values of e rec and e sen can be calculated by applying Exp.
Let κ denote the ratio of the discharging and recharging rates. The value of κ is shown in Exp. (4).
The time line can be divided into several cycles, each cycle is denoted by T , which consists of ϑ equal sized time slots where ϑ = κ+1. It is obvious that the value of e rec is κe sen such that each sensor can recharge energy for consuming in the sensing state because each sensor has an identical schedule in each cycle.
Let t k denote the k-th time slot in a cycle T . The following further defines three Boolean variables α rec j,k , α sen j,k and α slp j,k , which represent the operation of sensor s j stays at time slot t k . That is, For example, if the sensor s j stays in sensing & recharging state at certain time slot t k , then we have α rec j,k = 1, α sen j,k = 1 and α slp j,k = 0.

D. PROBLEM FORMULATION
This paper addresses the target coverage problem for solarpowered sensor networks. Our objective is to propose an activation schedule algorithm for the sensors which aims to maximize the monitoring quality of the POI with the minimal quality of monitoring among all POIs under the constraint of perpetual network lifetime. This section initially introduces the objective function and then the constraints which should be satisfied when achieving the maximal value of the objective function.
Utility function: Let S i denote the set of sensors that are able to monitor target o i . That is, Let S i,k denote the set of the activated sensors that can monitor the POI o i at time slot t k . The value of S i,k can be evaluated as shown in Exp. (9).
The following introduces the cooperative sensing probability among sensors which monitor the common object at the same time slot. The un detection probability of sensor s j to target o i is 1 − p s j , o i . It implies that the probability of all sensors s j ∈S i,k not detecting the event occurred at the target o i is Let p i,k denote the detection probability of POI o i for any sensor s j ∈ S i,k at time slot t k . The value of p i,k can be derived by Exp. (10).
Let u i,k denote the detection probability of POI o i at time slot t k . This paper defines u i,k as the event detection probability p i,k divided by the weight of the POI o i . That is, The following presents the objective function and the constraints of the solar-powered sensor networks.
Objective function: The objective function of the proposed mechanism is to maximize the minimal QoM at each time slot for a given set of sensors S and the POIs O while maintaining the perpetual lifetime of WSNs. Some constraints given below should be satisfied.
Exp. (14) gives the state constraint which ensures that each sensor can stay in one of the four possible states, including sensing-only, recharging-only, sensing & recharging and sleeping state, at any given time. (14) Recall that each cycle is denoted by T . The following active constraint guarantees that the summation of numbers of the active sensors in all time slots of a cycle is equal to or smaller than the total number of the sensors in the entire network.

2) ACTIVE CONSTRAINT
As shown in Exp. (16), the energy constraint guarantees that the energy consumption of the sensor during the network lifetime is less than or equal to the energy harvested by the solar power. This constraint guarantees the perpetual lifetime of each sensor.

3) ENERGY CONSTRAINT t k ∈T
(e j,k + e rec )α rec j,k ≥ e sen + e rpt α sen j,k ∀s j ∈ S (16) The following section presents the proposed scheduling algorithm which aims to achieve our objective function given in (13) while satisfying the constraints (14), (15) and (16).

IV. THE PROPOSED SCHEDULING ALGORITHM
This paper presents two scheduling approaches to the sensors, called Centralized Target Coverage Mechanism (C-MMQT) and Distributed Target Coverage Mechanism (D-MMQT). The C-MMQT is executed in the base station which should collect all information about the sensors and targets, including their locations and the weight of each target. Then the scheduling results are delivered to the corresponding sensors. Alternatively, applying the D-MMQT, each sensor exchanges its location information with neighbors, makes the decision for its own schedule, and then notifies its schedule to the neighboring sensors. Although the C-MMQT mechanism can schedule the sensors with complete information, it has disadvantages including time and energy consumptions for data collection and scheduling result notification, as well as high computational complexity, as compared with the D-MMQT. The following presents the details of the proposed MMQT mechanisms.

A. C-MMQT MECHANISM
The proposed C-MMQT mechanism assumes that the locations of all sensors and POIs are known. The proposed C-MMQT mechanism consists of two phases: Network Initialization Phase (NI Phase) and Scheduling Phase (SC Phase). In the NI Phase, the length of each cycle and the detection probability of each sensor to each POI should be calculated. In the SC Phase, the sensors will be scheduled one by one according to current cooperative sensing probability.

1) PHASE I: NETWORK INITIALIZATION (NI PHASE)
In the NI Phase, the length of each cycle should be firstly calculated. This paper uses the ratio between the recharge and discharge times as its work period. For example, if there is a sensor that uses two time slots to recharge its battery 50J, that 50J can support the sensor to cover POIs only for a single time slot. That is to say, a sensor can recharge 25J for each time slot in the recharging-only state, but it consumes 50J for a single time slot in the sensing-only state. Therefore, the ratio between the recharge and discharge time is 2/1 and the length of each cycle for all sensors is 2+1. The sensors can only monitor the POIs for one time slot and have to recharge its battery in the other two time slots to guarantee that the sensor satisfies a perpetual lifetime. Assume that there are σ cycles for the entire day. Among them, there are β cycles in the daytime and σ − β cycles in the nighttime.
The sensors have to reserve some energy recharged in the daytime to monitor the POIs in the nighttime since the sensors are solar-powered and they cannot recharge their battery in the nighttime. Let notation e night denote the reserved energy of the sensors for the nighttime. Assume that the reserved energy e night can support the energy consumption during the nighttime. Therefore, the reserved energy e night have to be greater than or equal to the energy consumption of the sensors during the nighttime. That is, Hence, the sensors cannot utilize all of the energy e max in the daytime. They have to deduct the reserved energy e night , and the energy required for sensors to activate its solar panel e min . As a result, the energy that a sensor can utilize in the daytime is shown in Exp. (18).
In terms of recharging-only state, in order to make sure that the energy consumption and harvesting is balancing, the sensors have to supply the energy which was consumed and apportion the reserved energy e night during each cycle in the daytime. The required energy of each sensor during each cycle in the daytime is shown in Exp. (19).
When the base station completes the calculation of the energy consumption and the energy supplement of each sensor during a cycle, it will calculate the recharging and discharging times. The energy consumption of sensors in each cycle is e sen + e rpt . Let ϕ daytime_sen denote the number of time slots that sensors can monitor the POIs in the daytime. The value of ϕ daytime_sen can be calculated by applying Exp. (20).
In the daytime, the proposed C-MMQT mechanism will use the ratio of recharging time ϕ daytime_rec and discharging time ϕ daytime_sen to calculate the length of one cycle. Let notation γ daytime be the ratio of recharging time and discharging time. The γ daytime can be calculated by applying Exp. (22).
The value of γ daytime can be derived by applying the following expression. Fig. 4 depicts the relation of cycles in the daytime and nighttime. Recall that τ denotes the length of time slot. According to the recharging and discharging model, the length of e sen is τ and the length of e rec is κτ . Let L denote the length of a whole day. One day can be divided into two intervals: daytime and nighttime which are denoted by L day and L night respectively. Obviously, we have L = L day + L night and they can be partitioned into a number of equal-length slots as shown in Fig. 4.
Recall that notation e night denotes the energy consumption of sensors in the nighttime. The number of time slots that After the NI Phase, the length of one cycle have been calculated. Then the SC Phase will further schedule the sensors in one cycle to achieve the maximal QoM of the lowest target at any given time slot and to maintain the perpetual operation of the network.

2) PHASE II: SCHEDULING PHASE (SC PHASE)
In the SC Phase, the base station will schedule the sensors for one cycle in the daytime and then in the nighttime separately.
In this phase, there are three main tasks. First, the base station will find the space time points which have the smallest value. Second, it will find the sensors which can maximize the space time point that have the smallest value. Finally, it will schedule one best sensor from the unscheduled sensors. The above mentioned three tasks will be repeatedly performed until all sensors have been scheduled in the cycle. In the following, the three tasks will be described.   In the next two tasks, the base station will schedule one sensor which has the largest contribution to the bottleneck space time point, in terms of QoM.

b: Task 2: Selecting the Best Sensor for the ''Bottleneck''
This task aims to select the best sensor from the unscheduled sensor set to improve the cooperative detection probability of the weakest space time points Let S un_sch denote the set of all unscheduled sensors. The set of S un_sch can be calculated by using the following equation.
The base station is responsible for repeatedly performing this task until all the sensors which have a contribution to (o weak i , t weak j ) ∈ ST weak have been scheduled. Let ℘ weak denote the weakest space time point obtained from the first task. That is, Recall that this task aims to find the best sensor to be scheduled to maximize the QoM of current M QoM . Consider each unscheduled sensor s x ∈ S un_sch . The next issue is to evaluate the contribution to the QoM of current M QoM if sensor s x is scheduled.
Let b weak i,j,x denote the benefit of the sensor s x monitoring o i at t j . The value of b weak i,j,x can be calculated by applying Exp.
Let ρ i,j be a Boolean variable representing whether or not ℘ weak i,j belongs to ST weak . That is, Let B weak i,j,x denote the total benefit of the sensor s x to all weakest space time points in ST weak .
Similarly, let B non_weak i,j,x denote the total benefit of the sensor s x to all space time points not in ST weak . We have Let O x denote the set of targets covered by a sensor s x . The total benefit of the sensor s x to the QoM of all targets o i ∈ O.
where ω is the weight for combining two benefits B weak i,j,x and B non−weak i,j,x . Let B best i,j be the maximal benefit of the weakest space time point (o weak i , t weak j ) obtained by considering all possible s x ∈ S i . We have Let s best i,j denote the best sensor that has the largest contribution to weakest space time point According to the Exp. (40), the base station selects the s best from the S un_sch to monitor the space time point If there is more than one sensor which can maximize the cooperative detection probability of o weak i at t weak j , the base station will select the best sensor s best to monitor the target o weak i at time slot t weak j for obtaining the maximal benefit of surveillance quality. In the following task, the base station will schedule a sensor s best to the bottleneck space time point.

c: TASK 3: SCHEDULING THE SENSOR FOR THE ''BOTTLENECK''
This task schedules the best sensor s best obtained in the second task to monitor the weakest space time point for improving its cooperative detection probability. First, the s best should join the space time scheduling matrix. That is, All elements in theĵ-th column of space time QoM matrix should be updated accordingly, as shown in Exp. (42).
for each oˆi in the coverage of s best . After that, the s best should be removed from S un_sch . That is, The sensor s best also needs to be included in the set S sch of scheduled sensors.
The new weakest space time point should be re-identified by applying Exp. (27). The base station will repeatedly perform the three tasks designed in this phase until all the sensors have been scheduled. Fig. 5 gives an example of selecting the best sensor to improve the QoM of the weakest space time point. Assume  [2,3] and M QoM [3,3] are updated according to the schedule of sensors.
Though the proposed centralized algorithm C-MMQT can efficiently schedule all sensors aiming to maximize the QoM of the target with the minimal QoM, it assumes that the information of all sensors and POIs are known to each sensor. The following subsection further presents a distributed algorithm, called D-MMQT, which only needs to maintain the local information for each sensor.

B. D-MMQT MECHANISM
This section proposed a distributed scheduling algorithm, called D-MMQT. Assume that each sensor is only aware of the information of its neighbors. All sensors are clock synchronized. There are several challenges when designing D-MMQT. The first challenge is that the local information maintained by all nodes might be different, even though they are neighbors. The contradiction among local decisions made by neighbors might exist. To cope with this problem, D-MMQT should guarantee that the larger benefit of the local decision will be the final decision when the decisions exist contradiction. Second, the broadcast packets containing the local decisions might have collisions. The D-MMQT should avoid collision occurrence. To cope with the decision-contradiction VOLUME 8, 2020 In the RB phase, each sensor waits for a back-off time based on the contribution of its scheduling decision. After waiting for the back-off time, each sensor enters the DA phase which broadcasts its decision to notify its neighbors. All neighbors will update its space time QoM and space time scheduling information according to the received decision from neighbors. The following presents the details of each phase.

1) PHASE I: SCHEDULING (SC PHASE)
Each sensor, say s v , in SC phase should perform four tasks. The first task is to calculate the probability of each neighboring sensor to each target covered by s v . Let O v denote the set of targets in the sensing range of sensor s v . Let N v denote the set of neighbors of sensor s v . That is, Similarly, let ℘ weak,v

2) PHASE II: RANDOM BACK-OFF PHASE (RB PHASE)
In the RB Phase, each sensor waits for a random time. Two major reasons for applying the random back-off policy in the second phase. First, the decisions made by a sensor s v . The design of random back-off policy should guarantee that the better decision should be announced earlier and the worse decision should be given up accordingly. Another important reason for applying the random back-off policy is to avoid packet collisions occurred among neighbors. To cope with the contradiction problem and guarantee that better decision should be adopted, the waiting time of each sensor s v should be determined according to the contribution of its own decision. Let R v denote the random back-off time of the sensor s v . Since the random back-off time should guarantee two criteria: (1) decision with larger benefit should be announced earlier and (2)collision avoidance, the value of R v can be determined by applying Exp. (48).
It indicates that R v is inversely proportional to the benefit B v and the number of neighbors of sensor s v . All the sensors would countdown from its back-off time to 0. As shown in Fig. 6, sensors s v and s k have made their decisions D v and D k , respectively. However, the two decisions contradict to each other because both of them schedule the same neighboring sensor s u to work in different time slots (t v j = t k j ). In this example, s k has a larger random back-off value than s v because that D v leads to a larger benefit than D k . During the random back-off period, if s v receives the decision D k = (s k u , o k i , t k j ) from its neighbor s k , it will check if its If it is the case, sensor s v will give up its decision. Otherwise, the sensor s v can still keep its decision and wait for the counter R v achieving zero for broadcasting its decision. Herein, it is noticed that no matter whether or not decisions D v and D k have a contradiction, all sensors which have received the decision D k should update its space time scheduling and QoM matrices according to decision D k = (s k u , o k i , t k j ). Continue the example shown in Fig. 6, Sensor s k should give up its decision D k in the next phase.
The following presents the check conditions for identifying if the contradiction existed between two decisions D v and D k . Let ξ i,v sensor be the Boolean variable representing whether or not s i u is equal to the s v u . That is, Similarly, let ψ v,k time denote the Boolean variable representing whether or not t v j is equal to t k j . That is, Decisions D v and D k exist contradiction if the following condition holds.
This occurs because of that sensors s v and s k schedule the same sensor s u to monitor certain targets at different time slots. In case that Condition (51) holds, sensor s v should give up its decision and then update its scheduling and QoM matrices according to decision D k .

3) PHASE III: DECISION ANNOUNCEMENT PHASE (DA PHASE)
In the DA Phase, each sensor simply broadcasts its decision which is made in SC phase and updates its scheduling matrix.

V. PERFORMANCE EVALUATION
This section evaluates the performance improvement of the proposed C-MMQT, D-MMQT against the existing Quality Aware Target Coverage Mechanisms (C-QATC, D-QATC) and Greedy Hill-Climbing Activation Scheme (GHCAS). The QATC algorithm [14] aimed to schedule different subsets of sensors. Each sensor set was activated in some certain time slot, which leads to the situation that different subsets of targets can be covered at some certain time slots. The GHCAS algorithm [15], is presented to address the utility based target coverage problem by scheduling a sensor into a timeslot to maximize the incremental utility together with the sensor which is previously scheduled. The following firstly illustrates the simulation environment and then presents the simulation results.

A. SIMULATION MODEL
The simulation parameters are given in Table 2. In the experimental study, the MATLAB is used as the simulation tool. The sensor nodes and the POIs are randomly deployed in the monitoring area as shown in Fig. 7. The size of the monitoring region is 400m × 400m while the number of deployed sensors is ranging from 500 to 2000. The communication radius is 20m while the sensing radius is 10m. The guarantee sensing range for sensor detection is 5m. Let e max and e min denote the initial energy and the energy consumption of sensors to activate its solar panel, which is set at 1210 Joule and 10 Joule respectively. The recharging and discharging rates of the solar battery is 25 Joule/hour and 50 Joule/hour, respectively. That is to say, the ratio of recharging over discharging time periods is 2, and the cycle length is 3 time slots.     algorithm outperforms the C-QATC, D-MMQT, D-QATC and GHCAS in terms of the quality of monitoring of randomly selected targets. This occurs because the proposed C-MMQT considers the bottleneck quality of monitoring of the targets and maximizes the minimal QoM of targets at any time slot and balance their QoM which results in high quality of monitoring. Besides, the C-QATC, D-QATC and GHCAS algorithms aim to maximize the overall coverage quality for the monitoring region. This policy might lead to the imbalanced QoM of each target at any given time because it is possible that a target with the minimal quality still remain with the lowest QoM while the other target with the highest quality obtains the QoM improvement. Fig. 11 further studies the fairness indices of the compared five algorithms. The number of sensors is varied ranging from 500 to 2000 while the number of POIs ranging from 20 to 110. The Fairness Index ζ fairness of quality of monitoring is defined as shown in Exp. (52). Let n denote the number of sensor nodes and x i denote the quality of monitoring of sensor node s i in each cycle.

B. SIMULATION RESULTS
In comparison, the proposed C-MMQT outperforms the other four algorithms in terms of the fairness index. This occurs because the C-QATC, D-QATC and GHCAS did not consider the importance of POIs and the lowest quality of the target. Therefore, in some time slots, some POIs are undetected which results in low fairness. The proposed C-MMQT considers the importance of POIs, finds the weakest space time points and schedules the best unscheduled sensor to improve the quality of the weakest space time point. Therefore, the fairness index of C-MMQT is close to 1. Fig. 12 compares the fairness indices of QoM of 9 randomly selected targets. The observed locations are similar to those as shown in Fig. 10. The fairness index of quality of monitoring can be calculated for a given n time slots or given m locations. Let q i,j denote the quality of monitoring of j-th location at i-th time slot in one cycle. Let ζ j and ζ i denote the fairness indices of the j-th location for n time slots and the i-th slot on m locations respectively. The value of ζ j and ζ i is defined as shown in Exp. (53) and Exp. (54), respectively.
The fairness indices of the 9 randomly selected target locations being approximate to 1 which indicates that the quality of monitoring is stable. Fig. 12(a) compares the fairness indices of three time slots on 9 random locations. As shown in Fig. 12(a), the proposed C-MMQT outperforms the other four C-QATC, D-MMQT, D-QATC, and GHCAS algorithms in terms of fairness index and almost achieves 0.987 for all cases. This occurs because the C-MMQT considers the bottleneck POIs and allocates an unscheduled sensor to cooperatively monitor the bottleneck POIs with the lowest quality of monitoring. Similar to the results of Fig. 12(a), Fig. 12(b) depicts that the proposed C-MMQT outperforms the C-QATC, The proposed algorithm identifies the target with the lowest quality of monitoring and schedules a sensor in order to maximize its quality of monitoring. As a result, the quality of monitoring of all the POIs can be significantly increased, which leads to higher efficiency. However, when the number of POIs increases each sensor can monitor a higher number of POIs in each time slot. Therefore, the contribution of each sensor is high which leads to higher efficiency.   The coverage range of each sensor is set at 10m, 20m, 30m and 40m. The number of POIs is varied ranging from 20 to 110. As shown in Fig. 14, a common trend of five compared algorithms is that the QoMs of targets are increased with the coverage range of a sensor but are decreased with the number of POIs. This occurs because when the number of deployed sensors is fixed and the coverage range of sensor increases, each sensor can have a larger coverage area that can cover more POIs. Therefore, each POIs is much easier to be covered by any sensor which increases the quality of monitoring. On the other hand, the QoMs of targets decrease with the number of POIs. This occurs because when the number of sensors is fixed, some sensors should move to monitor the weakest time slot. Then all the other sensors have smaller monitoring opportunities when the number of POIs increases. Hence, all the other POIs have a lower quality of monitoring. In comparison, the proposed C-MMQT algorithm  outperforms the other four algorithms in terms of the quality of monitoring. This occurs because that the proposed C-MMQT balances the QoM of each POIs at any given time and applies PSM to evaluate the sensing probability which can reflect the physical features of the sensing behavior which results in high quality of monitoring. Fig. 15 further compares the quality of monitoring by varying the VIP ratio. The number of sensors and the number of POIs is set at 500 and 50, respectively. There are three types of different POIs: the low, middle and high importance of POIs. The VIP ratio represents the ratio of the number of each type of PIOs to the total number of POIs. For instance, VIP ratio = (20%, 20%, 60%) represents that the numbers of types 1 and 2 of POIs are equally (20%) while the number type 3 of POIs is 60%, as compared to the total number of POIs. The experimental results show that the C-MMQT outperforms the other four algorithms. This occurs because the C-MMQT considered the importance of POIs and always schedules the sensor to the POIs with higher importance. The third VIP ratio (60%, 20%, 20%) has a higher quality of monitoring when compared to the other two VIP ratios. The main reason is that when the POIs 1 is more important, some sensors which are monitoring the unimportant POIs will be scheduled to monitor POIs 1, leading to a high quality of monitoring of the proposed C-MMQT, as compared with the other four algorithms. Fig. 16 compares the fairness index by varying the VIP ratio. The number of sensors and the number of POIs is set at 500 and 50, respectively. The experimental results show that the proposed C-MMQT has better fairness when compared to the other four algorithms. A common trend as shown in Fig. 16 is that the fairness index gradually increases with the different VIP ratios. In the case of the first VIP ratio (20%, 20%, 60%), fairness is low when compared to the other VIP ratios. This occurs because when the number of sensors is fixed and the maximum number of sensors are scheduled to monitor POIs 3 results in low fairness. On the contrary, the fairness of the C-QATC, D-QATC, GHCAS algorithms is very low compared to the proposed algorithms. Regardless of the VIP ratio, the C-QATC, D-QATC, GHCAS algorithms schedule the sensors to monitors the POIs. Hence, some of the very important POIs are undetected in some time slots which results in low fairness.

VI. CONCLUSIONS
This paper proposes two efficient sensor activation schedules, called C-MMQT and D-MMQT, aiming at balancing the QoM of the POIs at any time slots by scheduling the solar-powered sensors. The proposed mechanisms apply the PSM by considering the importance of POIs and guarantees that all POIs can be well monitored at any given time slot. To maintain the sensor network with a perpetual lifetime, each sensor is carefully scheduled to maximize the minimal QoM of bottleneck POIs at any time slot. The proposed C-MMQT is a centralized approach that identifies the weakest space time point and schedules the sensor which has the maximal contribution for monitoring that point. On the contrary, the proposed D-MMQT is a distributed approach which only maintains the neighboring information and makes its own decision using the local information. Since the decisions among neighbors might contradict to each other, a random back-off policy is adopted based on the contributions of the local decisions. Experimental results show that the proposed C-MMQT achieves better performance than C-QATC, D-MMQT, D-QATC and GHCAS in all cases in terms of quality of monitoring.
The future work would relax the constraints of this paper and allow that sensors are partially recharged and with adjustable sensing range. Furthermore, we would like to study the heterogeneous sensor networks where different sensors have different charging and recharging pattern at the same time. BHARGAVI DANDE received the M.S. degree in computer science and information engineering from Tamkang University, Taipei, Taiwan, in 2019, where she is currently pursuing the Ph.D. degree in computer science and information engineering. Her current research interests include the Internet of Things, wireless sensor networks, and artificial intelligence. VOLUME 8, 2020