1 Introduction

Recently, a wireless sensor network (WSN) is being frequently utilized in military surveillance, disaster prediction [1], health-care monitoring [2], environment monitoring [3] and smart home applications [4], etc [5]. Depending on the application, sensors (SNs) collect various types of environmental data from their surroundings. However, because the SNs have constrained battery capacities, reliable network operation can be difficult or almost impossible. Consequently, conserving SNs’ energies is critical for WSNs’ long-term operation. When the SNs’ batteries run out, replacing them may be a simple solution. Nonetheless, this strategy would be too costly and tedious.

Some WSN efforts are aimed at developing energy-efficient solutions to increase SN lifetime [6]. Even the most energy-efficient solutions, however, will ultimately deplete the SNs’ batteries. Another approach is to harvest/charge the SNs. However, this is also a challenging issue in WSNs because it has an impact on SNs lives, especially when deploying a WSN for long-term monitoring. Due to dynamism, energy harvesting is extremely dependent on external conditions, implying that stable and reliable energy provisioning to SNs can’t be guaranteed [7].

Wireless energy transfer (WET) has been shown in research studies to provide stable energy to the SNs [8]. As a result, it ensures the durability of WSNs based on tight coupling magnetic resonance technology. The authors in [9] first explained the efficacy of WET using strong coupling magnetic resonance. In ref. [10], the authors used WET with a WSN and named it a WRSN. In this network, a mobile charging element (MCE) can wirelessly charge SNs [11]. The WET has several advantages, including excellent power transmission efficiency, resilience to the outside environment, and no need for direct contact or a line of sight. To replenish energy in WRSNs, two charging methods are typically used: periodic [12, 13] and on-demand [14]. In the first charging method, the MCE provides energy to the SNs using a fixed charge-schedule, which may be unsuitable due to charging requirement uncertainties and energy consumption dynamism. On the contrary, in the second charging method, the MCE charges the low-energy SNs that have made charging requests to it. As a result, it is more advantageous in the WRSN research community [15]. MCE can charge SN in two modes in both charging methods: single-node charging mode [16] and multi-node charging mode [17]. MCE can only charge one node in the first mode, so charging efficiency is low; however, in the latter mode, it can charge multiple nodes simultaneously. It’s worth mentioning that the network elements that influence MCE’s charging efficacy and network performances must be blended when determining the charge-schedule.

In such instances, charging strategies based on improved heuristic algorithms can be a very effective scheduling method. This is owing to its ease of implementation and ability to achieve the near-optimal solution fast and with less time complexity, making it more ideal for WSNs. Furthermore, it is capable of effectively combining and evaluating diverse network elements.

This paper proposes a charging scheme that employs an improved heuristic approach to find an on-demand charge-schedule. A charge request is sent to MCE by a SN when its remaining energy level is less than a given charging threshold. The charge-schedule is then determined using a heuristic approach for MCE to charge the SNs. The heuristic method uses a weight function for determining scheduling priorities of requesting SNs. The weight function includes three network elements as input parameters: residual energy, contribution-count, and distance to MCE.

Various studies on on-demand charging schemes with MCE(s) have been conducted. In comparison to other algorithms, the proposed algorithm’s potential features make it more efficient. For dynamic WRSNs, the proposed heuristic scheme finds an efficient charge-schedule. In this scheme, charge-requests from low-energy SNs are collected first. Following that, the scheme computes a charge-schedule based on a weight function that considers various network factors. The weight function improves the fairness of scheduling decisions by using real-time network data as input parameters. Furthermore, despite the limited MCE battery capacity, the proposed scheme can handle several charge-requests concurrently based on real-time weight values. Consequently, scalability of the proposed scheme is increased. In this work, the MCE is having multi-node charging feature [18, 19], which minimizes on-demand charging delay. The following are the primary contributions.

  • Propose a weighted heuristic scheme GOCS for determining a near-optimal preemptive charge-schedule to extend the lifetime of SNs.

  • The GOCS scheme assigns requesting SNs’ weights based on their residual energies, contribution-count values, and Euclidean distances from the MCE, and preferentially selects the requesting SNs that have the least weight to provide charging service.

  • Simulation tests comparing the proposed GOCS scheme to existing ones in terms of two network performance metrics: life-success ratio and energy utility ratio.

The rest of work is laid out as follows: The literature study is surveyed in Sect. 2. The system model with preliminaries and proposed problem definition are defined in Sect. 3. Section 4 provides the proposed scheme’s description. In Sect. 5 simulation study is presented to compare the proposed scheme to baseline schemes. The proposed work is summarized in Sect. 6.

2 Literature survey

In this section, some of the most important on-demand charging algorithms pertinent to this paper, are surveyed. In [14, 20], The MCE serves charge requests in compliance with FCFS policy. However, to charge requesting SNs, the MCE may necessitate excessive back-and-forth motions, leading to a longer charging delay. To address this issue, the study [21] included NJNP approach to find a charge schedule based on a geographical limit. In NJNP, a charge-schedule is designed based on the distance between MCE and the requesting SNs, i.e. MCE serves the SN that is closest to it first. However, if MCE receives a new charge-request from a nearby SN while charging, the MCE is pre-empted. However, due to the ad-hoc nature of SN deployment, requests can come from any SN, resulting in the premature death of many low-energy SNs that are far away from the MCE. This phenomenon causes a lower life-success ratio. In ref. [22,23,24], a charge-schedule is designed by proposing reinforcement learning-based charging method that uses only one network attribute, SN remaining energy.

Addressing this issue, in ref. [25], the SNs’ charge-requests are served based on spatial-temporal constraints. in ref. [26], the SNs’ charge-requests are served based on the distance between MCE and the requesting SNs and their variable energy consumption rates. Using the smallest enclosing disks concept, an approximation approach is introduced in ref. [27] to identify optimal sojourn locations for minimizing charging delay. In ref. [15], the authors aimed at optimizing covering utility by scheduling several MCEs. The MCE may charge a requesting SN while traveling. Their proposed algorithms were unable to significantly increase the network’s life-success ratio. But, in prior studies [15, 25], the MCE did not have a multi-node charging feature and could not evaluate numerous network factors to create the schedule, which is something that must be overlooked if charging efficiency is to be significantly increased. In ref. [28], the authors also employed a multi-node MCE. Their goals were to shorten the MCE’s tour-length and create a charge-schedule based on SNs’ charging utility gains. The amount of energy acquired by SNs from the MCE determines their charging utility gains. They did not, however, make use of numerous network properties for scheduling purposes (Table 1).

Table 1 Summary of on-demand charging scheduling schemes
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The aforementioned issues highlight the necessity to dig deeper into the charging problems and develop a charging scheme having the following features like (1) utilizing a multi-node MCE for simultaneous charging of SNs, (2) allowing MCE to preempt if a new charge-request with a higher weightage is received, and (3) combining various network features for making decisions. The scope of this work is to improve the life-success ratio as well as the energy utility ratio.

3 Network model and problem formulation

A WRSN has n rechargeable SNs in \(S = \{S_1, S_2, \cdots , S_n\}\), a base-station BS, a mobile charging element MCE with traveling speed \(V_x\) and battery capacity \(BC_{me}\). For the MCE, the BS functions as a charging station. At initially, the MCE is completely charged and located at the BS. The SNs with rechargeable battery capacity \(BC_{max}\) are dispersed at random across the network. Their energies are depleted when they are receiving and sending data, or in listening or sleeping states. Each sensor \(S_i\)’s average energy-consuming rate is  denoted by \(E_{con}(S_i)\). Furthermore, when moving across the network or charging the SNs, the MCE loses energy. The MCE’s charging range is  denoted by \(C_r\).


According to the proposed model, each sensor says \(S_i\) continuously monitors its residual energy \(RE(S_i)\) and sends a request to MCE when \(RE(S_i) < E_{th}\), where \(E_{th}\) denotes a energy threshold limit. The charge-request for a SN \(S_i\) includes its location \(LOC(S_i)\), residual energy \(RE(s_i)\), and a time-stamp value \(TS(S_i)\). It can be denoted as \(CH(s_i) = \{LOC(S_i), RE(S_i), TS(S_i)\}\). The MCE stores such requests in a queue called \(CHQ_{req}\). Then, to provide services, a charge-schedule \(CH_{sch}\) is determined. The MCE can go to charge a requesting SN if it has adequate energy before returning to the BS. Otherwise, the MCE recharges itself by returning to the BS. Following that, process the remaining SNs for charging. The MCE recharge time is presumed to be insignificant. Through multi-node charging, MCE may charge several \(SNs \in CHQ_{req}\) at the same time [28]. In comparison to MCE’s traversing time, its response time is considered negligible. At all times, the MCE is fully well aware of SNs’ residual energy levels. The actual charging rate for \(S_i\) is \(ACH_{rate}(S_i) = CH_{rate}\times \eta\), where \(CH_{rate}\) is charging power output of MCE. The term \(\eta\) ranges from 0 to 1. Since, in this work, \(C_r \approx 2.7 m\), \(\eta\) is set to 0.68 [29]. The Lifetime of SN \(S_i\) \((lf_{time}(S_i))\) is the time required for consuming the residual energy \(RE(S_i)\) of SN \(S_i\), defined as \(lf_{time}(S_i) = \frac{RE(S_i)}{E_{con}(S_i)}\). Furthermore, the service time of \(S_i\) \((T_c(S_i))\) is the time spent by MCE to travel and completely charge \(S_i\), expressed as, \(T_c(S_i) = \frac{D(S_i, me)}{V_x} + \frac{E_{max} - (RE(S_i) - \frac{D(S_i, me)}{V_x} \times E_{con}(S_i))}{ACH_{rate}(S_i)-E_{con}(S_i)}\). Here, \(\frac{D(S_i, mc)}{V_{x}}\) is MCE’s travel time to reach \(S_i\), \((RE(S_i) - \frac{D(rs_i, me)}{V_{x}} \times E_{con}(S_i))\) is the updated residual energy of SN \(S_i\) when the MCE reaches at SN \(S_i\). The required full charging time for the SN \(S_i\) is as follows. \(\frac{E_{max} - (RE(S_i) - \frac{D(S_i, me)}{V_{x}} \times E_{con}(S_i))}{(ACH_{rate}(S_i)-E_{con}(S_i))}\)A SN \(S_i\) is considered to be charged successfully if \(T_c(S_i) \le lf_{time}(S_i)\), else it is not. In both circumstances, MCE would charge \(S_i\).

In this work, the states of a SN \((S_i))\) is classified into three categories : critical \((S_i(crt))\), normal \((S_i(nrm))\), and dead \((S_i(dead))\). If a SN \(S_i\) requests a charge from MCE, it enters its critical state and expressed as \(S_i(crt) = 1\); otherwise \(S_i(crt) = 0\). If service time \(T_c(S_i)\) of a SN \(S_i\) is less than or equal to its lifetime \(lf_{time}(S_i)\), it enters its normal state, expressed as \(S_i(nrm) = 1\); otherwise \(S_i(nrm) = 0\). Furthermore, the dead state of SN \(S_i\) is expressed as \(S_i(nrm) = 1\) if \(RE(S_i) = 0\); otherwise \(S_i(nrm) = 1\).


The performance parameters for evaluating the proposed work are the Life-Success ratio \((LR_{ratio})\) and the Energy Utility Ratio (\(EUE_{ratio}\)). The life-success ratio \((LR_{ratio})\) is a ratio of the total number of SNs successfully charged by the MCE to the total number of requesting SNs, expressed as \(LR_{ratio} = \frac{\sum _{i=1}^{n} S_i(nrm). S_i(crt)}{\sum _{i=1}^{n} S_i(ctr)}\). The energy utility ratio (\(EUE_{ratio}\)) is a ratio of total energy obtained by SNs from MCE to total energy depleted by the MCE for traversing and charging during time T, and is defined as, \(EUE_{eff} = \frac{\sum _{i=1}^{n} E_{max} - RE(S_i) + T_c(S_i) \times E_{con}(S_i) }{E(T)} \times S_i(crt)\)where E(T) denotes energy depleted by MCE within time T. For clear understanding, consider the following WRSN example: a charge-request queue \(CH_{req} = \{S_1,S_2, S_3, \ldots , S_5\}\). Let \(vp_1=LOC(S_1), vp_2=LOC(S_2)\), and \(vp_3=LOC(S_3)\) are used to visit the SNs \(S_1, S_2\), and \(S_3\) respectively. The visiting point \(vp_4=LOC(S_4)\) is used to visit \(S_4\) and \(S_5\) at a time. Let MCE initially have \(BC_{me}\) = 20 J and its initial location is at BS. Let the schedule be \(CH_{sch} = BS \rightarrow S_1 \rightarrow S_2 \rightarrow S_3 \rightarrow S_4,S_5 \rightarrow BS\).

Fig. 1
figure 1

An example of charge-schedule

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Figure 1 depicts one such example, in which \(S_1,S_2\),\(S_4\), and S5 are classified as normal, while S3 are classified as dead. Even though it is marked as dead, the MCE will charge it. This figure contains five tables, one for each \(SN \in CH_{req}\). Each table has the following information: the SN’s amount of energy obtained, the MCE’s traversing time to go from the previous visiting location to a targeted visiting location, and the SN’s charging time. The total energy obtained by the SNs from MCE is (26 J + 24 J + 14.6 J + 22.4 J + 11.2 J) = 98.2 J. Thus, the energy utility ratio \(EU_{eff} =\frac{17.4}{100}\) = 0.982. Also, as only four SNs are charged successfully among 5 SNs, the life-success ratio is \(LR_{ratio}\)= 0.8. The notations used throughout the proposed work is listed in Table 2.

Table 2 Summary of notations
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3.1 Problem definition

A set of charge-requests denoted by \(CHQ_{req} = \{CR(S_i),\ldots ,CR(S_m) \}\) is received by MCE, the goal is to discover a charge-schedule \(CH_{sch}\) for the MCE to improve the network life. To put it another way, a charging algorithm must be used to improve the network’s life-success ratio and energy utility ratio in order to extend its life. This is known as Computing charge-schedule for enhancing sensor-lifetime (CSSL) problem.

4 Proposed solution

The proposed heuristic-based charging solution called Generated-on-demand charge-scheduling with pre-emption (or GOCS), is detailed here to solve the proposed CSSL problem. The MCE, in this algorithm, buffers charging-request messages from low-energy SNs. It prioritizes them by using a weight function. Specifically, each requesting SN is assigned a weight based on its residual energy, contribution-count value, and Euclidean distance from the MCE’s current position. The contribution-count of a requesting SN is based on its neighbors which have also made requests to the MCE. Then, the proposed scheme aims to find an efficient charge-schedule \((CH_{sch})\) as an output to optimize the network’s life-success ratio \((LR_{ratio})\) and energy utility ratio \((EUE_{eff})\). The following are a few more terminology used, followed by the proposed scheme’s detailed description.

Definition 1

(Charging-overlapped SNs): If the Euclidean distance between two SNs \(S_i\) and \(S_j\) is less than \(C_r\), they are said to be charging-overlapped. Furthermore, the set of SNs that are charging-overlapped with \(S_i\) is called as its neighbor set (\(N(S_i)\)).

Definition 2

(Requesting-neighbor set of sensor \(S_i\) (\(RNS(S_i)\))): The requesting-neighbor set of \(S_i\) is the set of requesting \(SNs \in CHQ_{req}\) that are charging-overlapped with the sensor \(S_i\). Its contribution-count is the size of its requesting-neighbor set i.e., \(CC(S_i) = |RNS(S_i)|\).

Fig. 2
figure 2

An example of MCE’s charging range for the SNs

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In Fig. 2, the dotted circles denotes charging regions of the MCE for the SNs in \(S = \{S_1, S_2, \ldots , S_7\}\). In this Fig., \(S_1\) is charging-overlapped with \(S_2\), \(S_2\) is charging-overlapped with both \(S_1\) and \(S_3\), \(S_5\) is charging-overlapped with \(S_6\), and \(S_4\)’s charging region is isolated from others. The Neighbor sets of \(SNs \in S\) are \(N(S_1) = \{S_2\}, N(S_2) = \{S_1,S_3\},N(S_3) = \{S_2\}, N(S_4) = \{\emptyset \}, N(S_5) = \{S_6\}\), and \(N(S_6) = \{S_5\}\). Let the SNs \(S_2\), \(S_3\), \(S_4\) and \(S_6\) have low-energy and send request for charging to the MCE i.e. \(CHQ_{req} = \{S_2, S_3, S_4 ,S_6\}\). In this case, the requesting-neighbor sets of the requesting sensors \(SNs \in CHQ_{req}\) are \(RNS(S_2) = \{S_3\}, RNS(S_3) = \{S_2\}, RNS(S_4) = \{\emptyset \}\), and \(RNS(S_6) = \{\emptyset \}\).

After storing charge-requests from low-energy SNs in a queue \(CHQ_{req}\), the MCE first computes a contribution-count \(CC(S_i)\) for each requesting sensor \(S_i \in CHQ_{req}\). Based on the information obtained from the charging-request message, it later updates the remaining information like remaining energy (\(RE(S_i)\)) and distance to MCE (\(D(me, S_i)\): distance from the MCE’s current position to the SN \(S_i\)) for all requesting \(S_i \in CHQ_{req}\). The MCE uses a weighted scheduling function to compute a charge-schedule (\(CH_{sch}\)). The MCE roams the network and provides service to the requesting SNs. If new charge-requests arise in the meanwhile, they are likewise stored in the same queue \(CHQ_{req}\) and would be served under the same charging-schedule \(CH_{sch}\). The MCE switch to an incoming-requesting SN if the new requesting SN has a minimum weight value among all values of \(SNs \in CHQ_{req}\). Before providing service to a requesting sensor \(S_i\), the MCE checks to see if its residual energy is adequate to reach BS after charging it. Otherwise, if possible, it charges at the nearest requesting \(SN \in CHQ_{req}\) and immediately visits the BS for energy replenishment. The following sub-section discusses the heuristic weighted scheduling function.

4.1 Weighted scheduling function

Here, we explain how the GOCS scheme computes a weight value based on the contribution-count \(CC(S_i)\), residual energy \(RE(S_i)\), and distance to MCE \(D(me, S_i)\) corresponding to each requesting SN \(Si \in CHQ_{req}\). The GOCS prioritizes requesting SNs with the minimum weight as the first sensor to be charged by the MCE. Let \(W(S_i)\) denotes a weight value of a SN \(S_i\), then its weight is computed as:

$$\begin{aligned} W(S_i) = \frac{D(me, S_i) * RE(S_i)}{1+ CC(S_i)}. \end{aligned}$$
(1)

According to the weight function, requesting \(SNs \in CHQ_{req}\) with less residual energy, smaller distance from MCE, and larger contribution-count receives the minimum weight. As a result, requesting \(SNs \in CHQ_{req}\) that are nearby to the MCE, have multiple requesting-neighboring SNs, and have the least residual energy have a better chance of obtaining energy from the MCE. The amount of energy spent by MCE is proportional to the Euclidean distance between the MCE and a requesting SN, as well as the number of requesting neighbors and the amount of obtained energy from the MCE. As a result, visiting the requested SN with minimum weight reduces the MCE’s travel distance as well as the life-success ratio, thereby minimizing energy consumption. A special case occurs when multiple SNs have the same weight. In this case, the remaining energy of the SNs with the same weight value must be compared, and the SN with the least remaining energy must be chosen as the next charging node.

figure a

It is worth noting that each charging schedule is selected only when the requesting SN and its neighbours (if any) are charged, or when a new charge request is made. There is only one charging request selected at each charging schedule. Because all network attributes, such as the distance between other SNs and the MCE, as well as the energy consumption rate and neighbouring SNs, may change. As a result, at the start of the next charging schedule, the previous order of the SNs should be updated. As previously stated, the estimation of remaining energy, distance to MCE, and neighbouring SNs is time-dependent, and when a charging request is served after determining the charge schedule, all network attributes may be changed, implying that all network attributes are subject to real-time change. As a result, the proposed GOCS scheme is both real-time and dynamic. The Algorithm 1 summaries how the GOCS scheme works.

5 Performance evaluation

The proposed GOCS scheme’s performance is reported in terms of life-success ratio (\(LR_{ratio}\)), and energy utility ratio (\(EUE_{ratio}\)) metrics. Simulated experiments in MATLAB are used to verify the results. The GOCS scheme is compared to two existing on-demand charging schemes: FCFS scheme [14], which schedules requesting SNs based on the arrival of charge requests, and the NJNP-MS scheme [21], which schedules requesting SNs’ based on the spatial and temporal limits. Whereas, in GOCS scheme, the charge-schedule is determined by multiple factors such as spatial, temporal, and residual energy. To reflect the fact that MCE now has multi-node charging capability, we renamed the FCFS scheme to FCFS-MS. A WRSN with 200–300 sensors is considered for simulation set-up. The SNs are randomly distributed in a 100 \(\times\) 100 \(m^2\) region. The BS is located in the middle of the deployment region [21]. Each SN \(S_i\) has a battery capacity \(BC_{max}\) = 10.8 kJ [30], and a charging range \(C_r\) = 2.7 m [29]. Each SN \(S_i\) has remaining energy [0.1–10.8] KJ and the average rate of energy depletion [0.0001–0.05] J/Sec. The MCE’s battery capacity is \(BC_{me}\) = 4000 kJ, an its energy-charging rate is \(CH_{rate}\) = 5 J/Sec. The charging efficiency is set to \(\eta\) = 0.68 [29]. The MCE looses energy at the rate of 600 J/m [28] while travelling at speed 5 m/Sec. The simulation outcomes are averaged across 30 distinct random sensor-deployments.

The proposed GOCS scheme’s performance is measured in terms of life-success ratio and energy utility ratio. The impact of the number of SNs on performance metrics is discussed in the subsequent sub-sections. The Life-success ratio (\(LR_{ratio}\)) is calculated based on the number of SNs. Figure 3(a) reports that, increasing the number of SNs reduces the \(LR_{ratio}\). This is because as the number of SNs increased, so does the charge-request list’s size \(|CHQ_{req}|\), putting a higher load on MCE to deliver charging services to the requesting SNs. More SNs are likely to die as a result, reducing the \(LR_{ratio}\) over time. Furthermore, the GOCS scheme outperforms the others in terms of \(LR_{ratio}\). This is since GOCS combines multiple network variables, leading to an increased number of requested SNs being charged. The FCFS-MS scheme, unlike the GCPS scheme, prioritizes recharging the requested SNs based solely on the time constraint. Due to a lack of energy, distance, and time constraints in charging-scheduling decisions, the requesting SNs may be more likely to die. Furthermore, hardly any of the existing schemes employ all three factors in association with the pre-emption capability.

Fig. 3
figure 3

Performance of GOCS algorithm by varying number of SNs

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Here, various charging methods’ energy utility ratios (\(EUE_{ratio}\)) are compared by varying numbers of SNs. \(EUE_{ratio}\) increases as the number of SNs increases, as in  Fig. 3(b). It’s because of the increase in \(|CHQ _{req}|\). As a result, a greater number of SNs will be able to charge, resulting in an increase of the amount of total energy obtained by SNs, increasing \(EUE_{ratio}\)’s value. It’s also seen from Fig. 3(b) that GOCS algorithm succeeds in achieving the highest \(EUE_{ratio}\). It is because GOCS algorithm employs multiple network variables with pre-emption to create an effective schedule, reducing the waiting time of requesting SNs.

6 Conclusion

In this work, a novel charging method termed GOCS is devised for on-demand charging in WRSNs using a mobile charging element (MCE). The GOCS scheme determines an efficient charge schedule for requesting SNs in dynamic WSNs. It creates a charge-schedule considering various network factors of incoming requests and then serves each one individually. It enables the MCE to serve a new requesting SN if that requesting SN has a minimum weight value. To quantify the SNs’ scheduling priority, the weight function includes residual energy, contribution-count, and distance to MCE. Using experimental simulation, the GOCS’s charging performances are evaluated concerning life-success ratio and energy utility ratio. The results report that the GOCS outperforms other existing schemes. However, in large-scale WRSNs, a single MCE is insufficient for charging the SNs. The use of multiple MCEs and their efficient coordination among themselves for recharging the SNs as well as themselves may enhance overall charging performance even more, particularly in large-scale WRSNs. So, in the future, we will strive to integrate this feature into our work by investigating a new weighted multi-attribute based heuristic method.