# A New on-Demand Recharging Strategy Based on Cycle-Limitation in a WRSN

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## Abstract

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## 1. Introduction

- (1)
- Although simultaneous data gathering and charging is the best way to enhance the charging efficiency of mobile chargers, this is difficult to achieve with current technology. In this paper, we used a K-means algorithm to divide all sensor nodes in a region that only for mobile chargers to gather data from sensor nodes [19]. We also used the NJNP charging strategy to schematize the charging path. The clustering centers were added in the charging path to allow the mobile charger to gather the data. The mobile chargers only moved to the sensor nodes for energy charging and finished the task of data gathering at the centers of the clusters;
- (2)
- As the charging queue was calculated completely, we proposed the Periodically Restricted Dynamic Mobile Chargers (PRDMCs) algorithm to cut the charging path; the original charging path was divided into several parts and corresponded to several mobile chargers. The number of mobile chargers after cutting was the appropriate number. At the same time, to make sure that the sensing data could be gathered at a certain time, we also discussed the maximum service time of each mobile charger;
- (3)
- We compared our algorithms with the normal CRCM in terms of the data acquisition cycle, etc. The results suggest that by increasing the number of mobile chargers, the length of the data acquisition cycle can be guaranteed.

## 2. Related Works

## 3. System Model

#### 3.1. Network Model of the New CRCM

#### 3.2. Network Model of the New CRCM

#### 3.3. Model of Mobile Charger Energy Consumption

## 4. Proposed Strategy

#### 4.1. Clustering of the New CRCM

#### 4.2. Planning the Charging Path

#### 4.3. Periodically Restricted Dynamic Mobile Chargers

Algorithm 1. The Periodically Restricted Dynamic Mobile Chargers (PRDMCs) algorithm. |

1: Input: The queue $Q$, count number $t$, and length of $Q$ |

2: Output: The number of mobile chargers $k$ |

3: $t=2$ |

4: $k=1$ |

5: let $l$ be the length of $Q$ |

6: if ${T}_{storage}>400$ or ${T}_{\mathrm{int}}>150$ then |

7: ${T}_{ch}=300-{T}_{\mathrm{int}}$ |

8: for All $Q(t)\in Q(1<t\le l)$ do |

9: Calculate the waiting times ${t}_{w}^{i}$ and ${t}_{w}^{j}$ |

10: end for |

11: Calculate the $\varphi $ |

12: if $\varphi <0.7$ then |

13: ${{T}^{\prime}}_{ch}=\frac{{T}_{storege}+{t}_{exer}}{\lceil {T}_{storage}/{T}_{ch}\rceil}$ |

14: end if |

15: while $l>1$ do |

16: if $T<{T}_{ch}$ then |

17: $t=t+1$ |

18: else |

19: Remove the elements from 2 to $t-1$ and update the $Q$ |

20: $k=k+1$ |

21: $t=2$ |

22: update the $l$ |

23: for All $Q(t)\in Q(1<t\le l)$ do |

24: Calculate the waiting times ${t}_{w}^{i}$ and ${t}_{w}^{j}$ |

25: end for |

26: end if |

27: if $l=t-1$ then |

28: $l=0$ |

29: end if |

30: end while |

31: end if |

32: Return: $k$ |

## 5. Simulations

#### 5.1. Simulation Parameters

#### 5.2. Distribution and Clustering of Sensor Nodes

#### 5.3. Residual Energy of One Sensor Node

#### 5.4. Number of Mobile Chargers Used in Each Charging Cycle

#### 5.5. Charging Path of Mobile Chargers

#### 5.6. Average Service Time of Mobile Chargers in Each Charging Cycle

#### 5.7. Length of Storage Time

#### 5.8. Average Data Gathering Cycle

#### 5.9. Average Number of Mobile Chargers Used in Each Charging Cycle

## 6. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 2.**Distribution and clustering of the sensor nodes. The four black diagonal crosses are the centers of each cluster. The black horizontal cross in the middle of the region is the sink node. The dotted lines indicate node–mobile charger data transfer that is performed when the mobile charger arrives at the center of the cluster.

**Figure 6.**The original charging path of a mobile charger before cutting, the blue stars represent sensor nodes that need to be charged in the present charging cycle.

**Figure 7.**Charging paths of multiple mobile chargers. The differently colored lines represent the driving paths of different mobile chargers.

**Figure 8.**Average service time of mobile chargers for two CRCMs (Combined Recharging and Collecting Data Model).

Symbol | Definition |
---|---|

${S}_{i}$ | sensor node $i$ |

${C}_{j}$ | the center of cluster $j$ |

$L$ | the length of the region |

$\theta $ | charging threshold |

${E}_{o}$ | the initial energy of each sensor node |

$\epsilon $ | the charging efficiency of the mobile charger |

${P}_{c}$ | the charging power of the mobile charger |

${E}_{i}$ | the residual energy of sensor node $i$ when sending a charging request to the sink |

${P}_{i}$ | the energy consumption of sensor node $i$ |

${\tau}_{c}^{i}$ | the charging time for sensor node $i$ |

${t}_{w}^{i}$ | the time required for the mobile charger to leave sensor node $i$ |

${\tau}_{d}^{j}$ | the time required for data collection when the mobile charger is operating in the center of cluster $j$ |

${E}_{d}^{i}$ | energy consumption for 1 bit data transmission in the Free Space Model |

${E}_{e}$ | energy consumption in the transmitting circuit when dealing with 1 bit data information |

${t}_{w}^{j}$ | the time required for the mobile charger to leave cluster $j$ |

${t}_{d}^{i}$ | the time required to collect data from sensor node $i$ |

$K$ | the number of clusters |

${O}_{i}$ | the data size of sensor node $i$ |

${t}_{exer}$ | the increase in time after cutting the charging queue |

$k$ | the number of mobile chargers |

${V}_{c}$ | the moving speed of the mobile charger |

${t}_{total}$ | the total time required for the charging queue |

${T}_{storage}$ | the length of the storage time |

${T}_{ch}$ | the service time of the mobile charger |

${T}_{\mathrm{int}}$ | the interval time among two charging cycles |

Parameters | Value |
---|---|

Number of nodes | 50 |

Field size (m^{2}) | $100\times 100$ |

Number of clusters | 4 |

Initial energy of the node ${\mathrm{E}}_{0}$ (KJ) | 0.5 |

Energy consumption during communication per datum (nJ/bit) | 50 |

Speed of the mobile charger (m/s) | 1 |

Energy conversion rate of mobile chargers (ω) | 0.8 |

Charging threshold (KJ) | 0.2 |

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**MDPI and ACS Style**

Wang, Y.; Dong, Y.; Li, S.; Huang, R.; Shang, Y.
A New on-Demand Recharging Strategy Based on Cycle-Limitation in a WRSN. *Symmetry* **2019**, *11*, 1028.
https://doi.org/10.3390/sym11081028

**AMA Style**

Wang Y, Dong Y, Li S, Huang R, Shang Y.
A New on-Demand Recharging Strategy Based on Cycle-Limitation in a WRSN. *Symmetry*. 2019; 11(8):1028.
https://doi.org/10.3390/sym11081028

**Chicago/Turabian Style**

Wang, Yuhou, Ying Dong, Shiyuan Li, Ruoyu Huang, and Yuhao Shang.
2019. "A New on-Demand Recharging Strategy Based on Cycle-Limitation in a WRSN" *Symmetry* 11, no. 8: 1028.
https://doi.org/10.3390/sym11081028