# CRCM: A New Combined Data Gathering and Energy Charging Model for WRSN

^{*}

## Abstract

**:**

## 1. Introduction

- To reduce the energy consumption to the largest extent, we consider the MC as a moving sink to gather sensing data from sensor nodes when charging them. A new recharging model, combined recharging and collecting data model on-demand (CRCM), was established in which the MC will recharge the on-demand sensor nodes and collect all of the data of the sensor nodes in the cluster at the same time.
- To establish the CRCM, we have considered the hexagon-based [21] (HB) algorithm to sort all sensor nodes into different clusters. While NJNP cannot satisfy the scheduler with high charging efficiency to structure the charging path, we then consider both the residual energy and geographic position of each sensor node, the REGP algorithm is proposed to calculate the priority of each cluster, and the charging queue is ultimately established.
- In a large WRSN, we have also considered the multi-MC’s algorithm to adapt the increasing quantity of sensor nodes. To make sure no sensor nodes exhaust their energy while waiting for the next charging cycle, we have calculated the longest cycle time a MC can serve. The DMC algorithm is subsequently raised to solve the least number of MCs problem.
- The remainder of this paper is constituted as follows: in Section 2, we have discussed the related works about previous studies and experiments of WPT; in Section 3 we have shown the system model and three algorithms to solve the problems; then some simulations have been realized to compare each parameter to Earliest Deadline First (EDF) [22] and NJNP in Section 4; and, finally, we conclude this paper in Section 5.

## 2. Related Works

## 3. System Model and Proposed Scheme

#### 3.1. System Model

#### 3.2. Problem Formulation

**Problem**

**1:**

**Problem**

**2:**

**Problem**

**3:**

#### 3.3. The Hexagon-Based Algorithm

Algorithm 1: Hexagon-Based Algorithm (HB) |

1: Initialization: sensor nodes ${S}_{i}$ and clusters ${C}_{j}$ |

2: for All ${S}_{i}\in S(0<i\le n)$ do |

3: if $0\le dist({S}_{i},{C}_{j})<\frac{\sqrt{3}}{2}d$ then |

4: Bound the ${S}_{i}.x1$ to the value of $j$ |

5: else if $dist({S}_{i},{C}_{j})=\frac{\sqrt{3}}{2}d$ then |

6: Bound the ${S}_{i}.x1$ and ${S}_{i}.x3$ to the two values of $j$ |

7: else if $\frac{\sqrt{3}}{2}d<dist({S}_{i},{C}_{j})<d$ then |

8: Bound the ${S}_{i}.x2$ to the value of $j$ |

9: else if $dist({S}_{i},{C}_{j})=d$ then |

10: Bound the ${S}_{i}.x1$ and ${S}_{i}.x2$ and ${S}_{i}.x3$ to the three values of $j$ |

11: end if |

12: end for |

13: for All ${S}_{i}\in S$ do |

14: if ${S}_{i}.x1>0$ and ${S}_{i}.x3>0$ and ${S}_{i}.x2=0$ then |

15: ${S}_{i}.x3=0$ |

16: else if ${S}_{i}.x1>0$ and ${S}_{i}.x2>0$ and ${S}_{i}.x3=0$ then |

17: Select the cluster which is the closest to the sink, if the distance is equal, choose randomly from the two clusters, bound ${S}_{i}.x1$ to the value of $j$ and ${S}_{i}.x2$ to the value of 0 |

18: else if ${S}_{i}.x1>0$ and ${S}_{i}.x2>0$ and ${S}_{i}.x3>0$ then |

19: Select the cluster which is the closest to the sink, if the distance is equal, choose randomly from the two or three clusters, bound ${S}_{i}.x1$ to the value of $j$ and ${S}_{i}.x2$, ${S}_{i}.x3$ to the value of 0 |

20: end if21: end for |

**Theorem**

**1.**

**Proof.**

#### 3.4. The Residual Energy and Geographic Position Algorithm

Algorithm 2: Residual Energy and Geographic Position Algorithm (REGP) |

Input: The empty sequence of $Q$, sensor nodes ${S}_{i}$ and clusters ${C}_{j}$ |

Output: The optimized charging sequence $Q$ |

1: Let Sink be the head $\in Q$ |

2: for All ${S}_{i}\in S(0<i\le n)$ do |

3: if Energy of ${S}_{i}<\theta $ then |

4: ${C}_{j}.type=1$, where $j={S}_{i}.x1$ |

5: end if |

6: end for |

7: while Exiting ${C}_{j}.type=1$ do |

8: for All ${C}_{j}\in C(0<j\le m)$ do |

9: if ${C}_{j}.type=1$ then |

10: Calculate the $P(j)$ and find the largest $P(j)$ of ${C}_{j}$ |

11: $Q\leftarrow Q\cup \left\{{C}_{j}\right\}$ |

12: ${C}_{j}.type=0$ |

13: end if |

14: end for |

15: end while |

16: return $Q$ |

**Theorem**

**2.**

**Proof.**

#### 3.5. The Dynamic Mobile Charger Algorithm

Algorithm 3: Dynamic Mobile Charger Algorithm (DMC) | |||

Input: The sequence of $Q$, count number $t$ and the length of $Q$ | |||

Output: The number of MCs $k$ | |||

1: $t=2$ | |||

2: $k=1$ | |||

3: Let $l$ as the length of $Q$ | |||

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

5: Calculate the waiting time ${t}_{w}^{j}$ | |||

6: end for | |||

7: while $l>1$ do | |||

8: if The residual time of cluster $Q(t)>{t}_{w}^{j}$ and $T<\frac{\theta}{{P}_{i\mathrm{max}}}-\frac{L}{\sqrt{2}{V}_{c}}$ then | |||

9: $t=t+1$ | |||

10: else | |||

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

12: $k=k+1$ | |||

13: $t=2$ | |||

14: Update the $l$ | |||

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

16: Calculate the waiting time ${t}_{w}^{j}$ | |||

17: end for | |||

18: end if | |||

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

20: $l=0$ | |||

21: end if | |||

22: end while | |||

23: return $k$ |

**Theorem**

**3.**

**Proof.**

## 4. Simulations

#### 4.1. The Energy Change of a Sensor Node

#### 4.2. Path Diagram of One Charging Cycle

#### 4.3. Number of MCs in Each Charging Cycle

#### 4.4. Total number of MCs in the Whole Process

#### 4.5. Total Number of Emergency Sensor Nodes in the Whole Process

#### 4.6. Average Serving Time of a MC in the Whole Process

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 8.**The comparison of the path diagram by three algorithms. (

**a**) The path diagram of REGP; (

**b**) the path diagram of NJNP; and (

**c**) the path diagram of EDF.

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

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

${C}_{j}$ | Cluster $j$ |

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

${e}_{i}^{j}$ | Residual energy of sensor node ${S}_{i}$ in cluster ${C}_{j}$ when reporting to the sink |

$L$ | The length of the region |

$\theta $ | Charging threshold |

${V}_{c}$ | The traveling velocity of MC |

$d$ | The valid and farthest charging distance |

${\tau}_{j}$ | The serving time of cluster ${C}_{j}$ |

${t}_{d}^{j}$ | The time of data gathering in cluster ${C}_{j}$ |

${t}_{c}^{i}$ | The time of charging for sensor node ${S}_{i}$ |

${t}_{r}^{i}$ | The residual time of sensor node ${S}_{i}$ |

${t}_{w}^{j}$ | The waiting time for MC’s coming to cluster ${C}_{j}$ |

${P}_{c}$ | Charging rate of MC |

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

${P}_{d}(j)$ | The geographic position priority of cluster ${C}_{j}$ |

${P}_{e}(j)$ | The residual energy priority of cluster ${C}_{j}$ |

$P(j)$ | The combined priority of cluster ${C}_{j}$ |

${\epsilon}_{i}$ | Charging efficiency of sensor node ${S}_{i}$ |

$T$ | A charging cycle |

Sensor Node | x1 | x2 | x3 |
---|---|---|---|

${S}_{1}$ | 1 | 0 | 0 |

${S}_{2}$ | 4 | 0 | 3 |

${S}_{3}$ | 5 | 6 | 0 |

${S}_{4}$ | 7 | 8 | 9 |

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**MDPI and ACS Style**

Wang, Y.; Dong, Y.; Li, S.; Wu, H.; Cui, M.
CRCM: A New Combined Data Gathering and Energy Charging Model for WRSN. *Symmetry* **2018**, *10*, 319.
https://doi.org/10.3390/sym10080319

**AMA Style**

Wang Y, Dong Y, Li S, Wu H, Cui M.
CRCM: A New Combined Data Gathering and Energy Charging Model for WRSN. *Symmetry*. 2018; 10(8):319.
https://doi.org/10.3390/sym10080319

**Chicago/Turabian Style**

Wang, Yuhou, Ying Dong, Shiyuan Li, Hao Wu, and Mengyao Cui.
2018. "CRCM: A New Combined Data Gathering and Energy Charging Model for WRSN" *Symmetry* 10, no. 8: 319.
https://doi.org/10.3390/sym10080319