# Recharging Schedule for Mitigating Data Loss in Wireless Rechargeable Sensor Network

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## Abstract

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## 1. Introduction

- To the best of our knowledge, this is the first work to consider the node’s disjointed state in the mobile charger scheduling problem. Compared to the state-of-arts, we distinguish the inactive nodes into two groups, the sleep nodes whose energy is exhausted and the disjointed nodes which are active but can’t send data to the base station via any available routing path. Most existing works only consider how to decrease the sleep node’s nonfunctional time with the help of a mobile charger, but ignore the disjointed node’s data loss. In our work, to maintain network connectivity as long as possible and mitigate the data loss, we consider reducing the inactive time of both sleep nodes and disjointed nodes via the mobile charger with limited charging ability.
- We introduce a metric called the criticality index to quantify the node’s criticality, which indicates a node’s contribution to network connectivity. It measures the dissimilarity between the node’s neighboring set and its neighbors’ neighboring sets. A node has a higher index if it plays a more important role as a bridge between two or more node sets. In addition, energy criticality is also considered, which indicates a node’s consumed energy ratio and can be used to measure the node’s desire for charging. We use this ratio to weight the criticality index to reduce the possibility of charging the full energy nodes. Otherwise, some higher criticality nodes will always be selected to be charged even if they have a great amount of residual energy.
- We formulate the charging scheduling problem as a novel optimization problem, with an objective of maximizing the total criticality indexes of nodes selected in the charging tour and subject to the mobile charger’s traveling distance constraint. To solve this NP-hard problem, we propose a heuristic algorithm. The heuristic algorithm includes three steps, which are spanning tree growing, tour construction, and tour improvement.

## 2. Related Works

#### 2.1. Wireless Power Transfer Technology

#### 2.2. Mobile Charger Schedule

## 3. Network Model and Charging Scheme

#### 3.1. Network Model

#### 3.2. Energy Consumption Model

#### 3.3. Node’s Criticality Definition

#### 3.4. Problem Formulation

## 4. A Heuristic Algorithm

#### 4.1. Spanning Tree Growing

Algorithm 1. Tree growing. | |||

Input:$G=(V,E)$, traveling distance constraint $L$; | |||

Output: spanning tree $T$ | |||

1: | $T:=\left\{{v}_{0}\right\}$ | ||

2: | while$C(T)\le L$ and $V\backslash T\ne \varphi $ do | ||

3: | $R:=\varphi $ | ||

4: | for each ${v}_{i}\in V$ and ${v}_{i}\notin T$ do | ||

5: | ${c}_{i}:=\underset{{v}_{k}\in T}{\mathrm{min}}\text{}{c}_{ik}$ | ||

6: | ${c}_{i}^{\prime}:=\mathrm{min}\{{c}_{i},{c}_{i}+{c}_{p(k)i}-{c}_{p(k)k}\}$ | ||

7: | $R(i,T):={\widehat{r}}_{i}/{c}_{i}^{\prime}$ | ||

8: | $R:=R\cup \{R(i,T)\}$ | ||

9: | end for | ||

10: | find the biggest $R(i,T)$ in $R$ | ||

11: | ${v}_{i}:=\mathrm{arg}\text{}\underset{R(i,T)\in R}{\mathrm{max}}\text{}R(i,T)$ | ||

12: | $C(T\cup \{{v}_{i}\}):=2({c}_{p(i)i}+{\displaystyle {\sum}_{\begin{array}{l}{v}_{k}\in T,\\ k\ne 0\end{array}}{c}_{p(k)k}})$ | ||

13: | if $C(T\cup \{{v}_{i}\})\le L$ then | ||

14: | $C(T):=C(T\cup \{{v}_{i}\})$ | ||

15: | $T:=T\cup \left\{{v}_{i}\right\}$ | ||

16: | else | ||

17: | break | ||

18: | end if | ||

19: | end while | ||

20: | return$T$ |

#### 4.2. Tour Construction

Algorithm 2. Tour construction. | |||

Input: Spanning tree $T$, traveling distance constraint $L$; | |||

Output: A charging tour $P$ starts from and ends at ${v}_{0}$ | |||

1: | repeat | ||

2: | compute shortest path in the $T$,$P:=\mathrm{LKH}(T)$ | ||

3: | If ${C}_{\mathrm{LKH}}(P)\le L$ then | ||

4: | Declare $P$ is accepted | ||

5: | else | ||

6: | Delete the last added node from $T$ | ||

7: | end if | ||

8: | until$P$ is accepted | ||

9: | return$P$ |

#### 4.3. Tour Improvement

Algorithm 3. Tour improvement. | ||||

Input: $G=(V,E)$, initial charging tour $P$, traveling distance constraint $L$; | ||||

Output: An improved charging tour $P$ | ||||

1: | repeat | |||

2: | $R:=\varphi $ | |||

3: | for each vertex ${v}_{i}\in V$ and ${v}_{i}\notin P$ do | |||

4: | ${c}_{i}^{\u2033}:=\underset{{v}_{x},{v}_{y}\in P}{\mathrm{min}}\text{}{c}_{ix}+{c}_{iy}-{c}_{xy}$ | |||

5: | if ${c}_{i}^{\u2033}+{C}_{LKH}(P)\le L$ then | |||

6: | $R(i,P):={\widehat{r}}_{i}/{c}_{i}^{\u2033}$ | |||

7: | $R:=R\cup \{R(i,P)\}$ | |||

8: | else | |||

9: | continue | |||

10: | end if | |||

11: | end for | |||

12: | ${v}_{i}:=\mathrm{arg}\text{}\underset{R(i,P)\in R}{\mathrm{max}}\text{}R(i,P)$ | |||

13: | insert ${v}_{i}$ into $P$ at the location with minimum insertion cost | |||

14: | until no more feasible vertices in $V\backslash P$ | |||

15: | return$P$ |

#### 4.4. Time Complexity Analysis

## 5. Simulation Evaluations

#### 5.1. Simulation Environment

#### 5.2. Property Analysis

#### 5.3. Performance Comparison

#### 5.3.1. Impact of Network Scale

#### 5.3.2. Impact of Charger’s Traveling Distance Constraint

#### 5.3.3. Impact of Charger’s Traveling Speed

#### 5.3.4. Impact of Charging Power

## 6. Conclusions and Future Work

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 3.**Example of network. (

**a**) The original network; (

**b**) The network of node E removed; (

**c**) The network of node B removed.

**Figure 5.**Impact of $\left|N\right|$ on the charging scheduling algorithms: (

**a**) Total nodes’ disjointed time; (

**b**) Total nodes’ inactive time; (

**c**) Network’s data loss rate.

**Figure 6.**Impact of $L$ on the charging scheduling algorithms: (

**a**) Total nodes’ disjointed time; (

**b**) Total nodes’ inactive time; (

**c**) Network’s data loss rate.

**Figure 7.**Impact of $v$ on the charging scheduling algorithms: (

**a**) Total nodes’ disjointed time; (

**b**) Total nodes’ inactive time; (

**c**) Network’s data loss rate.

**Figure 8.**Impact of ${p}_{r}$ on the charging scheduling algorithms: (

**a**) Total nodes’ disjointed time; (

**b**) Total nodes’ inactive time; (

**c**) Network’s data loss rate.

Notation | Definition |
---|---|

$N$ | node sets |

${E}_{max}$ | the node’s battery capacity |

${E}_{min}$ | the node’s minimum energy level for operation |

${E}_{i}$ | node $i$’s residual energy level |

$v$ | the charger’s traveling speed |

$L$ | the charger’s traveling distance constraint |

${p}_{r}$ | the node’s received charging rate |

${T}_{w}$ | the period of time for the charger’s replenishment |

${d}_{s}$ | the node’s sensing range |

${d}_{r}$ | the node’s maximum transmission range |

${e}_{s}$ | energy consumed to sense an event |

${e}_{t}$ | energy consumed to transmit a packet |

${e}_{r}$ | energy consumed to receive a packet |

${e}_{c}$ | energy consumed to combine a packet |

Parameters | Values |
---|---|

Network Size | 100 × 100 m^{2} |

Number of nodes | 100 |

${E}_{max}$ | 1000 J |

${E}_{min}$ | 0 J |

$v$ | 1 m/s |

$L$ | 600 m |

${p}_{r}$ | 5 W |

${T}_{w}$ | 1000 s |

${d}_{s}$ | 10 m |

${d}_{r}$ | 25 m |

${e}_{s}$ | 0.15 mJ |

${e}_{t}$ | 5 mJ |

${e}_{r}$ | 1.6 mJ |

${e}_{c}$ | 0.05 mJ |

Simulation time | 100,000 s |

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## Share and Cite

**MDPI and ACS Style**

Liu, H.; Deng, Q.; Tian, S.; Peng, X.; Pei, T.
Recharging Schedule for Mitigating Data Loss in Wireless Rechargeable Sensor Network. *Sensors* **2018**, *18*, 2223.
https://doi.org/10.3390/s18072223

**AMA Style**

Liu H, Deng Q, Tian S, Peng X, Pei T.
Recharging Schedule for Mitigating Data Loss in Wireless Rechargeable Sensor Network. *Sensors*. 2018; 18(7):2223.
https://doi.org/10.3390/s18072223

**Chicago/Turabian Style**

Liu, Haolin, Qingyong Deng, Shujuan Tian, Xin Peng, and Tingrui Pei.
2018. "Recharging Schedule for Mitigating Data Loss in Wireless Rechargeable Sensor Network" *Sensors* 18, no. 7: 2223.
https://doi.org/10.3390/s18072223