# Mobile Charging Scheduling Approach for Wireless
## 3 System Model and Problem Formulation  
### System Model  
Figure 1 describes the network model of WRSN, which mainly consists of four components: \(n\) sensors, a charging service station, an MC, and a base station. Four units are equipped on each sensor, including a sensing unit, a wireless energy receiver, a processing unit, and a transceiver unit. Each sensor has the same energy capacity \(E_{sn}^{max}\); the set of the sensors is defined as \(SN=\{sn_{1},sn_{2},\ldots,sn_{n}\}\). The position of each sensor is \(p_{sn_{i}}=(x_{i},y_{i})\), and the remaining energy of each sensor is \(E_{sn_{i}}^{r},i=\{1,2,\ldots,n\}\), where \(i\) is the integral index of the sensors. The position of charging service station is \(p_{d}=(x_{d},y_{d})\); the distance  
\begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline  & \multicolumn{3}{c}{**Periodic Charging**} & \multicolumn{3}{c}{**On-Demand Charging**} & \multicolumn{3}{c}{**DRL-Based Approaches**} \\ \cline{2-13}  & [5] & [6] & [7] & [8] & [9] & [10] & [12] & [13] & [14] & **This Work** \\ \hline Is the MC involved? & \(\surd\) & \(\surd\) & \(\surd\) & \(\surd\) & \(\surd\) & \(\surd\) & \(\surd\) & \(\surd\) & \(\surd\) & \(\surd\) \\ Are sensors charged with WET? & \(\surd\) & \(\surd\) & \(\surd\) & \(\surd\) & \(\surd\) & \(\surd\) & \(\surd\) & \(\surd\) & \(\surd\) & \(\surd\) \\ Are energy consumption rates dynamic? & & & & & & \(\surd\) & \(\surd\) & \(\surd\) & \(\surd\) & \(\surd\) & \(\surd\) \\ Is charging upper threshold adaptively adjusted? & & & & & & & & & \(\surd\) & \(\surd\) & \(\surd\) \\ Is the energy capacity of MC limited? & & & & & & & & & \(\surd\) & \(\surd\) & \(\surd\) \\ Is there charging sequence scheduling? & & \(\surd\) & \(\surd\) & \(\surd\) & \(\surd\) & \(\surd\) & \(\surd\) & \(\surd\) & \(\surd\) & \(\surd\) \\ Is there a joint optimization? & & & & & & & & & & \(\surd\) \\ Are there multiple action spaces? & & & & & & & & & & \(\surd\) \\ \hline \hline \end{tabular}
\end{table}
Table 1: A comparison between existing studies and this study.  
between any two charging destinations of the MC, including the sensors and the charging service station, is \(d_{i,j}\), where \(d_{i,j}=\sqrt[2]{\left(x_{i}-x_{j}\right)^{2}+\left(y_{i}-y_{j}\right)^{2}}\).  
A wireless energy transfer module is equipped on the MC, which can transfer energy to the sensors and move freely in the network without obstacles. If the remaining energy of the MC is not enough to continue the charging task, it needs to return to the charging service station to change its battery. The process of starting from the charging service station, performing the charging task in the network, and returning to the charging service station to replace the battery can be regarded as a charging tour of MC. Furthermore, the sensor and the MC must communicate with the base station periodically. The MC transmits its own location and remaining energy information and obtains the charging policy from the base station. The sensors adopt classic MAC and routing protocols [15] and transmit their monitored information to the base station in a multi-hop communication via the path with minimum energy consumption.