# Recharging Schedule for Mitigating Data Loss in Wireless Rechargeable Sensor Network
## 3 Network Model and Charging Scheme
### Network Model  
Figure 2 illustrates the network model in this paper. We consider a WRSN consisting of a set \(N=\{1,2,\cdots,|N|\}\) of sensor nodes randomly deployed in a rectangle area for environmental monitoring, where \(|\cdot|\) denotes the cardinality of the set. A stationary base station is located at the center of rectangle area for data gathering and acts as a mobile charger's depot. Each sensor node is powered by a rechargeable battery with a capacity of \(E_{max}\) and consumes energy on sensing and wireless data transmission. We assume that each node uploads its sensory data to the base station via a routing path determined by a shortest multi-hop routing algorithm, e.g., [PERSON]'s routing algorithm. When the residual energy level of a node falls below \(E_{min}\), the node will enter into a sleep mode and turn off most functions, including sensing and data transmission, until it gets the mobile charger's energy replenishment.  
To recharge the battery at each node, a mobile charger equipped with a powerful wireless energy transfer device is employed in the network. We assume that the mobile charger is driven by petrol or electricity, it can travel at a constant speed \(v\) and its traveling distance per tour is bounded by a given value \(L\). The mobile charger is equipped with a high capacity battery that is sufficient to charge all sensor nodes on its charging tour. Due to the large scale of devices and the higher energy loss in the omnidirectional radiation pattern [13; 26], in this paper, we adopt the point-to-point (direct) wireless power transfer pattern to maximize the energy wireless transfer efficiency. We assume the mobile charger charges only one node each time and each node will be fully-charged if the mobile charger visits, and the node's received energy power \(p_{r}\) is constant. During each tour, the mobile charger starts from the base station to charge nodes on its closed charging tour and returns before its traveling energy runs out. After finishing these point-to-point charging tasks, the mobile charger will stay at the base station to refuel or recharge itself for a period of time \(T_{w}\). The major notations used in this paper are listed in Table 1.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Notation** & **Definition** \\ \hline \(N\) & 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 \\ \hline \hline \end{tabular}
\end{table}
Table 1: List of notations.