# Swarm Intelligence Techniques for Mobile Wireless Charging
## 3 The Network Model
### Network Elements  
Sensor data is generated at normal nodes and is aggregated at cluster heads (CHs) in a multi-hop fashion. Figure 1 shows a clear description of the entire network. Since the network is partitioned into multiple clusters inside a particular region, it is appropriate to have some cluster heads (CHs). Here, CHs are sensor-nodes that collect data packets from other nodes and transmit them to the MCs (here, the MCs are also the DCs). Hence,the rechargeable sensor-nodes consist of the normal nodes and CHs. Other nodes can forward their data to CHs using a multi-hop routing mechanism. The base station can be sited at the central position of the network, and it can be used for the data processing and recharging of the MCs to maintain continuous network operations. Finally, we will determine the CHs and the shortest moving distance of the MCs in each small region. The MCs (also serving as DCs) stay at the CHs in each region and collect the data aggregated by the CHs, while also replenishing the energy of the sensors within that vicinity. Moreover, the selection of the CHs is dynamic, as every region reselects the CH to avoid/minimize the hotspot problem and the data request flooding problem for multi-hop clustering. Then, the geometric traveling salesman problem (G-TSP) path of the MCs is structured to minimize the total traveling cost, the movement-energy consumption, and the data collection delays. The MCs can serve as both energy transmitters and data collectors. While traversing the network, the MCs collect the aggregated data from the CHs and recharge the sensor-nodes located within the vicinity of the CHs. Collected data are subsequently uploaded to the base station or the big data collection center. We propose a point-to-point charging of the sensor-nodes based on charging request priorities. Once an MC uses up its energy to charge the sensors, it quickly returns to the base station for energy replenishment.  
A detailed list of notations and their descriptions are presented in Table 1.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Notation** & **Description** \\ \hline \(\mathcal{N}\) & The number of sensor-nodes \\ \(\bigstar\) & Area of circular sensing field \\ \(\Re\) & Radius of circular sensing field \\ \(n\) & Number of mobile chargers \\ \(\$\) & Density of network \\ \(\mathrm{d}\) & Transmission range of sensor-nodes \\ \(\delta\) & Rate of packet generation by sensor-nodes \\ \(R_{c}\) & Recharge capacity of the MC \\ v & Speed of the MC \\ \(E_{j}\) & The residual energy of the sensor-node \(j\) before charging \\ \(\mathrm{t_{p}}\) & The charging time of the MC \\ \(P_{t}\) & The transmit power \\ \(\mathrm{R_{mc}}\) & The charging radius of the MC \\ \(P_{L}\) & The polarization loss \\ \(\eta\) & The rectifier efficiency \\ \(\mathrm{\Pi}\) & An adjustable parameter \\ \(G_{t}\) & Transmit gain \\ \(G_{r}\) & Receive gain \\ \(\lambda\) & Wavelength \\ \(\mathrm{\chi}\) & Message (in bits) transmitted or received \\ \(d^{\beta}\) & Power needed to transmit a message \\ \(\mathrm{x_{m,n}}\) & Relative density \\ \(\mathrm{E_{0}}\) & Initial energy of the sensors \\ \(\mathrm{\Gamma}\) & Recharge time of the sensor-node’s battery \\ \(\mathrm{\psi_{s}}\) & Battery capacity of the sensor-nodes \\ \(E_{r}\) & Total energy replenished into the network \\ \hline \hline \end{tabular}
\end{table}
Table 1: Notations with their descriptions.