# An Efficient Mobility Model for Improving Transmissions in Multi-UAVs Enabled WSNs
## 4 System Model and Proposed Approach
### Proposed Approach  
The proposed approach initiates by grouping together the ground nodes into clusters and then segregating them on the basis of dense and scarce. The density of a particular cluster is associated with the number of transmissions originating from the cluster in a given time interval. As the UAV banking is based on the coordinates of the particular row-column of the subdivided area matrix, the square space as a whole is considered to be one cluster. The WSN nodes falling into a particular sector (block of the matrix) are default considered into the same cluster. Equation (4) outlines the cluster head selection process, where \(H_{d}\) is the average one hop distance. Equation (5) gives the metric calculation for a single node:  
\[Min(H_{d}),\] \begin{table}
\begin{tabular}{l l} \hline \hline
**Symbol** & **Description** \\ \hline \(H_{d}\) & Average One Hop Distance \\ \(R_{T}\) & Number of Transmission per Unit Time \\ \(S_{i}\) & Number of Nodes Transmitting per Unit Time \\ \(C_{n}\) & Number of Nodes in a Sector/Square/Region \\ \(S_{a}\) & Sector Area \\ \(R_{T,ys}\) & Number of Transmissions per Unit Time in the System \\ \(S_{i,ys}\) & Number of Nodes Transmitting per Unit Time in the System \\ \(C_{n,ys}\) & Number of Nodes in the System \\ \(S_{a,ys}\) & Overall System Area \\ \(\mathcal{T}_{A,area}\) & Average number of Transmissions in a Self Cluster \\ \(\mathcal{T}_{A,system}\) & Average number of Transmissions in Overall System \\ \(F_{A}\) & Attraction Function of a Sector/Square/Region \\ \(F_{A,ys}\) & Attraction Function for the Overall System \\ \(\mathcal{W}_{a}\) & Edge Weight \\ \(\mathcal{W}_{c+}\) & Normalized Edge Weight \\ \(D_{b}\) & Average Hops Towards Base Station \\ \(D_{d}\) & Average Hops Towards Neighbouring Dense Sector/Square/Region \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Symbol Table. \[H_{d_{i}}=\frac{\sum_{i=1}^{C_{n}}D_{hop}}{C_{n}}, \tag{5}\]  
where \(H_{d_{i}}\) is the node under consideration, \(D_{hop}\) are one hop distance from the node under consideration, given that the node coordinates lie within \((c,x_{i},y_{i})\), \((c,x_{j},y_{j})\), \((c,x_{k},y_{k})\),\((c,x_{l},y_{l})\) that is within the same sector, where \(c_{i}\) is the base station, and \(C_{n}\) is the number of nodes in the self-cluster. The transfer between UAV and sensor nodes always happens through the cluster-head, with the condition of Head Swap. The nodes with data to send forward this data towards their cluster head where data is accumulated. When UAV is in range of the cluster head, the Head Swap occurs. UAV becomes the cluster head of the sector to facilitate transfer not only from the designated cluster head, but also allows the cluster members to send data directed towards the UAV. The UAV way-points are set in a way that it moves from one dense cluster head towards another dense cluster head. UAV way-points are decided on the basis of transmission density and distance. Equation (6) defines the calculation of attraction function \(F_{A}\) by means of transmission density:  
\[F_{A}=\sqrt{\left(\frac{R_{T}}{S_{i}}\right)\times\left(\frac{C_{n}}{S_{a}} \right)}, \tag{6}\]  
where \(R_{T}\) is the number of transmissions per unit time in a sector, \(S_{i}\) is the number of nodes transmitting per unit time in a given sector, \(C_{n}\) is the number of nodes in a sector and \(S_{a}\) is the sector area. Similarly, the \(F_{A_{sys}}\) for the whole system is calculated according to Equation (7):  
\[F_{A_{sys}}=\sqrt{\left(\frac{R_{T_{sys}}}{S_{i_{sys}}}\right)\times\left( \frac{C_{n_{sys}}}{S_{a_{sys}}}\right)}, \tag{7}\]  
where \(R_{T_{sys}}\) is the number of transmissions per unit time in the whole system, \(S_{i_{sys}}\) is the number of nodes transmitting per unit in the system, \(C_{n_{sys}}\) is the number of nodes in the system and \(S_{n_{sys}}\) is the overall area.