# An Efficient Mobility Model for Improving Transmissions in Multi-UAVs Enabled WSNs
## 4 System Model and Proposed Approach
### Proposed Approach
The average number of transmissions in a given area or square which is effectively a self-cluster and the overall average transmissions in the system are given by Equations (8) and (9):  
\[\mathcal{T}_{A,area}=\frac{\sum_{i}^{C_{n}}\left(\frac{R_{T}}{C_{n}}\right)} {C_{n}}, \tag{8}\]  
\[\mathcal{T}_{A,system}=\frac{\sum_{i}^{C_{n_{sys}}}\left(\frac{R_{T_{sys}}}{ C_{n_{sys}}}\right)}{C_{n_{sys}}}, \tag{9}\]  
where \(\mathcal{T}_{A,area}\) and \(\mathcal{T}_{A,system}\) are the average number of transmissions in a self-cluster and overall system, respectively. The inequality in Equation (10) identifies the dense clusters from the scares ones. The clusters lying on the left side of the inequality are considered to be dense clusters, whereas the clusters lying on the right side of the inequality are considered to be scarce clusters:  
\[\mathcal{T}_{A,area}\leq F_{A}<\mathcal{T}_{A,system}. \tag{10}\]The model uses a modified version of [PERSON]'s Single Source Shortest Path algorithm where edge weights are given by Equations (11) and (12):  
\[\mathcal{W}_{e}=\sqrt{\left(\frac{\sum_{i}^{C_{n}}\left(\frac{R_{T}}{C_{n}} \right)}{C_{n}}-\frac{\sum_{i}^{C_{n_{\text{sys}}}}\left(\frac{R_{T_{\text{sys} }}}{C_{n_{\text{sys}}}}\right)}{C_{n_{\text{sys}}}}\right)^{2}}, \tag{11}\]  
\[\mathcal{W}_{e+}=\frac{1}{F_{A_{\text{sys}}}-\mathcal{W}_{e}}, \tag{12}\]  
where \(\mathcal{W}_{e}\) is the edge weight and \(\mathcal{W}_{e+}\) are the normalized edge weights used by the Single Source Shortest Path (SSSP) algorithm. The densely populated sectors are serviced by UAV maneuvers directly along with the sectors which fall in line with two consecutive UAV banks. The scarce sectors that don't fall in the path of UAV are the designated Lone sectors. Lone sectors send hello packets towards nearby dense regions and the base station when the network is initialized. The purpose of the hello packets is to determine the number of active nodes in the region and number of hops required to reach dense sector and base station, respectively. Cluster heads belonging to the lone sectors forward packets towards the base station when the inequality in Equation (13) is satisfied; otherwise, packets are forwarded towards dense regions of the geographical area:  
\[\mathcal{D}_{b}\leq\mathcal{D}_{d}, \tag{13}\]  
where \(\mathcal{D}_{b}\) and \(\mathcal{D}_{d}\) are the average number of hop counts from the base station and nearest dense cluster, respectively. The overall proposed approach is presented in Figure 3 in the form of an activity flow scenario. The complete Mobility Model alongside cluster and way-point selection is underlined in Algorithm 1. Algorithm 1 on initiation calls Algorithm 2, which deals with cluster head selection and overall topology formation. The algorithm further identifies the regions as dense and scarce. The link costs that are further used for deciding the UAV traversal routine are also determined by the Algorithm 2. The UAV path is generated by the Algorithm 3. Algorithm 4 is responsible for the control and coordination of data transmission. The algorithm facilitates transfer of data from scarce clusters, the clusters that don't directly fall under the UAV path. These clusters are identified as the Lone clusters. The Lone clusters or regions estimate their average hop distance from the base station and the adjacent dense region. This hop count information is used for facilitating the data transmission to and from the Lone regions. \[H_{d_{i}}=\frac{\sum_{i=1}^{C_{n}}D_{hop}}{C_{n}}, \tag{5}\]0 Proposed approach activity flow.