## 5 The Proposed Protocol
### Network Area Division (DFGs Division)  
Hexagonal data fusion grouping ensures uniform coverage, reduces edge effects, and enhances data storage, addressing issues like ungrouped SNs. Unlike circular DFGs, which leave gaps and lead to inefficient space use and irregular neighbor spacing, hexagonal grids offer superior adjacency and clarity, making them ideal for IoT networks. Managing DFGs in IoT networks improves efficiency, scalability, and energy conservation by aggregating data at a central point (i.e., DFH) instead of transmitting it from multiple SNs. This reduces communication load and power consumption, vital for battery-powered SNs. The network sensing area (\(W\times W\)) is partitioned into hexagonal DFGs of the same size with a pointy top orientation, following a methodology similar to that presented in [32], with density calculated for both the overall network and individual groups. The sink node adjusts DFGs dynamically, aiming for balance between network density and DFG density. If the densities mismatch, merging or redistribution strategies are employed to optimize connectivity, load distribution, and network performance, minimizing redundancy and ensuring efficient operation. Each hexagonal DFG's side length (\(S\)) can be determined by applying the formula given in Equation (19).  
\[S=W/f, \tag{19}\]  
where \(W\) refers to the network size measured in (m) and \(f\) is a constant defined by the simulation.  
In the pointy top orientation, the vertical distance (\(v\)) between neighboring hexagonal centers is \(v=\left(\frac{3}{4}\right)\times height=\left(\frac{3}{2}\right)\times S\). However, the horizontal distance (\(h\)) is \(h=width=\sqrt{3}\times S\), as represented in Figure 4. Based on this division, Figure 5a illustrates the network before partitioning, covering an area of 200 \(\times\) 200 m\({}^{2}\). Subsequently, Figure 5b,\(c\) demonstrate the network post-partitioning and the distribution of SNs into the constructed DFG.  
Figure 4: Partitioning the network area into equally sized hexagonal DFG.  
In our proposed protocol, each network size is representative of a specific IoT application, with an assumed network density of 0.0025 nodes/m\({}^{2}\), which is also equivalent to a DFG density. Table 3 provides a comprehensive overview of these applications. Additionally, Figure 6a-e depicts models of a smart logistics park, smart medical center, smart factories zone, smart university, and smart city, along with their corresponding network sizes. Algorithm 1 shows the detailed steps of the setup phase.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Network Size (\(W\))** & **Hexagonal Side Length (S)** & **SNs Count (N)** & **IoT Application Type** & **The Sink Node Location** \\ \hline \(100\times 100\) m\({}^{2}\) & 20 m & 25 & Smart logistics park & (0,75) \\ \hline \(200\times 200\) m\({}^{2}\) & 40 m & 100 & Smart medical center & (0,125) \\ \hline \hline \end{tabular}
\end{table}
Table 3: Variations in network area sizes and their corresponding details.  
Figure 5: Partitioning the network area into equally sized hexagonal DFGs. (**a**) A 300 \(\times\) 300 m\({}^{2}\) network area before partitioning. (**b**) Partitioning network area into equal-sized hexagonal DFGs. (**c**) Distributing SNs into the formed DFGs based on their locations.  
Figure 6: A variety of IoT applications spanning different network areas. (**a**) Model for smart logistics park for 100 \(\times\) 100 m\({}^{2}\) of network area. (**b**) Model for smart medical center for 200 \(\times\) 200 m\({}^{2}\) of network area. (**c**) Model for smart factories zone for 300 \(\times\) 300 m\({}^{2}\) of network area. (**d**) Model for smart university for 400 \(\times\) 400 m\({}^{2}\) of network area. (**e**) Model for smart city for 500 \(\times\) 500 m\({}^{2}\) of network area.