## 5 Proposed Model
### Multi-Tier Federated Scheduling  
After performing clustering and CL selection, the WSN nodes are scheduled to reduce the unwanted interference and data collision in the network. Leveraging the issues faced by the conventional scheduling techniques, this research performs a multi-tier hierarchical scheduling technique into three states such as transmission, reception, and sleep in which the first tier involves scheduling of WSN nodes within the clusters by the CL based on their priority and energy level. To be clearer, the first-tier scheduling is performed among WSN\({}^{\text{CL}}\) and WSN\({}^{\text{CL}}\)s in which every WSN\({}^{\text{CL}}\) in the environment updates the scheduling cycle for completing the transactions. The WSN\({}^{\text{CL}}\) took resilient decision to its WSN\({}^{\text{cm}}\)s based on the priority \(\left(\text{pri}_{\text{WSN}}\right)\) and energy level \(\left(\text{enew}_{\text{WSN}}\right)\). In such a case, the WSN\({}^{\text{CL}}\) that resides closer to the LBS might lose more energy when compared to the WSN\({}^{\text{CL}}\) with a longer distance from the LBS. Thus, the closer resided WSN\({}^{\text{CL}}\) tends to update its scheduling cycle in a shorter period of time. Therefore, the update of the scheduling cycle by the WSN\({}^{\text{CL}}\) for the first tier can be formulated as:  
\[1\text{st tier}\left(\text{SC}^{\text{j}}\right)=\left(\text{pri}_{\text{ WSN}}^{\text{j}},\text{eneew}_{\text{WSN}}^{\text{j}}\right) \tag{12}\]  
Equation (12) is suitable for both transmission and reception, respectively, along with sleep time period. When the first cycle expires, another scheduling cycle is initiated by  
\[1\text{st tier}\left(\text{SC}^{\text{j+1}}\right)=\left(\text{pri}_{\text{ WSN}}^{\text{j+1}},\text{eneew}_{\text{WSN}}^{\text{j+1}},\text{SC}^{\text{j}} \right)\rightarrow\left\{ \begin{aligned} \text{Txion}\\ \text{Rxion}\\ \text{Sleep}\end{aligned} \right. \tag{13}\]  
In Equations (12) and (13), \(\text{pri}_{\text{WSN}}^{\text{j}}\) and \(\text{pri}_{\text{WSN}}^{\text{j+1}}\) denotes the WSN node priority for j-th and j+1-th cycles, respectively; \(\text{enew}_{\text{WSN}}^{\text{j}}\) and \(\text{enew}_{\text{WSN}}^{\text{j+1}}\) denotes the WSN energy level in j-th and j+1-th cycles, respectively. Figure 2 represents the first-tier scheduling model among the WSN\({}^{\text{CL}}\) and WSN\({}^{\text{CL}}\)s.  
The second tier involves federated scheduling of CLs based on their results in first-tier scheduling by the local gateways using the Non-Cooperative Fuzzy Theory (NCFT) ap  
Figure 2: First-tier scheduling model. proach. The second-tier scheduling determines which CL performs transmission, reception, and sleep based on the weighted average of priority \(\left(\text{Wei}^{\text{pri}}\right)\), energy constraints \(\left(\text{ene}^{\text{cons}}\right)\), transmission time interval \(\left(\text{TTI}\right)\), and deadline \(\left(\text{dl}\right)\). The formulation of second-tier scheduling is provided below:  
\[\text{2 nd tier}=\text{CL}_{\text{n}=1,2,...,n}(^{\text{Wei}^{\text{pri}}, \text{ene}^{\text{cons}},\text{TTI},\text{dl}\ )}\rightarrow \begin{cases}\text{Txion} \\ \text{Rxion}\\ \text{Sleep}\end{cases}  \tag{14}\]  
where Txion, Rxion, and Sleep denotes the transmission, reception, and sleep, respectively. The LBS in the hexagonal grid schedules the CLs based on the metrics as mentioned in Equation (14). Finally, the third tier involves federated scheduling of local gateways by the sink nodes using the NCFT based on the results in the second level and other metrics such as priority \(\left(\text{pri}\right)\), energy constraints \(\left(\text{ene}^{\text{cons}}\right)\), transmission time interval \(\left(\text{TTI}\right)\), channel quality information \(\left(\text{CQI}\right)\), and deadline \(\left(\text{dl}\right)\). The third-tier scheduling determines which local gateways perform transmission, reception, and sleep, respectively.