## 7 Conclusions  
In our study, we introduced MFG-LEACH, an enhanced LEACH protocol leveraging MFG theory to tackle energy optimization, scalability, and network longevity challenges in WSNs. Our approach enables dynamic adjustment of transmission strategies, resulting in balanced energy consumption and improved scalability and throughput compared to traditional protocols such as EAMR, EZ-SEP, and BRE, as demonstrated in Table 4. Additionally, the optimized energy usage extends the network's lifespan, reducing maintenance needs. Future research could further explore dynamic CH selection using the MFG framework, examine the performance of the protocol with multiple or mobile sinks to enhance adaptability, and focus on real-world experimental validation and integration with other protocols while also addressing security considerations. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Node Density**} & \multicolumn{3}{c}{**Energy Consumption (\%)**} \\ \cline{2-4}  & **EAMR** & **EZ-SEP** & **BRE** \\ \hline
0.001 & 73.36 & 73.74 & 73.88 \\ \hline
0.01 & 50.88 & 46.80 & 52.15 \\ \hline
0.05 & 65.0 & 23.84 & 16.10 \\ \hline
0.1 & 115.51 & 57.66 & 33.97 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Performance Improvement of MFG-LEACH (%). Figure 7: Network lifetime analysis based on the first and last node death events using the MFG-LEACH protocol. (**a**) Time until the first node death. (**b**) Time until the last node death. **Author Contributions:** Conceptualization, U.N., B.B. and H.A. ; methodology, U.N. and B.B. ; software, U.N.; validation, U.N. and J.C.; formal analysis, U.N., B.B. and H.A. ; investigation, U.N. and J.C.; writing--original draft preparation, U.N.; writing--review and editing, U.N.; supervision, B.B. and H.A. and J.C. All authors have read and agreed to the published version of the manuscript. **Funding:** H. Alves was partially supported by the Research Council of Finland (former Academy of Finland) 6G Flagship Programme (Grant Number: 346208). **Institutional Review Board Statement:** Not applicable. **Informed Consent Statement:** Not applicable. **Data Availability Statement:** Data are contained within the article. **Conflicts of Interest:** The authors declare no conflicts of interest. * [PERSON] et al. (2021) [PERSON]; [PERSON]; [PERSON] Efficient Rate and Power Allocation in Wireless Sensor Networks with Big Data Constraint. _Optik_**2021**, _64_, 3458-3469. [CrossRef]
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