## 5 Energy Optimization Approach Based on MAC/Routing Cross-Layer (EOAMRCL)
### Clusters Formation Phase (Network Layer)
* Clustering Overhead:
* Measures the communication and computational costs associated with cluster formation and maintenance;
* Lower overhead indicates more efficient clustering mechanisms, reducing strain on network resources;
* Essential for evaluating the protocol's impact on network performance and energy consumption. * Percentage of Packets Received
* Indicates the reliability of data transmission by measuring the percentage of packets successfully received;
* Higher percentages suggest better data integrity and communication efficiency;
* Crucial for ensuring consistent and accurate data flow within the network. ### Experimental Results and Interpretation

This section presents the experimental results and a detailed analysis of the performance of EOAMRCL and peer protocols. The experiments were conducted to evaluate various aspects of network efficiency, including energy management, node longevity, clustering overhead, and data transmission reliability. By comparing these protocols across multiple metrics, we aimed to highlight the strengths and weaknesses of each and demonstrate the superior performance of EOAMRCL in enhancing the operational lifespan and efficiency of WSNs. The subsequent figures and their interpretations provide insights into the effectiveness of these protocols under different conditions and performance criteria. Figure 8 compares the average remaining energy over 500 iterations. The graph highlights each protocol's energy management and network longevity. The DWEHC protocol exhibits the steepest decline in average remaining energy, indicating a higher rate of energy consumption compared with other protocols. By around 100 iterations, the average remaining energy drops significantly and continues to decline steadily. This can be attributed to DWEHC's lack of an optimized energy management strategy, resulting in faster depletion of nodes' energy reserves and a shorter network lifespan. In comparison, the EEUC protocol performs better than DWEHC but still shows a considerable drop in energy levels as iterations progress. The energy consumption is more controlled, but by approximately 300 iterations, the average remaining energy is

Figure 8: Comparison of average residual energy. substantially reduced. EEUC's strategies help prolong network life to some extent, but they are not as effective as more advanced protocols, lacking the optimization needed for longer durations. The CGA-GWO protocol demonstrates a more balanced energy consumption pattern, with a slower decline in average remaining energy. The integration of the GWO algorithm allows for more efficient clustering and routing decisions, conserving energy and extending the network's lifespan. CGA-GWO achieves better longevity and sustained performance over extended periods. EOAMRCL outperforms all other protocols, maintaining the highest average remaining energy throughout the 500 iterations. This superior performance is due to its effective cross-layer optimization approach, integrating the MAC and network layers for enhanced energy efficiency. By leveraging GWO, EOAMRCL optimally selects cluster heads and routes, minimizing energy consumption during data transmission. The protocol's duty-cycle scheduling at the MAC layer allows nodes to switch between active and sleep modes, further conserving energy. This results in a significantly extended network lifetime and consistent energy levels, showcasing EOAMRCL's effectiveness in managing energy consumption efficiently. In Figure 9, the DWEHC protocol shows a rapid progression from FND to LND. The FND occurs relatively early, indicating that the energy consumption among nodes is not well balanced. As a result, nodes begin to die off quickly, leading to a shorter network lifespan. The HND and LND metrics further confirm this, with a significant number of nodes dying earlier compared with the other protocols. This suggests that DWEHC lacks effective mechanisms for managing energy consumption and distributing load evenly across nodes.