## 6 Test and Analysis of Results
Moreover, it utilizes a mix of single-hop and multihop transmissions, resulting in FND occurring only after approximately 50 rounds. In the EBRP-TL, cluster heads are elected based on node degree and distance to the sink. The protocol selects the optimal next-hop cluster head during intercluster routing. As a result, the protocol experiences its FND around 130 rounds, with only about 20 rounds passing between the first and last node failures. This demonstrates that the protocol achieves more balanced energy consumption among network nodes, extending the network's lifespan. The number of clusters, or the number of cluster heads, is a crucial indicator for assessing network performance. Significant fluctuations in the number of cluster heads indicate substantial differences in energy consumption per round, leading to network imbalance and lower performance. The document in [30] proved that when the number of clusters reaches 3% to 5% of the total number of nodes, the network's energy efficiency is at its highest. In this paper, the number of nodes is 200, so we assume that the network's energy efficiency is highest when the number of cluster heads is at 5%. Figure 12 shows how the number of cluster heads varies with network rounds for three different protocols under the same conditions. In the LEACH protocol, where cluster heads are selected randomly, the number of cluster heads fluctuates considerably. Additionally, due to the rapid failure of nodes, the overall number of cluster heads shows a downward trend. E-LEACH takes the remaining energy of nodes into account during cluster head election,resulting in a significant reduction in the number of cluster heads. However, due to the inherent randomness in the cluster head election process, there is still considerable variation in the number of cluster heads. In contrast, while EEUC maintains a relatively stable number of cluster heads, this number is close to 10% of the total number of nodes, leading to lower energy efficiency. In contrast, EBRP-TL utilizes a timing mechanism for cluster head election based on uneven clustering, considering nodes' remaining energy, degree, and distance to the sink. Nodes prioritized to become heads will have neighboring nodes within their communication radius join their cluster. This causes some nodes that might have become cluster heads to join clusters that broadcast earlier, electing the optimal cluster head and effectively controlling the number of clusters. As a result, the number of cluster heads corresponding to EBRP-TL in the graph remains around 5% of the total number of nodes, which is the optimal number of cluster heads. Figure 11: Number of surviving nodes. Figure 12: Number of cluster heads. To visually compare the energy balance differences among the three protocols, we analyzed how the total network energy changes with each round under different protocols. As shown in Figure 13, the initial total energy of the network is 60\(J\), and the curve's slope represents the energy change rate. Obviously, with the EBRP-TL, the network's energy decreases almost uniformly, meaning the energy consumption per round is nearly equal. This result is consistent with the findings from the previous two experiments and further validates EBRP-TL's advantage in energy balance. The energy utilization rate refers to the ratio of energy consumed by the network during operation to the initial total energy. When the network experiences energy imbalance, the failure of a few nodes can disrupt regular network operation. However, the remaining nodes retain significant energy, leading to a decrease in energy utilization rate. After calculations, until the occurrence of 20 failed nodes (10% of total nodes), LEACH achieves an energy utilization rate of 38.2%, E-LEACH reaches 42.8%, and EEUC reaches 56.2%, whereas EBRP-TL reaches a high efficiency of 95.1%. In summary, multiple experiments were conducted in different scenarios to compare the proposed method with existing classical protocols regarding FND, the number of cluster heads, and energy consumption.