## 5 Simulation
### Performance Evaluation
As shown in Figures 9 and 10, we can see almost the same trend of the curve while comparing with Figures 7 and 8, respectively. That is, the stable period and the whole lifetime of the four algorithms are all extended with the increasing of \(\lambda\) under the network density of \(n=200\). However, from the comparison of Figures 7 and 9, we can find that the first node is dead relatively earlier under \(n=200\) than the scenario of \(n=100\) within the same energy heterogeneity factor in most of the algorithms. The main reason is there are too many nodes located in the same smaller monitoring area, which would exchange much more messages in the local network. At the same time, too many nodes inevitably make much more communication interference among clusters and nodes. It could result in nodes failure or even the partial network paralysis. Specially, the complex underwater environment may cause increasing the number of link-hops, which expands the burden of the relay nodes. Hence, it leads to depleting extra energy on frequently resending the data to enable the normal work and make the entire network load balance as well as stabilization. Figure 10: The comparison of whole lifetime under different energy heterogeneity factor (\(n=200\)). Figure 9: The comparison of stable period under different energy heterogeneity factor (\(n=200\)). In Figure 10, the lifetime in TCEB is evidently better than other three algorithms. Without loss of generality, combined with aforementioned analysis, the TCEB has the merit of energy-efficiency over the other three algorithms under different network density even if there are equipped with the different energy heterogeneity parameter. From the energy-efficiency point of view, the proposed TCEB can contribute to currently further underwater applications. Furthermore, Figures 11 and 12 show the comparison of average end-to-end delay in TCEB and other typical algorithms under \(n=100\) and \(n=200\), respectively, when the energy heterogeneity factor (\(\lambda\)) changes. In Figure 11, we can clearly see that there is only tiny fluctuation for the curve of each algorithm under different \(\lambda\). That means the average end-to-end delay is relatively stable under \(n=100\) when the total energy of the network changes (i.e., \(\lambda\) changes). Meanwhile, compared with other algorithms, TCEB has less average end-to-end delay because it takes more real situations into consideration. In contrast, LEACH has highest average end-to-end delay within four algorithms since it is more suitable for ideal homogeneous environments. As shown in Figure 12, it reflects almost the same trends for each of algorithm under \(n=200\) while comparing with the scenario of \(n=100\). However, in Figures 11 and 12, we find that the average end-to-end delay for each algorithm is rising when the network scale enlarges, but the varied amplitude is small. This is because each algorithm adopts more or fewer mechanisms to reduce the end-to-end delay. Finally, Figures 13 and 14 show the comparison of throughput in TCEB and other typical algorithms under \(n=100\) and \(n=200\), respectively, when the energy heterogeneity factor (\(\lambda\)) changes. We can clearly see the throughput is increased in all four algorithms under different network density (both \(n=100\) and \(n=200\)) when the \(\lambda\) becomes larger. Obviously, it follows the rule that the more energy the network equips, the higher the throughput is. On the other hand, no matter the network density is 100 or 200 nodes, the throughput in TCEB is higher than the three other algorithms with the same \(\lambda\). This is because TCEB has more efficient clustering-based scheme with a load balance strategy to deal with the complicated underwater communication. It not only saves energy and prolongs the lifetime of the network, but also brings the higher throughput. In addition, it also reflects from the other side that the TCEB has higher transmission success rate than the three other algorithms, thereby increases the throughput of the network.