## 5 Simulation
### Performance Evaluation  
In this section, we compare the performance of TCEB with typical LEACH, EDCS, and GR-CTC in the underwater environment. We pay attention to when the first node and all of the nodes are dead, the average end-to-end delay, and the throughput of the network. For the first two aspects, we focus on the energy-efficiency which is presented as the time period (namely, round) including the stable phase and the whole lifetime of the network. Moreover, the latter is to examine the communication performance of the network. It also reflects from the side the QoS, e.g., the packet delivery loss rate, which is too high to result in the substantial increase of the last received data packets. All of the algorithms are evaluated under different deployed nodes density (\(n=100\) or \(n=200\)) with equipping different energy, where the results are averaged over multiple times to eliminate the randomness. Figures 7 and 8 are, respectively, given to show the comparison of four algorithms into the stable phase (i.e., the time when first node is dead) and the whole lifetime (i.e., the time when all nodes are dead) under different energy heterogeneity factor, in which the number of deployed nodes is 100. Basically, with the enlargement of \(\lambda\), the death of the first node and the death of all nodes are postponed in four algorithms. That means to equip more energy for each node can help prolong both the stable period and the whole lifetime. Nevertheless, from a longitudinal comparison, the TCEB is better than the three other algorithms under the same \(\lambda\) in both stable period and whole lifetime. Obviously, the typical LEACH has the worst energy-efficiency since it has a shorter lifetime. As far as we know, LEACH was once the classical clustering-based algorithm for the homogeneous TWSN. However underwater is a very complicated environment, and easily cut LEACH down on communication efficiency due to various factors. Since LEACH cannot respond to a variety of underwater emergencies, it would not be suitable for applying to UWSN which is a special heterogeneous wireless network. Figure 6: The total energy consumption (J) for control message of the whole network under different energy heterogeneity factor. On the other hand, EDCS and GR-CTC are also better than LEACH in the lifetime under the network scale of 100 nodes, where the EDCS is designed for general heterogeneous wireless sensor network and the GR-CTC is proposed for UWSN. In EDCS, many impact factors or existing difficult problems have been concerned in design, but it still ignores the complex status of underwater acoustic communication. The same packets may be forwarded multiple times since there might be higher packet delivery loss rate. That is the reason to lead to dissipating more energy on resending the packets. We can find there is a centralized strategy adopted in GR-CTC which makes the extra interaction between the nodes. It spends some energy and reduces the efficiency of the GR-CTC, even if it is specifically designed for underwater scenarios. Unlike with LEACH, EDCS, and GR-CTC, the proposed TCEBt combines the characteristics of the heterogeneous network and the particularities of the underwater environment; simultaneously, the larger underwater energy consumption and the multipath propagation, as well as the link stability, are all taken into account to guide to select the cluster-heads and build the multi-hop tree topology. Moreover, with a serial of strategies of load balance on energy consumption between nodes, the TCEB prolongs both the stable period and the whole of the lifetime, naturally. Figure 8: The comparison of whole lifetime under different energy heterogeneity factor \((n=100)\). Figure 7: The comparison of stable period under different energy heterogeneity factor \((n=100)\). Next, we observe the comparison of the stable period and the whole of lifetime under the nodes density of \(n=200\), when the energy heterogeneity factor (\(\lambda\)) increases.