# Hybrid Dual-Link Data Transmission Based on Internet of Vessels
## 4 Simulation Experiments
In underwater sensor networks, algorithms with low time complexity can reduce computational and energy consumption, improve real-time performance and stability, lower the communication overhead, and optimize overall performance. Especially in large-scale and dynamic environments, they ensure efficient operation, extend network lifespan, and enhance system reliability. In Table 2, we summarize and compare the complexity of crowdsourcing allocation algorithms from other references, and the results show that the HDTA algorithm has a clear advantage in terms of complexity. Figure 11: 10% selfish ship worker task delivery success rate. As shown in Figure 13, the experiment analyzes the effect of the \(\alpha\) time decay factor on the correctness of relay vessel selection. The experiment simulates 1000 selections of relay vessels under different \(\alpha\) values. As \(\alpha\) increases, the weight of more distant historical time slices decays faster, making the recent behavior have a greater impact on the vessel's reputation value. This allows for a more accurate reflection of the vessel's true reputation. When \(\alpha=4.5\), the probability of selecting the correct vessel reaches its highest, with the algorithm's success rate at 99.1%. Based on the 95% confidence interval analysis, the confidence interval for the algorithm's success rate is [0.9851, 0.9969]. Figure 14 compares the time overhead of the HDTA algorithm with the IAEF algorithm [44] and SDCS [26] under the same packet size, transmission protocol, and transmission distance conditions. In the underwater part, the time overhead differences between the three algorithms are relatively small. When the target node is closer, the transmission path of the HDTA algorithm is mostly underwater, and the path length is slightly longer than that of the traditional multi-hop algorithm, resulting in a slightly higher time overhead. As the propagation medium and transmission bandwidth change, the propagation speed shows significant differences. With increasing the transmission distance, the time overhead of IAEF and SDCS increases significantly, while the HDTA algorithm, by selecting vessels as relay nodes and using Very High Frequency (VHF) radio for vessel-to-vessel communication, significantly increases the transmission rate, thus greatly reducing the time overhead. Figure 15 compares the energy consumption of the HDTA algorithm with the IAEF and SDCS algorithms at different transmission distances. It can be seen that as the transmission distance increases, the energy consumption of the HDTA algorithm is significantly \begin{table}
\begin{tabular}{c l l l} \hline \hline
**Reference** & **Allocation Strategy** & **Analysis Model** & **Time Complexity** \\ \hline GREEDY [40] & Dynamic & AO & \(O(n^{2})\) \\ \hline Allocation [41] & Static & & \(O(n^{2})\) \\ \hline LP-ALG [42] & Dynamic & KIID & \(O(n)\) \\ \hline MMD-HST [43] & Dynamic & AO & \(O(n^{2})\) \\ \hline HDTA & Static & & \(O(n)\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Time complexity of comparison algorithms. Figure 12: Packet transmission success rate. lower than that of IAEF and SDCS. This is because in the HDTA algorithm, the energy consumption of the vessels selected as relay nodes is negligible, while in traditional multi-hop algorithms, the energy consumption increases with distance. The HDTA algorithm reduces unnecessary energy consumption and increases the survival time of underwater nodes. Figure 14: Comparison of the time overhead. Figure 13: The effect of the time decay factor on algorithm performance. Dual-head nodes are relatively inexpensive to design and manufacture and are suitable for large-scale deployment on a wide range of vessels, including cruise ships, cargo ships, and fishing boats. Compared to the deployment of Unmanned Aerial Vehicle (UAV), Automated Underwater Vehicle (AUV), or Unmanned Surface Vehicle (USV) assisted data transmission solutions, dual-head nodes offer significant advantages in terms of cost and deployment efficiency.