## 5 Performance Evaluation
### Data Collection Performance Comparison  
In previous work, we proposed two probabilistic neighborhood-based data collection algorithms for 3D UASNs. To evaluate the performance of our algorithms, we compared them with one of the most widely used 3D path planning method, the basic Nearest-neighbor Heuristic. In the basic Nearest-neighbor Heuristic, the AUV moves to the nearest node without any probabilistic neighborhoods, which means that the AUV needs to visit all nodes. Simulations were run for the three schemes varying parameters \(p\) and \(n\). The parameter \(p\) represents the design decision when implementing the probabilistic neighborhood contour based on our proposed algorithms. The value of parameter \(p\) indicates the size of probabilistic neighborhoods, and the higher the parameter \(p\) is, the smaller the size of the probabilistic neighborhoods. The moving speed of the AUV is set to 5 m/s. \begin{table}
\begin{tabular}{l l} \hline \hline
**Parameters** & **Value** \\ \hline Network Size & \(1000\times 1000\times 1000\) m\({}^{3}\) \\ Number of Nodes & 100–1000 \\ Parameter \(p\) & \(0.9,0.7,0.5,0.3,0.1\) \\ Probabilistic Neighborhood Contour & \(150,210,240,270,300\) (m) \\ Moving Speed of AUV & \(2.5,5\) (m/s) \\ Transmission Frequency & 10 kHz \\ Transmission Power & 1 W \\ Transmission Round & 1–10 \\ Bandwidth & 4 kHz \\ Number of Each Node’s Data Packets & 100 packets \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Parameter Configuration. (1) _The effects of \(p\)_: In our simulations, a value of \(p=0.9\) corresponds to approximately 150 m of neighborhood size, \(p=0.5\) to approximately 240 m of neighborhood size, and \(p=0.1\) to approximately 300 m of neighborhood size, respectively. The number of nodes was set to be 500. Figure 7 shows the average information gain and the average mission time with variable parameter \(p\). As expected, with the increase of parameter \(p\), corresponding to increased successful data transmission probability, there was increased information gain, as shown in Figure 6a. As data collection field at a tour point of GPN-LSCAN is a inscribed regular hexahedron and the volume accounts for only about 3/8 of the probabilistic neighborhood contour sphere, the information gain of GPN-LSCAN is higher than that of PNCS-GHA. In addition, as shown in Figure 6b, the average data collection completion time increases with the increase of \(p\). This is because as the value of \(p\) increases, the size of neighborhoods decreased, so the path length of the AUV increased, requiring additional time for data collection completion. Figure 8 shows the gain to cost ratio of our proposed algorithms. Both our GPN-LSCAN and PNCS-GHA perform much better than the basic algorithm. We also note that with a lower required probability, GPN-LSCAN showed a higher gain to cost ratio than PNCS-GHA, but at a high \(p\), the gain to cost ratio of GPN-LSCAN was lower than that of PNCS-GHA. This is because when the neighborhood size is large enough, the path length of GPN-LSCAN approaches that of the PNCS-GHA. When the grid size is small, the path length is significantly longer. (2) _The effects of the number of nodes \(n\)_: In this part, the parameter \(p\) was set to be 0.7. Figure 9a shows the variation of the average information gain for different \(n\) arguments in the GPN-LSCAN,  
Figure 8: Average gain to cost ratio VS \(p\). Figure 7: (a) Average information gain VS \(p\); (b) Average completion time VS \(p\). PNCS-GHA, and basic algorithm. In both the GPN-LSCAN and PNCS-GHA models, the average information gain significantly increased as \(n\) increased. Figure 9b validates the advantages of our proposed algorithm in average data collection completion time. Since the AUVs in GPN-LSCAN and PNCS-GHA do not need to visit every node in the 3D UASN, the average data collection completion time in our proposed algorithms are obviously shorter than that of the basic greedy algorithm.