## 4 Simulation Analysis of 3D Network Deployment Experiments
Figure 7 gives the variations of the coverage rate, the system utilization, and the spatial distribution diversion (SDD) respectively, depending on a different Debye length \(\lambda_{D}\) as a function of the calculation time steps. Generally, the coverage rage will be larger when \(\lambda_{D}\) increases, but the system utilization will decrease. It is very reasonable because the \(\lambda_{D}\) has the shielding effect in dusty plasma theory, which will push all nodes outward the system center. In such a case, the system utilization correspondingly becomes worse. Similarly with Figure 6, the SDD values decrease when the time steps increase. The convergence speed of the SDD is fastest at the 0-200 steps and then slightly rises at 500-1000 steps, which is related to the reverse of velocity and acceleration in the formula. It can be roughly seen that, when the \(\lambda_{D}\) is larger, the SDD will decrease faster at the early stage. After 2500 steps, the SDD values from different \(\lambda_{D}\) tend to be stable and also converge to around 0, but the final SDD value of the distribution with larger \(\lambda_{D}\) will also be larger. Based on these experiments, we can conclude that the increase of the Debye length \(\lambda_{D}\) will not change the final distributions of 3D sensor network deployment. Our 3D algorithm can work well and perform a very good stack structure of the truncated octahedrons. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Different \(\lambda_{D}\)** & **Average Moving Distance** & **Variance of Moving Distance** \\ \hline \(\lambda_{D}=0.5\times 0.0526\) & 1.4653\(\sim\)1.5113 & 0.2292\(\sim\)0.2314 \\ \(\lambda_{D}=1.0\times 0.0526\) & 1.2542\(\sim\)1.2815 & 0.1578\(\sim\)0.1654 \\ \(\lambda_{D}=1.5\times 0.0526\) & 1.1204\(\sim\)1.1341 & 0.1003\(\sim\)0.1107 \\ \(\lambda_{D}=2.0\times 0.0526\) & 1.0201\(\sim\)1.0317 & 0.0807\(\sim\)0.0824 \\ \(\lambda_{D}=2.5\times 0.0526\) & 0.9207\(\sim\)0.9295 & 0.0562\(\sim\)0.0573 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The ranges of average moving distances and their variances corresponding to different \(\lambda_{D}\) values. Figure 7: **(a)** The change of system coverage rate, (**b**) the change of system utilization rate, and (**c**) the variation of the spatial distribution diversion depending on different \(\lambda_{D}\) as a function of the calculation time steps. On the other hand, it is still worth checking the influence of the node sensing radius \(R_{S}\) on the performance of the 3D network deployment. Based on the formulae mentioned above, we have done a lot of experiments. Figure 8 presents the changes of the final system coverage rate at 3000 time steps developed by our 3D algorithm as a function of the node sensing radius \(R_{S}\), corresponding to different values of \(\lambda_{D}\). It can be clearly seen that, when the \(\lambda_{D}\) value is fixed, the system coverage rate will be larger when \(R_{S}\) increases. A large \(R_{S}\) can increase the sensing range of a single node, which will finally improve the whole coverage area. Besides, the system coverage rate for a large \(\lambda_{D}\) reaches a maximum value more quickly. This proves that, for a real WSN application, the \(R_{S}\) cannot be increased randomly since it will dramatically use the system energy and need a higher hardware cost. Furthermore, it is also found that, when the \(\lambda_{D}\) increases, the final coverage rate usually becomes higher. Moreover, in order to select the best \(R_{S}\) for better coverage rate and system utilization corresponding to a different Debye length \(\lambda_{D}\), we compare the relationship between the final coverage rate \(C\) and system utilization \(U\) at 3000 time steps deployed by our 3D deployment algorithm. As shown in Figure 9a, those curves give the variations of the final coverage rates and system utilization for \(\lambda_{D}\) = 0.5, 0.75, 1.0, 1.25, 1.5, 1.75, 2.0, 2.25, 2.5, 2.75, 3.0 \(\times\) 0.0526.