# Sensor Topology Optimization in Dense IoT Environments by Applying Neural Network Configuration
## 4 Use Case Scenarios and Simulations
### Aggregating the Results  
Aggregating the previous simulation results related to the total network lifetime extension, we plot the extension per network size type for each use case and the solver's number of hidden layers in Figure 5a. The lifetime extension depicts the comparison, in terms of total energy consumption, of the initial and final topologies per use case. All the initial topologies are based on the deterministic case, i.e., the CVT (Voronoi) graph topology. According to Figure 5a, the solver managed to extend the network lifetime in all use cases and for all network size types, which means that the algorithm scales polynomially. Moreover, we observed that the choice of three instead of two solver hidden layers led to a better network lifetime extension in all cases. In that sense, for the deterministic network types (i.e., the Voronoi graphs), the addition of one more hidden layer in the solver, in conjunction with the corresponding tuning of the model's training parameters, led to a longer network lifetime. In Figure 5b, we plot the percentage (%) of the relocated nodes, in each of the network type use cases, as compared to the total nodes of the initial topologies. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameters** & **Values** \\ \hline Type of topology & Deterministic \\ Deployment area & 150 m \(\times\) 150 m \\ Sensing area width & 150 \\ Sensing area length & 150 \\ Topology type & CVT \\ Number of initial nodes & 800 \\ Number of relocated nodes & 406 \\ Sink node coordinates & (0, 0) \\ Solver’s hidden layers & 2 (case 3a) and 3 (case 3b) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Simulation parameters for use case 3: large-size network. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameters** & **Values** \\ \hline Type of topology & Random \\ Deployment area & 20 m \(\times\) 20 m \\ Sensing area width & 20 \\ Sensing area length & 20 \\ Number of initial nodes & 15 \\ Number of relocated nodes & 8 \\ Sink node coordinates & (0, 0) \\ Solver’s hidden layers & 2 (case 4a) and 3 (case 4b) \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Simulation parameters for use case 4: small-size network—random deployment. For the cases of deterministic CVT initial topologies, no matter how much we tried to increase the number of relocating nodes, we did not actually succeed in further extending the network lifetime. This is due to the fact that the solver also tried to extend the area coverage; therefore, it did not have many degrees of freedom to move nodes to new locations. To this end, we obtained a final topology in polynomial time, but the relocation rate stayed low. Additionally, in dense sensor areas of interest, by relocating 46.38% of the total nodes on average, we extended the network lifetime by an average of 4.5%. In Figure 5(a), we plot the network lifetime extension rate, comparing 2-layer and 3-layer solvers, for the deterministic and random use case network topologies. Firstly, we can observe that the 3-layer NN configuration led to a greater lifetime extension in both cases. Secondly, for the random topology deployment (i.e., Gaussian), we obtained a better lifetime extension rate in both NN configurations. This is because in random topologies, the solver has more degrees of freedom to relocate nodes than in the deterministic case. This means that the solver outputs a better topology deployment, in terms of objective function, under the constraints. In Figure 5(b), we plot the actual lifetime values, in rounds, for these cases. Again, we can observe that for random initial topologies, the solver achieved 12,443 and 12,505 rounds for the 2-layer and 3-layer NN configuration, respectively. Table 6 presents the values of total energy consumption per round and the network lifetime for the initial and final topologies, respectively, for each use case. We can observe that the solver managed to reduce the total consumed energy; additionally, the choice of three instead of two solver hidden layers led to a greater reduction in all cases.