# A Power Planning Algorithm Based on RPL for AMI Wireless Sensor Networks
## 5 Evaluation
Afterwards, we show how the target parent set size affects the same parameters for a network with 100 nodes in the rural scenario (Figures 8 and 9). The imposed number of parents \(k=3\) is not achievable for all nodes because nodes that can communicate directly to the root have only one parent. This can be observed in the example shown in Figure 10, which represents the DODAG obtained after the convergence of the RPL. In the figure, the size of the nodes represents the transmission power (in dBm) and the color represents the rank. The darker lines connect the child to the preferred parent while the lighter lines to the other parents in the parent set. The nodes with rank equal to 512 connect directly to the root. All links represented in the graph satisfy the restriction imposed on ETX. The results for the rural area scenario are shown in Figures 4 and 5. In Figure 4, one observes that the sizes of parent sets obtained by the DODAG method are closer to the target than those obtained by the other methods. For networks with up to 100 nodes, the DODAG approach reaches an average size of approximately 2.19, while the Vertex method reaches 1.79 and the Fixed method 1.77. For larger networks, the average size is 2.48 for the DODAG method and 2.21 for the other methods. The costs of the paths through preferred parents are shown in Figure 5. They are equivalent for the three methods when considering networks with up to 100 nodes, but, for larger networks, the DODAG approach overcomes the other methods, providing paths with costs 14.2% lower then the costs provided by Vertex and Fixed methods. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter** & **Description** & **Value** \\ \hline Channel & Channel Type & Rural/Urban \\ \(f\) & Radio Operating Frequency & 914 MHz \\ \(\alpha\) & Path Loss Exponent & 2.5 (rural)/3 9 (urban) \\ \(m\) & Nakagami-\(m\) Fading Severity & 1 (urban)/2 (rural) \\ \(ETX\) & Maximum ETX & 1.2 \\ Area & Rural Area (disk radius) & 1 km \\ Area & Urban Area (disk radius) & 100 m \\ Power & Transmit Power Range (Rural) & \(-10\) dBm to 10 dBm (2 dBm steps) \\ Power & Transmit Power Range (Urban) & \(-12\) dBm to 0 dBm (1 dBm steps) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Evaluation parameters. The results for the urban area scenario are shown in Figures 6 and 7. In the first, we can observe that the sizes of parent sets obtained by the DODAG method are also closer to the target when compared to the other methods. For networks with up to 50 nodes, the average size obtained by the DODAG method is approximately 2.19, while the average size is 1.7 for the other methods. For larger networks, the average size is 2.57 for the DODAG approach and 2.11 for the other. The costs of the paths through preferred parents are presented in Figure 7. One can observe that the costs obtained by the DODAG method are slightly larger for networks with up to 50 nodes, but one can observe that the costs are statistically equivalent. For larger networks, the average costs obtained by the Fixed method are 5.6% lower when compared to the other methods. If we take both metrics simultaneously in both scenarios, we can consider that the DODAG method reached the proposed objectives, since the sizes obtained for the sets of parents are always as close as possible to the target, while the costs obtained for the paths passing by the preferred parents are the best in the rural setting or very close to the best in the urban setting. Please note that the last scenario corresponds to dense networks where the algorithm has little room to act. Figure 4: Parent set size in a rural area scenario. Figure 5: Preferred parent path cost in a rural area scenario. Figure 6: Parent set size in an urban area scenario. Figures 8 and 9 show the effect of using different target values for parent set sizes (\(k\)) in a rural area scenario with 100 nodes.