## 6 Evaluation
### Evaluation Results  
#### 6.3.1 Parameter Values That Meet Requirements, Relay Node Ratio  
We show the evaluation results in terms of the evaluation perspectives (Eval. 1) in Section 6.1.1 and (Eval. 2) in Section 6.1.2. Method of Randomly Selecting Relay Nodes  
(Eval. 1) For \"randomly selecting\", Figure 10 shows \"cluster split ratio\" and Figure 11 shows \"the number of isolated nodes\" for the \"relay function activation cut-off value\" at each relay node density. The \"cluster split ratio\" in Figure 10 is the percentage of experiments in which the cluster splitting occurred out of 100 experiments. The red box indicates the regions that meet the requirements. When the \"relay function activation cut-off value\" was about 50, \"the number of isolated nodes\" was almost zero. However, even a \"relay function activation cut-off value\" of 50 was not sufficient to meet the requirement because cluster splitting occurs in models with low relay node density. Since the relay node density has a significant impact on the \"cluster splitting ratio\", the \"relay function activation cut-off value\" should be set to a proper value by the relay node density. If the relay node density is 1.90, the \"relay function activation cut-off value\" must be greater than 90 to prevent cluster splitting. (Eval. 2) Figure 12 shows the \"relay node ratio\" at each \"relay function activation cut-off value\". The same characteristics were observed, regardless of the relay node density. The \"relay node ratio\" becomes close to 90% when the \"relay function activation cut-off value\" is larger than a 90 cluster, split does not occur even at a relay node density of 1.90, as shown in Figure 10 of Eval. 1. This means that almost all nodes become relay nodes, and that relay nodes are not being selected. Method of Selecting Nodes That Connect to More Adjacent Nodes  
(Eval. 1) In the \"more adjacent nodes\" and \"fewer adjacent nodes\", there are no isolated nodes because each node can select a relay node from its connected neighbors. As shown in Figure 13, as \"the number of relay nodes\" increases by one, the \"cluster split \begin{table}
\begin{tabular}{c c c} \hline \hline
**Relay Node Density** & **Model Size** & **Applicable Experiments** \\
**[/km\({}^{2}\)]** & **[km\({}^{2}\)]** & **Eval. 1 to 4** \\ \hline
1.31 & 12 km \(\times\) 12 km & Eval. 4 \\ \hline
1.57 & 11 km \(\times\) 11 km & Eval. 4 \\ \hline
1.72 & 10.5 km \(\times\) 10.5 km & Eval. 4 \\ \hline
1.90 & 10 km \(\times\) 10 km & Eval. 1–4 \\ \hline
2.35 & 9 km \(\times\) 9 km & Eval. 1–4 \\ \hline
2.97 & 8 km \(\times\) 8 km & Eval. 1–3 \\ \hline
3.88 & 7 km \(\times\) 7 km & Eval. 1–3 \\ \hline
5.27 & 6 km \(\times\) 6 km & Eval. 1–4 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Node arrangement models in Eval. 1 to 4.  
ratio\" improves by about 50%. For example, when the relay node density is 1.90 and \"the number of relay nodes\" increases from 2 to 3, the \"cluster split ratio\" improves from 30% to 10%. When the relay node density was low, the cluster split ratio was high. Even when the relay node density was the lowest (1.90), the cluster split ratio was kept to 0 if the number of relay nodes was set to more than 4. Regardless of the relay node density, it is expected that the requirements can be satisfied by selecting more than four nodes. Since the relay node density has a significant impact on meeting the requirements, \"the number of relay nodes\" should also be properly selected to the relay node density. (Eval. 2) The red box in Figure 14 indicates the \"relay node ratio\" to satisfy the requirement in all relay node densities. The \"relay node ratio\" becomes close to 70% when the \"the number of relay nodes\" is 4; cluster split does not occur even at a relay node density of 1.90, as shown in Figure 13 of Eval. 1. The \"relay node ratio\" to satisfy the requirement is lower than that of \"randomly selecting\". The results indicate that \"more adjacent nodes\" is more suitable for selecting relay nodes.