## 5 Performance Evaluation
### Simulation Results  
#### 5.2.1 Results for NSFNET  
We first evaluated the performance of our proposed method in the NSFNET, as shown in Figure 6a. The constant parameter \(\gamma\) in the proposed method was set to 0 or 1.0, unless stated otherwise. We defined the weight parameter \(W_{f}(R_{p})\) in the proposed method, as shown in Table 6, which was obtained from a preliminary experiment. Note that the table indicates that \(W_{f}(1)=0.0\) if \(f_{1}\leq f\leq f_{224}\); otherwise, \(W_{f}(1)=1.0\). A similar logic was followed for other values of \(R_{p}\). In the preliminary experiments, we obtained the number \(n(R_{p})\) of successfully established lightpaths for each required number \(R_{p}\) of FSs when using only the shortest paths. We determined the FS range based on this value by treating it as the intended number of lightpaths requiring \(R_{p}\) FSs to be established, as mentioned in Section 4.3. To achieve this, we calculated \(R_{p}\times n(R_{p})\), which represents the total number of frequency slots used for each \(R_{p}\). Then, the calculated value was normalized by the sum of the values of \(R_{p}\times n(R_{p})\) in the same group in such a way that the total became equal to the total number \(|\mathcal{F}|\) of available FSs. The normalized result was used as the FS width to be assigned to each \(R_{p}\). Accordingly, the prioritized FS range was determined, as discussed in Section 4.3. By doing so, we expected to perform resource allocation that reflected both the required number of frequency slots and the number of lightpath requests generated, as illustrated in Figure 4.  
In the experiments, we used two performance metrics: the blocking probability of lightpath establishment and the average number of inter-core crosstalk occurrences between established lightpaths. We define the blocking probability of lightpath establishment as  
\[=\frac{\text{number of blocked lightpath-setup requests}}{\text{total number of lightpath-setup requests}}. \tag{11}\]  
Additionally, we define the average number of inter-core crosstalk occurrences between established lightpaths as  
\[=\frac{\text{total number of inter-core crosstalk occurrences}}{\text{number of successfully established lightpaths}}. \tag{12}\]  
\begin{table}
\begin{tabular}{c c c c} \hline \hline \(R_{p}\) (Group) & **Assigned Width** & \(R_{p}\) (Group) & **Assigned Width** \\ \hline
1 (\(g_{3}\)) & \(f_{1}\leq f\leq f_{224}\) & 6 (\(g_{1}\)) & \(f_{303}\leq f\leq f_{310}\) \\
2 (\(g_{2}\)) & \(f_{1}\leq f\leq f_{256}\) & 7 (\(g_{3}\)) & \(f_{303}\leq f\leq f_{3  
In this paper, we define the occurrence of inter-core crosstalk between established lightpaths as the case where identical FSs are used in adjacent cores by the lightpaths. In the experiments, we counted the number of inter-core crosstalk occurrences at each FS whenever a new lightpath was established, and we used their total sum as the denominator in (12). The crosstalk level affecting the established lightpaths strongly depends on the number of inter-core crosstalk occurrences between the lightpaths. Note that we can calculate the crosstalk level using (2), but it depends on specific parameters that vary with assumed environments. In this paper, to conduct the performance evaluation independent of the assumed environments, instead of calculating the crosstalk level using (2), we employed the average number of inter-core crosstalk occurrences, defined in (12), as the performance metric. This performance metric corresponds to the evaluation criteria used in related works, such as the CP method [25] and other existing studies [19; 20; 24]. We examined the performance of the proposed method in the scenario where the number \(|\mathcal{C}|\) of cores in each fiber was small, i.e., \(|\mathcal{C}|=3\). Figure 6(a) shows the blocking probability of lightpath establishment as a function of the offered load \(\rho\) in NSFNET with \(|\mathcal{C}|=3\) cores.