## 5 Performance Evaluation  
### Model  
Through simulation experiments, we evaluate the performance of our proposed RCSA method. In this paper, we use two network models, as shown in Figure 6. The first network, named NSFNET, has 14 nodes and 21 bidirectional links. The second network, named the USA network, has 24 nodes and 43 bidirectional links. We assume that each node fills the roles of an intermediate switch, a sender node, and a receiver node. In the experiments, we use three types of multi-core fibers, i.e., \(|\mathcal{C}|=3\)-, 7-, and 13-core fibers, as shown in Figure 5, for each link. The number \(|\mathcal{F}|\) of available FSs in each fiber is set to 320. We construct \(K=3\) candidate routing paths using the \(K\)-shortest-path algorithm. Each sender node generates lightpath-setup requests according to a Poisson process with a rate of \(\lambda\) [1/sec]. The receiver node of each lightpath-setup request is independently selected with equal probability from all possible receiver nodes. The holding time of each lightpath is exponentially distributed with an average of \(H\) [sec], and the lightpath  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Core** & \begin{tabular}{c} **Group** \\ **\(g_{1}\)** \\ \end{tabular}  & \begin{tabular}{c} **Group** \\ **\(g_{2}\)** \\ \end{tabular}  & \begin{tabular}{c} **Group** \\ **\(g_{3}\)** \\ \end{tabular}  & **Core** & \begin{tabular}{c} **Group** \\ **\(g_{1}\)** \\ \end{tabular}  & \ \begin{tabular}{c} **Group** \\ **\(g_{2}\)** \\ \end{tabular}  & \begin{tabular}{c} **Group** \\ **\(g_{3}\)** \\ \end{tabular}  \\ \hline \(c_{1}\) & 0.0 & 1.0 & 1.0 & \(c_{8}\) & 0.75 & 1.0 & 1.0 \\ \(c_{2}\) & 0.25 & 1.0 & 1.0 & \(c_{9}\) & 1.0 & 0.5 & 1.0 \\ \(c_{3}\) & 1.0 & 0.0 & 1.0 & \(c_{10}\) & 1.0 & 0.75 & 1.0 \\ \(c_{4}\) & 1.0 & 0.  
is released after the holding time. The traffic demand \(D\) [Gbps] of each lightpath-setup request is randomly selected from the range [1; 2; 3; 4; 5; 6; 7; 8; 9; 10]. The transmission capacity \(T\) [Gbps] per FS for 1 bit/symbol transmission is set to 1. In this paper, to simplify the model, we assume that the length of each link is identical, with the objective of clarifying the potential effectiveness of the proposed method. In this case, the lightpath length is proportional to the number of hops. Thus, as shown in Table 5, we define the modulation level \(M_{p}\) in both networks based on the number of hops instead of the lightpath length. The required number \(R_{p}\) of FSs is determined by (1) with these values. We define the offered load \(\rho\) per FS in a core as  
\[\rho=\frac{\lambda H}{|\mathcal{F}||\mathcal{C}|}. \tag{10}\]  
From each simulation experiment, we obtain 20 independent samples to show the average performance. In each result, 95 % confidence intervals are shown (even though most of them are invisible). For comparison, we use the following three methods, whose concepts are related to our proposed method:  
1. **First-Fit (FF) Method:** The FF method is known to be highly effective in terms of the blocking probability of lightpath establishment, as it can prevent the occurrence of spectrum fragmentation. In the FF method, \(K\) candidate paths are prepared, as in our proposed method. It prioritizes the selection of the shortest path based on the number of hops and allocates available FSs along the selected path using a first-fit strategy. 2. **Core-Prioritized (CP) Method:** The CP method was proposed in [25] and is known to be effective in reducing both the blocking probability and inter-core crosstalk. In this method, cores are classified into groups based on priority. Then, lightpaths requiring the same number of FSs are allocated to the same core according to priority, similar to the proposed method. However, in [25], the authors assumed that there are only three types of the required number of FSs, i.e., \(R_{p}=3\), 4, and 5.