## 6 Numerical Results  
We evaluate the proposed MIP optimization model and the OSNR-LA-PSA method in three different networks: generic German (DT12), Spanish (TEL30), and European (EURO16), which are shown in Figure 2. The parameters of network topologies are summarized in Table 2.  
The flexible frequency grid has a 12.5 GHz granularity. We assume that each network link consists of a number of 100 km length spans and a residual span that complements the link according to its actual length. The candidate routing paths are generated using a \(k\)-shortest path algorithm. We assume that \(k\) candidate paths are available for each pair of nodes. The paths are ordered according to their ascending physical lengths. In Section 6.1, we study the impact of \(k\) on network performance with the aim to select such \(k\) that offers a good tradeoff between the obtained results and algorithm runtimes. We consider two MCFs (shown in Figure 3): a typical seven-core hexagonal weakly coupled MCF that consists of a central core and six regularly spaced outer cores (MCF-7) and a six-core MCF that lacks the central core (MCF-6).  
The optical carrier and the guard-band occupy, respectively, _three_ and _one_ frequency slices. Four modulation formats are considered: BPSK, QPSK, 8 QAM, and 16 QAM, with the carried bit rate of 50, 100, 150, and 200 Gbit/s per 32 GBd OC, respectively. Traffic demands have randomly generated end nodes, and bit rates were uniformly distributed between 50 Gbit/s and 1 Tbit/s with a 50 Gbit/s granularity.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Network**} & \multirow{2}{*}{**Nodes**} & \multirow{2}{*}{**Links**} & \multicolumn{4}{c}{**Length [km]**} \\ \cline{3-6}  & & & **Mean Link** & **Mean SP** & **Max SP** & **Max Path** \\ \hline DT12 & 12 & 40 & 243 & 483 & 1019 & 2056 \\ TEL30 & 30 & 112 & 148 & 450 & 944 & 1130 \\ EURO16 & 16 & 46 & 486 & 1185 & 2663 & 4781 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Characteristics of network topologies; SP means shortest path.  
Figure 3: Tested fibers: MCF-7 and MCF-6.  
Figure 2: Network topologies: DT12, TEL30, and EURO16.  
The levels of crosstalk depend on the design and physical properties of MCFs [9]. Different values of crosstalk are mentioned in the literature, and the latest measurements in a recirculating loop for PDM-16 QAM signals estimate it between \(-57\) and \(-60\) dB/km [32]. Low \(\mathrm{XT}\) levels are difficult to be achieved in a seven-core MCF of standard \(125~{}\upmu\mathrm{m}\) diameter due to low outer cladding thickness, which increases excess loss [33]. Therefore, we study the MCF scenarios in which the level of \(\mathrm{XT}\) between two adjacent cores (\(XT^{\mathrm{REF}}\)), i.e., due to signal leaking from one core to another core, is between \(-51\) and \(-61\) dB/km. Such values display the highest differences between the conventional \(\mathrm{XT}\)-based model and the considered OSNR-based model (as shown in Figure 1) and, at the same time, have a significant impact on the transmission reach.  
As a reference, we consider an SDM scenario in which \(\mathrm{XT}\) is not present (denoted by \"\(\infty\)\"), which might correspond to a network using single-mode fiber bundles (SMFB) [8]. The transmission model uses the assumptions formulated in Section 3. The system parameters and the required SNR levels for the MFs considered [34] are shown in Table 3.  
The evaluation was performed on a \(3.7\) GHz \(32\)-core Ryzen Threadripper-class machine (\(64\) logical threads) with \(64\) GB RAM. The Cplex solver v.12.9 [35], run with default settings in a parallel mode, was used to solve the MIP model.