## 6 Numerical Results
### Evaluation of Network Performance  
The last set of experiments was aimed at analyzing network performance in larger network scenarios that differ in topology, traffic demands, crosstalk levels, and MCFs used. The results were obtained after \(5\times 10^{5}\) iterations performed in the OSNR-LA-PSA method. In Figure 4, we present the number of used slices (\(z\)) in the SS-FON network using fiber MCF-7 after optimized planning of lightpaths for \(|\mathcal{D}|\) demands, assuming different topologies and XT levels. We can see that \(z\) increases with \(|\mathcal{D}|\), which is obvious as higher traffic demands result in higher bandwidth (spectrum) requirements. The smallest spectrum requirements are in network TEL30, which is due to both a larger number of links and shorter paths in this topology than in the other two networks (see Table 2). Indeed, the average link load is lower in a network with a larger number of links, while shorter paths enable the application of spectrally efficient modulation formats. The highest values of \(z\) are observed in EURO16, which is due to long transmission paths and, consequently, less efficient MFs that can be applied in this network. In Figure 4, we can also see that higher \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multicolumn{2}{c}{**Scenario**} & \multicolumn{3}{c}{**MIP Results**} & \multicolumn{3}{c}{**OSNR-LA-PSA Results**} & **Difference in \(z\)** \\ \hline \(\mathbf{k}\) & \(|\mathcal{D}|\) & \(\mathbf{X}\mathbf{T}^{\text{REF}}\) & \(\mathbf{z}^{\text{MIP}}\) & \(\mathbf{\Delta}^{\text{MIP}}\) & \(\mathbf{\Upsilon}^{\text{MIP}}\) & \(\mathbf{z}^{\text{OSNR-LA-PSA}}\) & \(\mathbf{\Lambda}^{\text{rel}}\) \\ \hline \multirow{8}{*}{1} & \(50\) & \(-\infty\) & 16 & 0\% & 0.1 & 16 & 0.3 & 0\% \\  & \(-57\) & 17 & 0\% & 216 & 17 & 1.5 & 0\% & \\  & \(-51\) & 26 & 0\% & 867 & 26 & 1.0 & 0\% & \\ \cline{2-10}  & \(80\) & \(-\infty\) & 19 & 0\% & 1.3 & 19 & 0.4 & 0\% \\  & \(-57\) & 26 & 23\% & 3600 & 26 & 2.4 & 0\% & \\  & \(-51\) & 37 & 43\% & 3600 & 36 & 1.7 & \(-3\%\) & \\ \cline{2-10}  & \(100\) & \(-\infty\) & 23 & 0\% & 2.6 & 23 & 0.5 & 0\% \\  & \(-57\) & 47 & 51\% & 3600 & 37 & 3.7 & \(-21\%\) \\  & \(-51\) & 52 & 56\% & 3600 & 49 & 3.2 & \(-6\%\) \\ \hline \multirow{8}{*}{3} & \(50\) & \(-\infty\) & 16 & 0\% & 2.0 & 16 & 0.3 & 0\% \\  & \(-57\) & 16 & 0\% & 2994 & 16 & 3.3 & 0\% \\  & \(-51\) & 20 & 20\% & 3600 & 20 & 2.4 & 0\% \\ \cline{1-1} \cline{2-10}  & \(80\) & \(-\infty\) & 19 & 0\% & 3.8 & 19 & 0.5 & 0\% \\  & \(-57\) & 27 & 30\% & 3600 & 20 & 6.9 & \(-26\%\) \\  & \(-51\) & 37 & 49\% & 3600 & 26 & 5.7 & \(-30\%\) \\ \hline \multirow{8}{*}{100} & \(100\) & \(-\infty\) & 22 & 0\% & 8.1 & 22 & 0.7 & 0\% \\  & \(-57\) & unknown & – & 3600 & 32 & 10.5 & – \\ \cline{1-1}  & \(-51\) & unknown & – & 3600 & 44 & 7.4 & – \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Comparison of MIP and OSNR-LA-PSA performance in different routing, traffic and crosstalk scenarios in network DT12; \(T^{\text{MIP}}\) and \(T^{\text{OSNR-LA-PSA}}\) in seconds. XT levels result in higher spectrum requirements. This can be explained by the fact that the allocation of lightpaths on neighbor MCF cores that would be acceptable in a low XT scenario might not be permitted in a high XT scenario due to an excessive degradation of QoT. In such a case, the lightpaths might need to be allocated within non-overlapping frequency ranges, thus increasing the spectrum requirements. In Figure 5, we show a relative difference in the number of used slices (\(\delta\)) for particular XT scenarios with respect to the SDM scenario in which XT is not present (\(XT^{\text{REF}}=-\infty\)). The value of \(\delta\) increases with the number of demands up to some level at which it stabilizes. In addition, in each network, we can see that the higher the XT level, then the higher the value of \(\delta\).