## 6 Numerical Results
### Evaluation of Network Performance
In particular, the spectrum requirements of the MCF-based network with a high level of XT (\(XT^{\text{REF}}=-51\) dB/km) might be more than twice as much as of the network connected using SMFB links. In general, the values of \(\delta\) are on comparable levels in different network topologies for particular XT levels. In Figure 6, we analyze the impact of the types of multi-core fiber used, namely, MCF-6 and MCF-7, on spectrum requirements in different XT scenarios. The bars represent the number of slices (\(z\)) required to allocate \(|\mathcal{D}|=500\) demands, while the lines reflect the relative difference (\(\delta\)) in the number of slices required in the MCF-6 scenario when compared to the MCF-7 case. We can see that in the XT-less scenario (\(XT^{\text{REF}}=-\infty\)), the networks take advantage of an additional core that is available in MCF-7 and utilize between about 14% (in \(\text{TEL30}\)) and 17% (in EURO16) spectrum resources less than in the case of MCF-6. However, if crosstalk is present, the gain in spectrum usage drops considerably down, to about 1%-2%, in all networks. In smaller networks DT12 and \(\text{TEL30}\), it happens for \(XT^{\text{REF}}=-61\) dB/km, while in EURO16, it is observed for \(XT^{\text{REF}}=-57\) dB/km. The  
Figure 4: The required number of slices in a function of the number of demands in different network and crosstalk scenarios assuming fiber MCF-7. Figure 5: Relative difference in the number of required slices with respect to the XT-less SDM scenario as a function of the number of demands in different network and crosstalk scenarios assuming fiber MCF-7. MCF-6 differs from MCF-7 only in the lack of the central core (see Figure 3). Note that this core is the one most affected by XT as it is adjacent to all six outer cores. Therefore, this core is likely to be utilized less if XT is present. As a consequence, it reduces the potential performance gain from the higher capacity available in MCF-7 when compared to MCF-6, which is reflected in the results in Figure 6.  
Eventually, in Figure 7, we report the computation times of the OSNR-LA-PSA method as a function of the number of processed demands for \(XT^{\text{REF}}=-57\) dB/km (left chart) and the crosstalk level for \(|\mathcal{D}|=500\) (right chart), assuming MCF-7 and \(5\times 10^{5}\) algorithm iterations. We can see that the algorithm runtimes increase almost linearly with \(|\mathcal{D}|\). At the same time, the presence of XT has a huge impact on algorithm computation times when compared to the XT-less scenario. This is mainly due to the need for a frequent, dynamic verification of QoT for every slice of each lightpath possibly affected by XT, which is a time-consuming process. Note that in a XT-less scenario, this process can be omitted, since the QoT estimation for particular lightpaths is static and not dependent on the actual allocation of spectral-spatial resources in the network. In addition, note that the application of both the proposed MFOB resource allocation approach and parallel processing in the optimization method (see Section 5) has allowed speeding up algorithm processing times, which would be very large otherwise.