## 7 Conclusions  
In this paper, we have addressed the problem of quality-of-transmission-aware planning of lightpath connections in spectrally-spatially flexible optical networks connected using weakly coupled multi-core fibers. For estimation of QoT, we made use of an OSNR-based estimator in which the crosstalk impairment occurring in MCFs is considered as a source of the OSNR degradation along with other physical-layer impairments. The application of the OSRN model allows obtaining reliable solutions, which may not be the  
Figure 6: Comparison of network performance for fibers MCF-6 and MCF-7 in different network and crosstalk scenarios assuming \(|\mathcal{D}|=500\): the required number of slices (bars) and relative difference in the number of required slices between both MCF options (lines). Figure 7: OSNR-LA-PSA computation times in a function of number of demands \(|\mathcal{D}|\) for \(XT^{\text{REF}}=-57\) dB/km (left chart) and reference crosstalk level \(XT^{\text{REF}}\) for \(|\mathcal{D}|=500\) (right chart). case for the methods proposed in prior works that are based on the verification of XT levels only. We have included the OSNR estimator into a mixed-integer programming model of the lightpath planning optimization problem as a set of problem variables and constraints. Moreover, in order to generate solutions for larger network instances, we have developed an effective and fast optimization method. The obtained results of numerical experiments show that the MIP model has a low scalability, especially at the presence of crosstalk impairment, which complicates significantly solving the model. On the contrary, the optimization method proposed is capable of generating good quality solutions and can provide solutions to larger problem instances in reasonable time, even though the XT effect has a negative impact on algorithm computation times, too. Inter-core crosstalk also affects network performance and may lead to much higher demand for spectrum resources-- even twice as much in the evaluated network scenarios--when compared to the case where this signal impairment is not present. Eventually, the capacity of a multi-core fiber may not be utilized fully it the MCF has a specific core arrangement that does not allow to utilize some of its cores due to excessive XT levels in these cores. In particular, we have shown that a six-core MCF that has a core arrangement corresponding to a typical seven-core MCF, but is deprived of the central core, may offer almost the same performance as the seven-core MCF in the networks in which crosstalk has a considerable impact on transmission quality. In future works, we will focus on reformulating and strengthening the MIP model proposed in this work, with the aim of enabling solving larger problem instances as well as improving the estimation of solution lower bounds. Conceptualization, M.K. ; Funding acquisition, M.K. ; Investigation, M.K. and M.J.; Methodology, M.K. and M.J.; Project administration, M.K. ; Software, M.K. ; Supervision, M.K. ; Visualization, M.K. ; Writing--original draft, M.K. ; Writing--review and editing, M.K. and M.J. All authors have read and agreed to the published version of the manuscript. This research was funded by National Science Centre, Poland under grants number 2016/21/B/ST7/02212 and 2018/31/B/ST7/03456. Not applicable. The author declares no conflict of interest. The following abbreviations are used in this manuscript: