# Towards Digital-Twin Assisted Software-Defined Quantum Satellite Networks
## 5 Results  
The developed framework with which we conducted the simulation campaign described in this Section was run on a machine with an Intel Core i7-8750 CPU at 3.2 GHz with 16384 MB of RAM and Ubuntu 22.04.5 LTS installed. Specifically, the software was developed using the satellite toolbox of Matlab [62] together with Netsquid [63], a Python library for the development of QNs. The framework interprets the data of the TLEs available in [64] to create the TG of the satellite constellation, which is composed of 75 satellites. The simulation has been conducted during a time interval of 6 h, creating a TG with an accuracy of 1 s for the time intervals. The two GSs were positioned at a distance of 20,000 km one from the other, placed on the Equator at the geographic coordinates \((0^{\circ},0^{\circ})\) and \((0^{\circ},180^{\circ})\). Considering that, as reported in [65; 66], the upper limit of the troposphere can reach 20 km, the section of the G2S links affected by atmospheric conditions was calculated considering this altitude. Moreover, given that the creation of a G2S or S2G quantum link is practically impossible under suboptimal meteorological conditions [67], we have considered an atmospheric attenuation of 0.032 km, which corresponds to a visibility of 100 m for a wavelength of 1550 nm, as reported in [12]. The parameters and the respective values adopted in the simulations to model the optical communication apparatuses are shown in Table 1.  
Figure 4: Sequence diagram of the proposed protocol. Figure 5 shows the attenuation of G2S links throughout the duration of the entire simulation calculated according to Equation (2) compared to the attenuation values of the inter-satellite links composing the E2E paths. The paths generated during the entire simulation were composed of 6 satellites. Despite the fact that the atmospheric attenuation component is not present in the inter-satellite links, in some cases the attenuation values are superior with respect to those obtained in the G2S links. In fact, as depicted in Figure 6, the inter-satellite links have a greater average distance than the G2S links, and this has a significant impact on attenuation. The total path lengths are represented in Figure 7.  
In Figure 8, the performance is depicted in terms of the RTT required to reach the single satellites composing the path derived from the processing performed by the DT, compared to the performance of a suboptimal path. As can be observed, in the case where the DT is employed, the performance improves by 10%. Figure 9 shows the performance of the best path configured according to the optimization performed by the DT compared with a less durable one with respect to a specific time interval. As can be seen, the time required to obtain entanglement is lower in the case of the best path, and the continuity of its distribution indicates that no disconnections occur during the considered time interval. This is due to the fact that the path is connected during the time interval in which the GSs are simultaneously in visibility with their related satellites; after this time interval has elapsed, it is necessary to establish another path that requires some time to reconnect. The connection time is mainly influenced by the pointing time in addition to the setup phase of the protocol. In fact, as can be seen from Figure 9, the histogram is not continuous because the suboptimal path consists of two consecutive paths, both of which exhibit worse performance compared to the DT assisted one whose duration equals the sum of the two suboptimal paths. Figure 8: Performance of the RTT reaching a single satellite of the E2E path according to the optimization performed by the DT compared with the performance of a suboptimal one. Figure 7: Length of generated E2E paths.