## 5 Algorithm
### E2E Operation and DGA Architecture
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \(\mathbf{N_{flows}}\) & **Test** & **s0-a** & **s0-b** & **s0-c** & **s0-d** & **s1-a** & **s1-b** & **s1-c** & **s1-d** \\ \hline \multirow{2}{*}{1000} & \(\mu\) & 0.067 & 0.06 & 0.044 & 0.063 & 0.062 & 0.065 & 0.059 & 0.062 \\  & \(\Delta[\%]\) & - & \(-11.7\) & \(-52.3\) & \(-6.3\) & - & 4.6 & \(-5.1\) & 0.0 \\ \hline \multirow{2}{*}{2000} & \(\mu\) & 0.072 & 0.065 & 0.048 & 0.069 & 0.069 & 0.073 & 0.067 & 0.07 \\  & \(\Delta[\%]\) & - & \(-10.8\) & \(-50.0\) & \(-4.3\) & - & 5.5 & \(-3.0\) & 1.4 \\ \hline \multirow{2}{*}{3000} & \(\mu\) & 0.075 & 0.067 & 0.051 & 0.072 & 0.073 & 0.077 & 0.07 & 0.073 \\  & \(\Delta[\%]\) & - & \(-11.9\) & \(-47.1\) & \(-4.2\) & - & 5.2 & \(-4.3\) & 0.0 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The mean (\(\mu\)) of \(std(u_{ij})\) in the best episode (aggregate over domains) and change \(\Delta\) compared to the baseline scenario (the lower, the better). Figure 10: Standard deviation of utilisation \(u_{ij}\) of links per domain (mean marked with red dot) for different loads. First, it can be observed that both of the trained models yield outstanding performance in the vast majority of the considered scenarios, decreasing the flow rejection rate (up to 14%) and improving the load distribution (up to \(\approx\)50% reduction in \(std(u_{ij})\)). Only in four cases was the rejection rate comparable to H-SP routing case, which regarded tests in highly sparse topologies (i.e., node degree equal to three and a small number of TN/NTN nodes) that effectively limited the agents' ability for routing improvements (despite the load distribution gains retained across setups, the congestion occurred). Finally, a very similar performance can be observed for s1-c and s0-c models operating in the T1 and T2 topologies, which further emphasises 3 DQR generalisation capabilities. The consistent performance across different setups is a result of using an attention mechanism within the agent--the contribution of edge and node utilisation to the candidate paths Q-values are relevantly scaled, which allows the agents to quickly identify the situations with a risk of congestion to avoid allocations to the expiring links. ### Topology Aggregation Interval Impact

The impact of adopting different aggregation time windows by GIMMF for NTN topology provisioning and predictions is shown in Figure 12. The results show both the rejected flow requests due to no viable QoS paths or no connection between the node pair, e.g., due to a disjoint graph. It can be observed that aggregation interval up to 5 s does not substantially impact rejected and rerouted flows. Increasing the duration of the aggregation interval increases the rejection rate up to 30% for 30 s and longer time frames. This phenomenon occurs due to the dynamicity of LEO topology and the progressively decreasing number of available links in the topology used for routing. An increasing aggregation interval decreases the number of viable links for SDNCs to route the traffic flows, ultimately leading to congestions and a higher probability of unavailable QoS-meeting paths or unreachability due to disjoint network graphs, altogether resulting in higher rejection rates. Moreover, adopting long aggregation intervals limits TE possibilities, which further aggravates the performance drop. Therefore, it is advisable to aggregate topology in rather short time windows to mitigate performance drops and, at the same time, conserve SDNCs computational resources that will be spent on frequent rerouting of flows. Figure 11: Performance comparison of H-SP-routing and 3 DQR model in terms of flow rejection rate (**left**) and load distribution (**right**). Codes 31 and 22 refer to topologies T1 and T2. ## 7 Considerations and Future Work

The 3 DQR algorithm enables improving routing decisions, utilising mobile network's resources, and decreasing rejection rates for each class.