## 5 Algorithm
### E2E Operation and DGA Architecture
The practical implementation and deployment of the algorithm, however, pose a set of challenges that need to be considered while deploying the concept in carrier-grade networks:

* **SDN CP distribution and operations granularity--**while hierarchical multi-controller architectures improve the SDN CP scalability, the information exchange needed to establish the E2E paths increases with the degree of distribution. Moreover, it impacts the complexity of an M-SDNC as it needs to synchronise the states and operations of several spatially distant components. Hence, an appropriate deployment strategy and granularity of the distribution need to be adopted, including SDNCs and M-SDNC placement, to avoid large coordination overheads [59]. * **Resource utilisation and flow fairness--**the allocations with fixed QoS guarantees can lead to resource underspending if the allocated resources differ from the ones actually consumed by flows. To this end, it is vital to properly classify the incoming traffic to minimise this effect and employ advanced monitoring mechanisms to obtain actual resource consumption. Moreover, in the case of excessive allocation by the SDNCs, the DP components would require queue-level mechanisms to enforce flow fairness. * **DRL Performance--**the MADRL setup enables decreasing the state space and variability, which allows the agents to converge faster. In certain cases, however, e.g., in sparse topologies, the observable gain from deploying a DRL optimisation agent might be minor due to limited action space. Hence, the 3 DQR deployment should also consider the complexity of individual network segments and DGAs deployment costs. * **SLA Violations--**due to dynamic conditions, the change of link parameters (e.g., partial ISL occlusion by debris) may result in QoS parameters and SLA violation. Here, allocation itself was focused. However, it is essential to develop monitoring and alerting extensions that allow the tracking of the network status and performing flow rerouting in case of SLA violation risks or mobility events. ## 8 Summary and Conclusions

This paper presented a novel routing and path allocation framework for future mobile 3D networks called 3 DQR. The concept uses hierarchical multi-controller SDN to address key issues of SDN, which involve scalability and interoperability by using operations and metrics abstractions. The framework exploits a MADRL setup for routing based on GNNs and operates on domain and E2E levels, targeting the minimisation of flow rejection and flow rerouting rates and the improvement of load distribution. To improve transferability across different topologies and network configurations, the agent performs the reasoning solely based on the input graph features (node- and link-related SDN DP metrics) and topology prediction data obtained from GIMMF. The conducted evaluation over real and synthetic topologies has proved substantial gains compared to the most common shortest

Figure 12: Impact of aggregation interval on flow rerouting and rejection rate. path routing methods regarding traffic distribution (improvement up to 52%) and rejection rate (up to 13.5% smaller) in medium-load to congested network conditions. Finally, considerations regarding deploying the 3 DQR concept, possible issues, and perspectives for future improvements have been outlined. Conceptualisation, R.K. and R.T.; methodology, R.K.; software, R.K. and R.T.; validation, R.K.; formal analysis, R.K.; investigation, R.K.; data curation, R.K.; writing--original draft preparation, R.K., R.T., L.T. and S.K. ; writing--review and editing, R.K., L.T. and S.K. ; visualisation, R.K. All authors have read and agreed to the published version of the manuscript. ## References

* (1) ITU-R. _Future Technology Trends of Terrestrial International Mobile Telecommunications Systems Towards 2030 and Beyond;_ Report M.2516-0; International Telecommunication Union--Radiocommunication Sector: Geneva, Switzerland, 2022. 3 GPP. Study on Using Satellite Access in 5G, ver.