## 4 3D QoS-Aware Routing (3 DQR)  
### Concept Principles  
Infrastructure mobility and the mitigation of its effects are a core challenge for TN and NTN integration. Introducing User Plane (UP) flexibility and mechanisms for optimal routing and QoS path allocation is vital for provisioning stable network services to the end customers worldwide (cf. Section 2). The hereby proposed 3 DQR concept aims to address this challenge by combining the powers of SDN, DRL, GNNs, and topology prediction. In 3 DQR, a network comprised of a multi-stratum (terrestrial, aerial, space) and multi-domain (multi-controller) hierarchical SDN architecture is considered, as shown in Figure 1.  
The network assets within strata (terrestrial, aerial, and satellite) form SDN domains (one or more per stratum). Each domain is controlled by a dedicated SDNC (one per domain), i.e., Terrestrial SDNCs (T-SDNCs), Aerial SDNCs (A-SDNCs), and Satellite SDNCs (S-SDNCs). SDNCs implement domain-specific CP protocols (e.g., OpenFlow (OF) [46]), enabling full control of the traffic flows within a domain (i.e., of SDN switches) and monitoring suite for network state information acquisition. Each SDNC is accompanied by a dedicated Domain QoS-aware Router (DQR) with embedded DRL-GNN Agent (DGA) (further described below)--TE application is responsible for the calculation of optimal routes for all of the flows traversing the domain and load distribution. The E2E functionality is implemented by the logically centralised and physically distributed global-level Main SDNC (M-SDNC) acting as the umbrella controller for the underlying set of SDNCs and assisted by Master QR (M-QR)--DQR equivalent handling cross-domain routing and load balancing. M-SDNC operates using the overlay network view of the network that refers to the following:  
* Monitoring--in spatially distributed networks, centralised SDNC suffers from CP link latency, which leads to obtaining obsolete monitoring data. The hierarchical approach partially addresses this issue, as SDNCs can be deployed in close proximity of switches. Moreover, growing network size increases the monitoring data volume dramatically. Therefore, instead of link-level metrics, SDNCs calculate the parameters of overlay links between domain ingress/egress nodes denoted as Border Nodes (BNs) (access nodes, gateways, satellites, etc. ; cf. Figure 1). This reduces the monitoring traffic while conveying information about domains' abilities to serve new flows (cf. Section 5.1). * CP operations--M-SDNC has a view limited to BNs, overlay links within domains, and interconnection links to domains. Hence, M-SDNC arranges the End-to-End Path (E2 EP) enforcement by instructing individual SDNCs to allocate Intra-Domain Path (IDP) between BN pairs (i.e., a path composed of two BNs and intermediary relay nodes). As inter-domain links are either physical or overlay links between BNs of  
Figure 1: Overall view of 3 DQR concept and interactions across components. two domains, installing relevant flow entries in the BNs is equivalent to establishing the inter-domain path. The full E2 EP allocation procedure is described in Section 4.2. The topology information, monitoring metrics, and flow allocation history are stored in dedicated Traffic Engineering Databases (TEDs)--local and E2E--and exposed to TE applications on demand. TED implements the data retention strategies based on the requirements of operating TE mechanisms (especially DRL-GNN agents described further in this section). The details, however, are out of the scope of this paper. The ultimate goal of 3 DQR is to perform optimal routing and E2E path allocation in the integrated 3D network, considering three major aspects: network-level performance (measured by the degree of traffic distribution over the network links), flow QoS constraints, and flow importance (determined arbitrarily by the network operator based, e.g., on service priority or associated profits).