## 3 Graph Neural Networks for Next-Generation Networks
### GNN in Core Networks
#### 3.3.2 Routing  
Routing optimization is a critical challenge in computer networks, significantly impacting network performance. The traditional routing protocols such as the Open Shortest Path First (OSPF) [103] and the Broader Gateway Protocol (BGP) [104] are performed on individual network devices based on only the local information. In contrast, SDN with its centralized controller offers a holistic network view, revolutionizing routing optimization by considering entire network configurations and topology. However, the routing optimization in SDN remains a challenging problem cause of the intractability of estimating the per-path E2E metrics (i.e., delay, jitters, and so on). Analytical models and packet-level simulators are classical solutions to this problem. While the analytical network models such as queueing theory and fluid models are constrained by unrealistic hypotheses, the packet-level simulators can accurately estimate those network metrics but at expensive computing costs. Data-driven methods, and especially those with GNN as the core module (Table 6), have emerged as an alternative due to their scalability and their capability of accurate modeling. In this section, we review two classes of GNN-based solutions: one focuses only on the estimation of the E2E metrics, and the other concerns the E2E DL architectures involved in the decision-making in plus. On the one hand, [PERSON] and [PERSON] [105] first propose the adoption of the MPNN for the estimation of delays in queuing networks. The framework is further improved with a bidirectional message passing between links-paths, so-called RouteNet [106]. The experiments are also carried out with the data generated by the packet-level simulator OMNeT++ [119] providing more realistic network traffic. Since then, many RouteNet variants have been proposed to improve the model and to adapt to the scenarios of more sophisticated network configurations. [PERSON] et al. [107] focus on the capability of modeling the network where forward devices would have different queue sizes. [PERSON] et al. [108] evaluate the generalization capabilities of the RouteNet in the larger networks of variable size (up to 50 nodes). TwinNet [109] introduces the notion of a queue state which led to a more complex message-passing scheme of three stages: (i) passing messages from queues, links to the associated paths, (ii) passing messages from \begin{table}
\begin{tabular}{c l l l l} \hline \hline
**Ref.** & **Model** & **Baseline** & **Simulator** & **Metric** \\ \hline
[105; 106; 107; 108; 109; 110] & MPNN & Queueing theory, Fluid model, RouteNet & OMNeT++ & Delays in queuing networks \\ \hline
[111] & MPNN & Genetic Algorithm & - & Edge utilization \\ \hline
[112] & MPNN, DRL & Equal-cost multi-path, DRL [113; 114] & OMNeT++ & Average E2E delay \\ \hline
[115] & MPNN, DRL & Shortest path, Q-Routing [116] & Mininet, Ryu & Packet delivery ratio and transmission delay \\ \hline
[117] & GCN, DRL & OSPF, DRL [118] & OMNeT++ & Packet loss rate, average delay, total number of packets forwarded \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Summary of application of GNN-based models for routing in core networks. paths to queues and (iii) passing messages from paths to links. This enables the model to capture different queue scheduling policies in a real-world network scenario. The most recent variant, RouteNet-F [110], attempts to fill the gap between the scale of the network testbeds or simulations, which are used for training, and the scale of the real network in the deployment. Indeed, this model aims to tackle the two challenges of RouteNet: (i) scaling to larger link capacities and (ii) different output ranges. The former challenges the neural networks to encode out-of-distribution numerical values of link capacities, which can reach infinity. The latter occurs when deploying the trained model into the real larger networks where the delay/jitter values can be very different due to higher link capacities and longer routing paths.