## 5 Performance Evaluation  
Since the LEO networks lack of the dataset for training, we use NSFNet dataset instead of the LEO dataset in this section for training. Both LEO networks and NSFNet are hierarchical routing networks. And some characteristics of LEO networks are similar to those of NSFNet. Changing the connecting state of some links in NSFNet can monitor the topological changes in LEO networks. Usually the topological changes in LEO are caused by link failure and node failure, and in this paper, they can be monitored by disabling the nodes in the NSFNet, which will cause link failure and node failure. Other than that, the node and link state are almost the same. The network modeling open-source dataset KDN (knowledge-defined networking) is used in this chapter, which is based on the real environment generated through OMNet++. The NSFNet network topology in KDN is shown in Figure 5. The NSFNet network contains the following: network node distribution, node attribute characteristics, traffic matrix, transmission delay, link bandwidth, etc. The GNN-DRL modeling algorithm uses the KDN dataset and is implemented based on the TensorFlow and OpenAIGym frameworks. All experiments were performed using standard hardware (Ubuntu 20.04.1 LTS (Canonical and friends, Boston, MA, USA), AMD Riptide 9 3950x16-core processor (AMD, Santa Clara, CA, USA), GTX-3080 graphics card (NVIDIA, Santa Clara, CA, USA)) without using any special hardware accelerators. The simulation environment is configured by initializing the link characteristics of each topology with its respective link capacities. In order to make the weights for all links equal, the network is set to have a bandwidth capacity of 100 Mbps for each link. Traffic demand is initially distributed on each node according to precomputed routing paths, then the simulation environment is sequentially updated when training by traffic demand. The DRL agent uses GraphSAGE to extract the hidden feature state of the links. In each execution of the GNN, T = 5 message passing steps are run, and a small batch of 50 samples is used. The optimizer used for training is the Adam optimizer, which has an initial learning rate of \(2\times 10^{-4}\) and follows an exponential learning rate decay during training. During the training of the GNN-DRL algorithm, the reward function converges very quickly. In order to evaluate the effectiveness of the routing algorithms based on graph neural networks, we will give the reward curves for all machine-learning-based algorithms in our experiments during online learning. For simplicity, the reward curves will be normalized as follows:  
\[R_{normalized}=(R-R_{min})(R_{max}-R_{min}). \tag{11}\]  
where \(R_{min}\) and \(R_{max}\) are the minimum and maximum rewards during online learning. The normalized reward curve is shown in Figure 6, and the results show that the cumulative reward of the GNN-DRL algorithm is better than that of the DQN algorithm. Three routing algorithms are compared in the simulation implementation: Dijkstra, DQN and GNN-DRL. The GNN-DRL is the proposed graph neural-network-based routing optimization method for LEO satellite networks in this chapter. After a comparison is made, the GNN-DRL algorithm can find a feasible solution to significantly improve the average network throughput and reduce the average end-to-end delay under different traffic demands, as shown in Figures 7 and 8. It can be seen that the GNN-DRL algorithm has better performance than that of the other two methods in terms of average throughput and end-to-end delay. Compared with Dijkstra and DQN, the GNN-DRL algorithm increases the average throughput by 29.47% and 18.42%, respectively, and reduces the average end-to-end delay by 39.76% and 15.29%, respectively. Figure 5: NSFNet network topology. Figure 6: Training process of GNN-DRL algorithm. Figure 7: Average throughput for different traffic demands.