# A Graph Convolutional Network-Based Method for Congested Link Identification
## 4 Performance Evaluation  
### Experimental Set-Up  
In adherence to the conventions established in [26], and with the aim of fostering a controlled environment which prioritizes simplicity and a keen focus on core concepts, we opted to employ a numerical simulation approach for validating our proposed method. Figure 3 shows the topology of the network designed for the experiment. There are nine nodes in this topology. Without loss of generality, we took node \(s\) as the source node and nodes \(d_{1}\), \(d_{2}\), \(d_{3}\), and \(d_{4}\) as the destination nodes. In this topology, there are two routes between the source node and each destination node, and there are some shared links between different path routes, which partly reflects the complexity of the network.  
To evaluate the performance of the GIC algorithm, we devised a simulation framework which incorporates the concept of maximum prior congestion probabilities for both links and nodes.  
For the links, we introduced the maximum link prior congestion probability threshold \(\delta_{l}\), which represents the upper limit of the potential congestion level within the network. We randomly assigned a prior congestion probability \(p_{l}^{k}\) to each link \(l_{k}\) within the interval \([0,\delta_{l}]\). This approach ensured that while the overall congestion level was bounded by \(\delta_{l}\), the specific congestion probabilities for individual links differed, reflecting the diversity in proneness to congestion across the network.  
Furthermore, to capture the impact of node-related factors on network congestion, we introduce the concept of node cause congestion probability. The node prior congestion probability threshold \(p_{n}^{k}\) represents the likelihood of congestion arising from the computational capacity, storage space, and energy limitations of node \(n_{k}\). When a node becomes congested, we assume that all links originating from that node are also considered congested. Analogous to the link-level approach, we define a maximum node prior congestion probability \(\delta_{n}\) for the network and randomly assign a congestion probability \(p_{n}\) to each node within the interval \([0,\delta_{n}]\). This mechanism ensures that, in addition to link-specific congestion, the simulation also accounts for the heterogeneous nature of node congestion, thereby enhancing the realism and relevance of the simulation outcomes.  
We assume that the congestion probability of a link \(l_{k}\) due to channel factors is independent of the node cause congestion probability caused by its sending node \(N_{l}\). Then, the congestion probability of a link \(p_{c}\) is obtained from the link factor congestion probability \(p_{l}\) and node factor congestion probability \(p_{n}\):  
\[p_{c}=p_{l}+p_{n}-p_{l}\times p_{n} \tag{15}\]  
In the simulation experiments, the congested links in the network were generated randomly according to the congestion probability, and we calculated the congestion probability of each link according to Equation (15).  
We then performed simulation experiments at different values of \(\delta_{l}\) and \(\delta_{n}\) and repeated each experiment 20 times. Each repeated experiment was called a scenario, and in each scenario, we regenerated the link-caused congestion probability \(P_{l}=[p_{1},\ldots,p_{n}]\) and the node-caused congestion probability \(P_{n}=[p_{1},\ldots,p_{k}]\) for each link in the network. We generated 1000 simulation data points for each scenario, of which the first 80% were used to train the models and the last 20% were used to validate the trained models.