# A Graph Convolutional Network-Based Method for Congested Link Identification
###### Abstract
Compared with the SCFS algorithm without prior probability [13] and the MCMC algorithm with consistent prior probability [24], congestion link inference performance is considerably improved. The authors of [25] elaborates on the ill-posed nature of network Boolean tomography by highlighting the significance of integrating link correlations. They modeled the problem as a maximum a posteriori (MAP) estimation problem and proposed a learning-based algorithm specifically utilizing long short-term memory (LSTM), which is adept at learning the statistical dependencies of sequence elements from historical data. Additionally, the authors of [26] treated the process of link inference as a Markov process, proving the rationality of the mathematical method employed. The fault diagnosis technology rooted in graph theory has gained prominence. It deduces the most likely fault explanation set, relying on the accuracy of the graph model, such as the Bayesian network. In this context, the results of end-to-end path performance detection serve as observed nodes, revealing the states of these nodes' variables and thus identifying the links most prone to congestion. The authors of [27] proposed a probabilistic symptom-fault map to isolate likely faults through incremental updates. On the other hand, the authors of [28] utilized a Bayesian network for root cause analysis, identifying the underlying reasons for faulty states. These techniques are crucial for efficient network fault troubleshooting. Figure 1: A simple multiple-route topology. However, none of the previous studies considered the congestion caused by the limited computing resources of nodes, which is a typical characteristic of a WSN. In contrast to traditional networks, WSNs are made up of sensor nodes which send and receive data through wireless communication. Consequently, congestion often occurs at the nodes and on the radio channel [29; 30]. In WSNs, the downstream data flow from the sink to the sensor nodes typically involves a one-to-many multicast paradigm, whereas the upstream communication from sensor nodes to the sink adopts a many-to-one model. These networks are prone to two distinct types of congestion, as highlighted in [30] and illustrated in Figure 2. The first congestion type, which is commonly encountered in traditional networks, is node-level congestion. It arises from buffer overruns within individual nodes, leading to packet discarding and longer queuing delays. The subsequent packet loss triggers retransmission processes, thereby escalating energy consumption. Since WSNs rely on shared wireless channels among multiple nodes utilizing protocols akin to Carrier Sense Multiple Access (CSMA), link-level congestion emerges when several active sensor nodes concurrently attempt to access the channel, causing collisions. This phenomenon escalates packet service times, undermines link utilization and overall network throughput, and depletes energy resources at the sensor nodes. The congested link identification algorithms have greatly improved over previous methods. However, they still face challenges in WSNs. Firstly, they often assume that there is a single congested link per path, reducing accuracy in multi-congestion scenarios. Secondly, they overlook congestion caused by node factors, further compromising accuracy. For example, when a node is congested, all links flowing into the node are unable to communicate normally, leading to link failure. The congestion caused by the node makes the link failure correlated. Ignoring this correlation will reduce the prediction accuracy. To address this, we introduced a Bayesian network model (BNM) and graph convolutional network (GCN) technology to extract network topology features. We propose a deep learning method based on the GCN to solve the above two challenges. Our main contributions are as follows:  
1. We model the issue of link congestion as a BNM, which makes it suitable for scenarios involving node congestion and multiple congested links. 2.