# Performance Evaluation of Graph Neural Network-Based RouteNet Model with Attention Mechanism
## 2 Background and Related Work  
### RouteNet Model  
RoutNet is a type of Recurrent Neural Network (RNN) that is designed to predict network Key Performance Indicators (KPIs) for specific source-destination pairs, based on a given network configuration [7]. RouteNet is trained on data collected from various network topologies, including their traffic and routing configurations, to learn the net work model. This model can then be used to predict network performance for specific source-destination pairs. The model can then predict network performance by capturing the intricate relationships between link properties and source-destination paths in the network topologies. The process of transforming the original network topology into the RouteNet input graph is illustrated in [8]. The input graph used by RouteNet is a modified version of the original graph that has been transformed by representing links as nodes and creating hyperedges for each sample. RouteNet exploits the link-path relationship to obtain states that encode useful information for predicting performance metrics, with paths depending on link states and links depending on path states. We consider the internal architecture of RouteNet presented in [9]. During a single message-passing iteration in RouteNet, first, the information propagates from paths to links. For each link, the state vectors of all paths that use that link element-wise are summed and feed the resulting output as input to the RNN that updates the link state. The RNN combines the previous state with new information to produce a more informed, updated link state. Next, the information propagates from links to paths. For each path, the sequence of link states that the path traverses is used as input to a different RNN that updates the path state. The output of this RNN, with its initial hidden state set to the current path state values, gives the updated path state. This step is repeated for several iterations until the states converge [8]. The Gated Recurrent Unit (GRU) is a recurrent neural network (RNN) architecture introduced by [PERSON] et al. in 2014 [10]. The GRU addresses the limitations of traditional RNNs by incorporating gating mechanisms that enable selective information updates and access over time. It consists of two main gates: the reset gate and the update gate. The reset gate determines the extent to which the previous hidden state is reset, while the update gate controls the integration of new information into the hidden state. These gates allow the GRU to selectively retain relevant information and capture long-term dependencies, making it effective in various tasks. The mathematical representation of the GRU, as depicted in Figure 1, can be described by the following equations:  
\[r_{t} =\sigma(W_{r}\cdot[h_{t-1},x_{t}]) \tag{1}\] \[z_{t} =\sigma(W_{z}\cdot[h_{t-1},x_{t}])\] (2) \[\tilde{h}_{t} =\tanh(W_{h}\cdot(r_{t}\odot h_{t-1})+x_{t})\] (3) \[h_{t} =(1-z_{t})\odot h_{t-1}+z_{t}\odot\tilde{h}_{t} \tag{4}\]  
where  
\(W_{r},W_{z},W_{h}\): Learnable weight matrices used to capture patterns in the input data. \(x_{t}\): Input at time step t in the sequence. \(h_{t-1}\): Previous hidden state at time step \(t+1\). \(\sigma(\cdot)\): Sigmoid function used for activation and gate control. \(r_{t}\): Reset gate output at time step t, determines previous state reset. \(z_{t}\): Update gate output at time step t, controls new information incorporation. \(\tilde{h}_{t}\): Candidate hidden state at time step t, computed using the reset gate and input. \(h_{t}\): Current hidden state at time step t, computed by combining the previous hidden state and the candidate hidden state based on the update gate. In the GRU, the reset and update gates, along with the candidate memory content, are computed based on the previous hidden state and current input. The hidden state is then updated by combining the previous hidden state with the candidate memory content weighted by the update gate.