## 2 Materials and Methods
### Handling Missing Traffic Flow Data  
In traffic flow prediction, missing data can have a significant impact on the accuracy and reliability of the prediction model. When the model relies on historical data for analysis and prediction, missing values in the historical data can lead to inaccurate predictions. Furthermore, if missing values are not handled properly, they can affect the model's fitting and generalization abilities, making the model more prone to overfitting to specific patterns in the existing data and unable to accurately predict new data. Therefore, in this paper, before predicting the traffic conditions during accidents and the duration of accidents, it is necessary to fill in the missing values to improve the accuracy and reliability of the model [23]. There are several methods for handling missing data, including:  
1. Deleting missing values: This method involves directly deleting data that contains missing values. However, this approach reduces the size of the training set and affects the accuracy of the model. In this paper, direct deletion would affect the range of the input variable, the ratio of traffic volume during accidents to the average traffic flow during the same period of the month. 2. Interpolation: Interpolation is a method of estimating missing data using known data. The most common interpolation method is linear interpolation, which estimates missing values using the straight line between two adjacent known data points. Other interpolation methods, such as Lagrange interpolation and spline interpolation, are also available. 3. Model-based approach: If the missing values in the dataset are relatively small, a model-based approach can be considered to predict the missing values. For example, regression models or time series models can be used to predict nighttime traffic flow. 4. Data imputation: Another method is to replace missing values with other values, such as the mean or median of the dataset. This method can maintain the size of the training set, but it may affect the accuracy of the model. In this paper, the missing traffic flow data mainly occurred during the time period from 10 p.m. to 2 a.m. on 30 November, from 9 p.m. to 11 p.m. on 10 December, and from 8 p.m. to 10 p.m. on 16 December. The Yingtian Street Tunnel Radar Detector records traffic flows at fifteen-minute intervals in seven different locations. Seven different locations can be thought of as nodes, and the connections within the tunnel as edges between the nodes. The seven nodes and their edges form a tunneling network of nodes, and each node's throughput is related not only to its own node throughput at historical times but also to the throughput of surrounding nodes. As a result, we can build a kind of message passing network, a GCN model, to explore the spatial characteristics of node A [24; 25]. Figure 1 shows the tunneling node network and computational diagram of node A. Additionally, as shown in Figure 2, we use the output fusion of the two models as a predictor of the traffic flow of node A using the long short-term memory network to extract the temporal characteristics of node A [26]. In summary, the GCN-LSTM model will be more accurate at filling in the missing value of the tunnel traffic volume, which is useful for improving the stability of the traffic accident prediction model. The graph convolution formula is as follows:  
\[H_{ne}^{(l+1)}=ReLU\left(\widetilde{D}_{ne}^{-\frac{1}{2}}\widetilde{A}_{ne} \widetilde{D}_{ne}^{-\frac{1}{2}}H_{ne}^{(l)}W_{ne}^{(l)}\right) \tag{1}\]  
where \(W_{ne}^{(l)}\) represents the learnable neural layer, \(\widetilde{A}_{ne}=A_{ne}+I\) and \(\widetilde{D}_{s,ii}=\sum_{j}\widetilde{A}_{s,ij}\). \(H_{ne}^{(0)}~{}=~{}X\in\mathbb{R}^{n\times f}\), where \(X\) denotes the feature matrix (traffic flow) of all sites in tunnel. Here, \(f\) denotes the feature dimension, \(H_{ne}^{(l)}\in\mathbb{R}^{n\times d}\) represents the \(I\)-th layer's output. The LSTM consists of three main components: the forget gate \(f\), the input gate \(i\), and output gate \(o\).