## 4 Model Design
### The Proposed ATS-GRU Model
In contrast, the smaller the prediction error is, the smaller the time-stepping size becomes. In particular, the value of the targeted prediction error bound \(E_{b}\) can be defined and adjusted by the manager based on different network requirements or application needs. If \(|e(n)|>E_{b}\), the time-stepping size should be increased; if \(|e(n)|<E_{b}\), the time-stepping size should be decreased; if \(|e(n)|=E_{b}\), the time-stepping size should be kept unchanged. \(S_{s}^{\max}\) is the upper bound of the time-stepping size, which represents a low sampling rate, leading to the bottom-line responding time of the predictor. \(S_{s}^{\min}\) is the lower bound of the time-stepping size, which can lead to lower prediction error but larger computational complexity as the value rises. \(\gamma\) decides how much the current time-stepping size is relying on its previous value rather than the prediction error. We have to leverage the value of remembering factor \(\gamma\) for the optimal performance of the predictor, with \(\gamma=70\%\) as a typical case. In deciding \(S_{s}^{\max}\), we are faced with the choice between prediction accuracy and compilation efficiency. High values of \(S_{s}^{\min}\) lead to decreased prediction errors, but also an increased computational complexity of the prediction method. Selection of \(S_{s}^{\max}\) implies that the linear predictor must react quickly enough to manage burst traffic. In SAGIN, each satellite layer serves distinct purposes, providing global communication, positioning, and data transmission services. It supports various applications such as the internet, weather monitoring, military communication, and emergency response. The system is influenced by dynamic factors like weather conditions in different geographical regions, fluctuations in user numbers and locations, varying application demands, and potential communication interferences like solar radiation and changes in the earth's atmospheric conditions. In this complex network environment, accurately predicting dynamic traffic loads helps optimize resource management, including rational allocation of satellite bandwidth and processing capabilities, to reduce resource wastage. These predictions can be used to adjust bandwidth allocation to compensate for adverse weather effects on signal transmission, ensuring uninterrupted service. Managing changes in user numbers and locations helps avoid network congestion and unstable signals, prompting proactive measures such as increasing bandwidth or adjusting satellite routes. Additionally, precise traffic load predictions aid in cost savings, reducing energy consumption and enhancing the economic efficiency of network operations. Overall, this forecasting contributes to improving the efficiency of the integrated satellite network in air and space and on earth. Our proposed ATS-GRU algorithm is divided into three primary components: data transformation and partitioning into training and test sets, training of the GRU network, and traffic flow prediction and verification. The model's critical steps are enumerated as follows:  
Step 1: The traffic flow data that were collected are partitioned into training and test sets, with a 7:3 ratio. Step 2: The one-dimensional traffic data are transformed into two-dimensional data based on the \"sliding window\" principle. Step 3: The raw data are pre-processed by utilizing multiple techniques, including normalization. Step 4: The training data are fed into the GRU network, operationalizing the optimization of the model parameters used to construct the prediction model. Step 5: The trained GRU neural network is evaluated using test input vectors by generating predicted results in comparison to the actual values, where the resulting model error is subsequently calculated.