## 4 Simulation Analysis
### Simulation Results
Moreover, the model's performance highlights its superiority in capturing complex data patterns that are missed by simple averaging. By leveraging historical demand data and focusing on individual beams, the model can account for the nonlinearity and seasonal variations inherent in the data. This ability to predict with higher precision and lower error margins makes it particularly suitable for scenarios that require advanced traffic allocation. The reduced volatility and enhanced stability of the model's predictions better meet the practical requirements for traffic management, ensuring that resources can be allocated efficiently and effectively. In summary, while using the average value for prediction offers a quick and straightforward approach, it falls short in terms of accuracy and reliability. The model's capability to capture and adapt to the specific patterns of each beam provides a more nuanced and stable prediction, making it a superior choice for applications that demand precise and dependable traffic forecasts. The best results are obtained when historical demand data for beams with similar trends are inputted into a single model for training, yielding an average predictive MSE of 0.0007 and a maximum MSE fluctuation of 0.014, both significantly lower than those of directly using the average value for prediction while maintaining excellent stability. Integrating historical demand data from beams with similar trends into a single model for training often yields superior results compared to training separate models for each beam individually. This is due to several reasons. Firstly, combining data increases the overall dataset size, providing a richer and more diverse set of samples, which helps the  
Figure 8: Comparison between model prediction and direct prediction. model generalize better and reduces the risk of overfitting to the specific patterns of a single beam. Secondly, beams with similar trends share common patterns, such as periodic fluctuations and nonlinear relationships, which the model can learn more effectively when trained on combined data. By leveraging these shared characteristics, the model enhances its ability to recognize and predict these patterns more accurately. Additionally, this approach improves the stability and reliability of predictions. Integrating similar beams helps smooth out individual anomalies and noise, leading to more consistent and stable predictions. It also addresses the long-tail distribution problem by balancing the dataset and ensuring that the model is adequately trained across various demand scenarios. Furthermore, training on a combined dataset enhances the model's robustness, making it more resilient to fluctuations and irregularities that might occur in practical applications. This combined training enables the model to better capture the temporal dependencies and cyclical trends that are crucial for accurate long-term forecasting. Currently, similarity is determined based on manual inspection and visually inspecting computer-generated charts of the historical demand patterns, where beams showing analogous fluctuations and trends over time are considered similar. Beams with similar trends are often in the same time zone range, which further supports their integration for more accurate modeling. However, the need for a more systematic and reproducible approach is acknowledged. As a future research direction, K-means clustering is planned to be employed to automatically group beams based on their historical demand data. K-means is particularly suitable for this task as it can handle large datasets and identify clusters of similar patterns based on features such as mean demand, variance, and periodicity. This method will enable more effective grouping of beams and provide a detailed, data-driven approach to enhancing model performance. This approach is expected to significantly improve the robustness and accuracy of predictions, ensuring that beams with similar trends are effectively identified and grouped.