## 5 Numerical Results
### Analysis of Results  
The paper demonstrates the results of multi-step prediction, where predictions for future time intervals are inferred by postponing the output by a predetermined number of time slots. It is demonstrated that the accuracy of predicting traffic statistics for upcoming time steps decreases. Additionally, the paper evaluates the influence of timeslot duration T and the number of GRU network observations on prediction outcomes. To achieve accurate predictions in traffic data analysis, it is essential to determine the GRU network's memory storage capacity and minimum traffic data requirements. These parameters impact the network's ability to store information and provide reliable predictions. We compare ATS-GRU with the traditional time series network traffic prediction method (FTS-GRU). To ensure a fair comparison, the two prediction methods used the same number of hidden layers. Figure 5 shows the prediction results of both methods \begin{table}
\begin{tabular}{c c} \hline \hline
**Hyperparameters Name** & **Value** \\ \hline Initial Learning Step Size & 100 \\ \hline Number of Epochs & 100 \\ \hline GRU Hidden States & 64 \\ \hline GRU Hidden Layers & 5 \\ \hline Optimization Algorithm & Adam \\ \hline Loss Function & MAE \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Training hyperparameters. on traffic flow within the same time span. To begin with, the results suggest that the FTS-GRU model exhibits relatively lower accuracy. This is primarily attributed to its tendency to produce predictions that closely align with the average traffic volume for the entire prediction period at each time point. Consequently, this approach may struggle to effectively capture fluctuations and abrupt shifts in traffic flow, potentially leading to inaccuracies in certain scenarios. Conversely, the ATS-GRU model excels in enhancing prediction accuracy by forecasting both the overarching trends and sudden fluctuations in traffic volume. As traffic flow undergoes changes, this model dynamically adapts by reducing the time step as the speed increases. This dynamic adjustment allows the prediction model to more adeptly capture rapid shifts in traffic flow, resulting in more precise prediction outcomes. In addition, we compare the average prediction error of both methods on ten traffic flow profiles using the NRMSE metric, as shown in Figure 6. Consistent with expectations, the ATS-GRU model has significantly lower prediction error than the FTS-GRU model for all traffic flow profiles, thus reinforcing the superior prediction performance of the ATS-GRU model. The difference in error between ATS-GRU and traditional FTS-GRU primarily stems from the differences in the time-stepping size used for prediction. As mentioned earlier in the article, FTS-GRU employs a fixed step size for data sampling to complete predictions. Regardless of whether this step size is large or small, it is challenging to accurately forecast data within each time period because a dataset invariably contains instances of both small and large fluctuations in traffic volume. In contrast, ATS-GRU can precisely monitor traffic fluctuations through error feedback and dynamically adjust the time-stepping size based on these fluctuations. Therefore, it can be confidently stated that the predictive performance of the ATS-GRU model is superior to that of the FTS-GRU model, with errors approaching zero. Next, the importance and advantages of the ATS method in traffic load prediction are further explained and illustrated through a comparison of the prediction results using three different step sizes based on NLMS, namely FSS, VSS, and ATS. Figure 7 exhibits the normalized processing time for the three NLMS-based prediction methods. The comparison of different methods' processing time is essential in determining the efficiency of each method. To avoid the reliance of simulations on specific hardware resources, the FSS-NLMS method's running time is set to one. The VSS-NLMS and ATS-NLMS methods' running time is then normalized based on this criterion.