## 4 Implementation Scenario and Conceptual Framework
### Accuracy of NTPA Using Different DL Models  
We used the sliding window technique to train our DL models and cross validation to avoid overfitting with a validation split of 0.1 as mentioned in Table 2 along with other training parameters. The validation split determines the fraction of training data used for validation. The validation data are not used for training but evaluate the loss at each epoch.  
\begin{table}
\begin{tabular}{c c c c c} \hline \multirow{2}{*}{**Parameter Name**} & \multicolumn{4}{c}{**Deep Learning Models**} \\ \cline{2-5}  & **LSTM** & **GRU** & **CNN** & **MLP** \\ \hline Learning Rate & 0.1 & 0.3 & 0.2 & 0.01 \\ \hline Validation-split & 0.1 & 0.1 & 0.1 & 0.1 \\ \hline Epochs & 20 & 20 & 20 & 20 \\ \hline Dropout & 0.2 & 0.1 & 0.2 & 0.2 \\ \hline Momentum & 0.9 & 0.8 & 0.7 & 0.9 \\ \hline Hidden-layer & 1 & 1 & 1 & 1 \\ \hline \end{tabular}
\end{table}
Table 2: Configuration parameters.  
Figure 8 illustrates the performance of the different Deep learning models, where the x-axis is day and the y-axis is traffic (terabit per second (Tbps)). In our experiment, we predicted traffic over different days with different DL models (GRU, CNN, MLP and LSTM) and took the average of the traffic and compared it with real traffic. Figure 8 shows the LSTM, GRU, MLP, and CNN based NTPA prediction results against the actual network traffic. As shown in the figure, there is no significant difference between their prediction results, while MLP predicts the network traffic differently. Overall, LSTM outperforms other models.  
To measure the accuracy for different models, we used two methods: root mean square error (RMSE) and mean absolute percentage error (MAPE). RMSE is a measure that evaluates how good or bad the prediction is, using the Euclidean distance by calculating the difference between the true value and prediction. Additionally, MAPE is a different method that measures the prediction accuracy as a ratio. RMSE and MAPE are expressed as follows:  
\[RMSE=\sqrt{\frac{\sum_{i=1}^{N}\parallel p(i)-\hat{p}(i)\parallel^{2}}{N}} \tag{6}\]  
\[MAPE=\frac{1}{n}\sum_{i=1}^{n}\left|\frac{V_{i}-P_{i}}{V_{i}}\right| \tag{7}\]  
where in Equation (6), \(N\) is the number of data points, \(p(i)\) is the measured true value, and \(\hat{p}(i)\) is the predicted value. In Equation (7), \(n\) is the number of fitted points, \(V_{i}\) is the actual value, and \(P_{i}\) is the predicted value.  
Figures 9 and 10 demonstrate the accuracy for DL models with respect to a different dataset size. We calculated the averages for one week, one month, three months, six months, and one year for the MSE and MAPE errors and compared different models. As shown in the figures, LSTM is the most accurate model to predict the network traffic. Additionally, as the training dataset size grows, the error value decreases. In other words, training the NTPA with larger datasets provides higher prediction accuracy. The RMSE error values for 1 year long dataset as shown in Figure 9, for LSTM, GRU, CNN, and MLP are 0.03, 0.06, 0.2, and 5.7, respectively. Moreover, the MAPE error values for 1 year long dataset as shown in Figure 10, for LSTM, GRU, CNN, and MLP are 0.24, 0.44, 0.77, and 7.17, respectively. Both figures indicate that LSTM has the most accurate prediction performance.