# Network Traffic Prediction Incorporating Prior Knowledge for an Intelligent Network
## 5 Experiments and Analysis of Results
### Experimental Results and Analysis  
#### 5.3.1 Results of the FPK-Net Model Compared with Other Baseline Models  
FPK-Net was compared with the above five methods on the experimental data set. Table 1 shows the results of predicting the network traffic in a future time period.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Models** & **MAE** & **MSE** & **RMSE** & \(R_{adapted}^{2}\) \\ \hline
**HA** & 0.447 & 0.341 & 0.584 & 0.604 \\
**ARIMA** & 0.615 & 0.573 & 0.757 & 0.509 \\
**SVM** & 0.391 & 0.339 & 0.583 & 0.677 \\
**LSTM** & 0.420 & 0.297 & 0.545 & 0.745 \\
**CNN-LSTM-Attention** & 0.387 & 0.286 & 0.535 & 0.750 \\
**Transformer** & 0.412 & 0.319 & 0.565 & 0.711 \\
**FPK-Net** & 0.369 & 0.259 & 0.509 & 0.769 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Performance comparison of different methods on the dataset.  
From the evaluation indicators of each model in Figure 7, Table 1, it can be seen that:  
1. The historical average model (HA) uses the average historical value for forecasting and, in this paper, the average value of the last eight steps was used to forecast the next step. For this method, the forecast error was large.
2. Due to the limitations of model building, traditional time-series models do not have satisfactory prediction results. Among them, the ARIMA model had the largest prediction error among the above 6 types of models, with MAE and RMSE of 0.615 and 0.757, respectively, and the smallest prediction accuracy, with an \(R^{2}_{adapted}\) value of 0.509. As the essence of the ARIMA model is to capture the linear relationship of the flow series without considering the influence of other factors, the ARIMA model had a lesser effective prediction effect.
3. The support vector machine model (SVM) had the advantages of using fewer training parameters and producing more accurate results. The prediction results were 0.391 for MAE, 0.583 for RMSE, and 0.677 for \(R^{2}_{adapted}\). Its prediction results were more accurate than those of traditional statistical methods.
4. The \(R^{2}_{adapted}\) of the LSTM model was 0.750, which indicates that it produced more accurate results than the linear prediction methods. Although the LSTM-based prediction was good and it has a certain degree of feature mining ability for long time-series, as the input series contained more information, it was difficult for the LSTM model to converge to the global optimum during training, which led to poor prediction results.
5. The transformer model uses a self-focus mechanism to model traffic sequences. The prediction results were 0.412 for MAE, 0.565 for RMSE, and 0.711 for \(R^{2}_{adapted}\). Its prediction results were more accurate than other linear prediction methods. Although the transformer forecasts are good, the transformer is less capable of establishing long-term dependence capturing when long time series need to be predicted.
6. Compared with the other 5 models, the proposed FPK-Net model achieved the best results, in terms of all 4 evaluation indices, and the absolute coefficient of correction of the FPK-Net model reached 76.9% while the root-mean-square error reached 0.509. Compared with the ARIMA model, the RMSE and \(R^{2}_{adapted}\) were decreased by 0.248 and improved by 26.0% through the use of FPK-Net, respectively. Meanwhile, compared with the SVM, FPK-Net improved the \(R^{2}_{adapted}\) value by 9.2%; the SVM was less effective in prediction as it used a linear kernel function.  
Overall, the analysis indicated the poor fitting ability of HA and ARIMA for unstable data and long time-series while the neural network models fit the non-linear data better.  
Figure 7: Comparison of prediction results and true values: (**a**) Prediction results of traditional prediction methods vs. true values; (**b**) Prediction results of deep learning models vs. true values.