## 6 Empirical Research
### Empirical Results and Analysis
The analysis is mainly carried out by means of root mean square error (RMSE), mean absolute error (MAE), mean absolute percentage error (MAPE) [25], Hill inequality coefficient (TIC), deviation rate (BP) and variance rate (VP). The analysis  
Figure 6: AR05 traffic demand prediction and error in 9:00–9:15 22 May 2017.  
results are shown in the left column diagram of each subgraph in Figure 6. From the figure, the following can be determined:  
* The RMSE is 0.56, and the MAE is 0.45. That is, the error is only about 0.5. For actual operation, it can be regarded as no error. * The MAPE is 1.59%, and it is generally believed that the prediction accuracy is higher if the MAPE is lower than 10%. * The TIC is 0.01. When the TIC is between 0 and 1, the smaller the value, the less difference there is between the fitting value and the true value, and the higher the prediction accuracy. When the TIC equals 0, it signifies a 100% fit. Therefore, the TIC value obtained here is very small, indicating very high prediction accuracy. * The BP is rounded to about 0, reflecting that there is almost no difference between the mean of predicted value and the mean of true value, that is, there is almost no systematic error. * The VP is about 0.32, reflecting the small difference between the standard deviation of the predicted value and the standard deviation of the true value. Additionally, the fact that the true value always equals 28 does not fluctuate, which indicates that the predicted value fluctuates very little, which is also consistent with the information provided in Figure 7.  
We also used the BP neural network method to predict the traffic demand value of AR05 from 9:00 to 9:15 on 21 May 2017 100 times. The root mean square error (RMSE), the mean absolute error (MAE), the mean absolute percentage error (MAPE), the Hill inequality coefficient (TIC), the deviation rate (BP) and the variance rate (VP) are shown in the middle column diagram of the subgraphs in Figure 7. Comparing the error parameters corresponding to the left column diagram obtained by the probability prediction method, it can be observed that the probabilistic prediction method exhibits better accuracy in prediction, system error, and prediction value fluctuation. The main reason for this difference is that the historical traffic flow data of en route sectors are not in a stationary sequence, making it  
Figure 7: Error comparison between probability prediction method and BP neural network prediction method before and after data processing. less suitable for the BP neural network prediction method. Specifically, the VP obtained by the BP neural network is 19.80, which is larger, and the true value remains constant at 28 without fluctuation. This indicates that the predicted value of the BP neural network method fluctuates significantly. In Figure 7, we can see that the single prediction error of the probability prediction method is basically within 4%. Therefore, if this error value is extrapolated to the BP neural network method, more than 4% of the predicted values can be excluded, leaving 59 of the remaining effective predicted values, which is compared with the probability density prediction results as shown in Figure 8.  
Analyzing these 59 prediction values, we obtain the right column diagram of Figure 6 (BP After). It is found that all the predictive error parameters are significantly improved, and compared with the predictive results obtained by the probabilistic prediction method, the following can be observed:  
* The MAE is 0.30, which is less than the 0.45 value corresponding to the probabilistic prediction method, indicating that the overall prediction accuracy is better. * The MAPE is 0.57%, which is lower than the 1.59% value corresponding to the probabilistic prediction method, which indicates that the prediction accuracy is higher. Although some prediction error parameter values (after BP) are better than those of the probabilistic prediction methods, this improvement results from the elimination of data with large fluctuations.