## 6 Empirical Research
### Empirical Results and Analysis  
According to the above contents, the samples obtained by the rolling method are brought into the quantile regression neural network, the neural network structure is trained, and 100 conditional quantiles of daily continuous traffic flow are brought into the kernel density estimation method; then, the complete probability density curve of the traffic demand of AR05 in the future daily 15 min is obtained. Because of the randomness of the neural network method, the traffic demand value in a 15-min interval of AR05 predicted by each time is different. Based on the data of 9:00-9:15 on 21 May 2017, nine probability density distributions of 100 predictions were selected randomly. The black line in Figure 5 represents the predicted values. As shown in Figure 5, it was found that the probability density distribution did not conform to a certain distribution law (such as normal distribution). This is because some traffic demand values correspond to a prediction probability of zero, resulting in discontinuities. This further confirms the correctness of the kernel density estimation method. Figure 5: AR05 traffic demand probability density distribution during 9:00–9:15 22 May 2017. Figure 5 shows a situation that differs from the case where the probability density meets the normal distribution. In scenarios where the probability density of the traffic demand value in the en route sector lacks an obvious pattern, the true value (depicted by the red line at 28) does not appear near the highest point on the probability density plot. However, the predicted value (represented by the black line) corresponding to the maximum obtained after integrating the probability density shows little difference with the actual value. Meanwhile, a comparison is made with the results obtained by the traditional BP neural network prediction method and the actual value. The difference between the values obtained by the method in this paper and the true value is smaller, as shown in Figure 6.  
In the left figure of Figure 6, the blue curve represents 100 predicted results using the BP neural network prediction method, and the red curve represents 100 predicted results using the probability density prediction method. The comparison between the two kinds of prediction results and the true value 28 (black dotted line) shows that the results of the BP neural network prediction method are more volatile, and the results of the probability density prediction method are more stable (always around the real value). If it is necessary to select the predicted value in the actual operation, the result obtained by the BP neural network method is likely to deviate too much from the true value, while the result obtained by the probability density prediction method is more accurate. Similarly, in the right figure of Figure 5, the blue shadow represents the prediction error corresponding to 100 predicted values obtained by the BP neural network prediction method, and the red shadow represents the prediction error corresponding to 100 predicted values obtained by the probability density prediction method. Comparing the two kinds of errors, it is found that the result error is very small through probability density prediction. On the contrary, the error deviation of the BP neural network prediction method is very large at the beginning; after 30 times of prediction, the result is more stable and close to the true value, but its accuracy still lags behind the probability density prediction. This shows that the BP neural network has a certain learning process, and this learning process will take a certain amount of time, which cannot fully meet the very strong practical timeliness requirements of ATC. In order to further prove the accuracy of the proposed method, a more in-depth error analysis is made between the 100 times prediction result of the AR05 traffic demand value and the true value 28.