## 7 Conclusions  
The existing uncertain traffic demand prediction for the en route sector imposes high requirements on the accumulation and collation of historical data, including radar data, ADS-B data, etc. Specifically, historical data must be targeted at a specific set of aircraft, constituting a collection of aircraft within a fixed period of time every day, over a fixed en route point, with a substantial amount of operational data. However, given the current limitations of China's air traffic flow management system and supported data management platform, obtaining historical data that fully meets the aforementioned conditions is currently unattainable. In light of the actual operation of China's air traffic flow management system, we approach prediction from an alternative perspective, utilizing the available historical data of air traffic flow in the en route sector. In this paper, we combine neural network and quantile regression methods to obtain quantiles of continuous traffic demand data in the future. This is achieved by leveraging the strong nonlinear adaptive ability of neural networks and the precise explanatory variable description provided by quantile regression. Subsequently, utilizing these continuous conditional quantiles, we derive the probability density function and probability density curve for future continuous traffic demand through kernel density estimation. This approach allows us not only to obtain specific point prediction values and their change intervals but also to determine the probability associated with each value within the prediction change interval for traffic demand in the en route sector. This results in obtaining more accurate point prediction values for the day. Based on empirical research in the central and southern regions of China, we compare the point prediction value with the highest probability, obtained by integrating the probability density, with the traditional BP neural network prediction result. The comparison results indicate that the probability prediction method proposed in this paper not only achieves more accurate results but also provides a continuous probability density curve for the future. This allows for a comprehensive reflection of the daily trend of traffic demand in the en route sector and its corresponding probability levels. If probabilistic prediction is applied to China's air traffic flow management system, it can offer more useful information for air traffic managers to make informed decisions. In this study, there are still some shortcomings that require further research and improvement. We used only 20 days of historical operational data as prediction samples may introduce sample specificity, so in subsequent studies, it would be beneficial to gather long-term historical data for prediction analysis. The probabilistic density prediction method employed is based on the combination of neural network quantile regression and kernel density estimation. In future research, other combinations of methods, such as error characteristic distribution, can be explored to further predict the uncertainty of traffic demand in the sector. It would be valuable to conduct comparative analyses of prediction results using various methods, expanding beyond the limitations of the BP neural network algorithm. **Author Contributions**: Conceptualization, W.T. and Y.G. ; methodology, W.T. and Y.Z. ; software, W.T., Y.Z. and Y.L. ; validation, W.T., Y.Z. and Y.L. ; formal analysis, W.T. and Y.G. ; investigation, W.T. ; resources, W.T. and Y.G. ; data curation, W.T., Y.Z. and Y.L. ; writing--original draft preparation, W.T., Y.G. and Y.Z. ; writing--review and editing, W.T. and Y.L. ; visualization, W.T. and Y.Z. ; supervision, Y.L. ; project administration, W.T. and Y.G. ; funding acquisition, W.T. and Y.Z. All authors have read and agreed to the published version of the manuscript.