# Reliability Analysis of an Air Traffic Network: From Network Structure to Transport Function
## 5 Conclusions  
Although some evaluation studies of controllers' reliability and equipment reliability have been conducted, there is little research on the reliability of the air traffic network. The reliability of the air traffic network is the basis of air traffic management. We propose a novel method of evaluating the reliability of air traffic networks from both network structure and traffic function perspectives.  
Figure 6: Member fuzzy set map for reliability evaluation of the US air traffic network.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Index** & **Uncertainty Transformation Models** \\ \hline CORN & Fuzzy set 1(0.4073,0,0) \\ TTRN & Fuzzy set 2(0.9199,0.0109,0.0049) \\ CARN & Fuzzy set 3(0.8300,0.0088,0.0103) \\ \hline \hline \end{tabular}
\end{table}
Table 9: Uncertainty transformation models of the CORN, TTRN, and CARN.  
In this paper, we establish models of the CORN, TTRN, and CARN on the basis of the network structure, flight time, and air traffic capacity, respectively. Fuzzy set theory can be used to solve problems involving fuzziness and randomness. A comprehensive evaluation model based on the uncertainty transformation model is constructed. The uncertainty transformation model can transform the quantitative data into qualitative language considering both the fuzziness and uncertainty of human thinking. The comprehensive evaluation model can be used to guide the formulation of flight plans, adjustment of route network structures, and implementation of traffic management strategies. We take the US air traffic network as an example and evaluate its reliability. The following conclusions can be drawn: (1) The CORN of the US air traffic network is low, with indirect routes accounting for approximately 70% of the routes. In contrast, the TTRN and CARN are much higher. The TTRN of US airports with a high CORN is much lower than that of airports with a low CORN because of their large traffic volume. The TTRN is the largest, indicating that the efficiency of US air traffic management is much higher than the connectivity. (2) The US air traffic network is generally reliable. The reliability of the US air traffic network can be further improved by optimizing the network structure, optimizing the route layout, and improving the service level of the airports. (3) The reliability of the US air traffic network in nonpeak hours is much higher than that in peak hours. The empirical analysis also reflects the validity of our calculation method based on the uncertainty transformation model.  
Based on this method, suggestions are made for optimizing the aviation network based on the analysis of the network reliability. The applications of the methodology (airport planning, fleet sizing, route planning, etc.) are not mentioned in this paper. These will be studied later.  
[PERSON] performed the research, analyzed the data and wrote the paper. [PERSON] co-designed the process of comprehensive evaluation. [PERSON] co-designed the research, and extensively updated the paper. All authors read and approved the final manuscript.  
This work was funded by the National Nature Science Foundation of China [Grant Number 71801215, U1833103] and the Fundamental Research Funds for the Central Universities [Grant Number 3122016C009].  
The authors declare no conflict of interest.