# Reliability Analysis of an Air Traffic Network: From Network Structure to Transport Function
## 1 Introduction  
Reliability is an important feature of complex systems. Many scholars have studied the reliability of different systems [1; 2; 3; 4; 5; 6; 7; 8; 9], such as composite materials [10], communication systems [11], and power systems [12]. In the field of civil aviation, there are a few studies on reliability, mainly focusing on controllers' reliability and equipment reliability. [PERSON] et al. propose an improved triangle whitening weight function and use it to measure the reliability of air traffic controllers [13]. [PERSON] synthesizes the Delphi and success likelihood index methods to analyze the human error probability in flight conflict resolution [14]. [PERSON] and [PERSON] propose a method of determining the maximum influence value of the controller's error based on Delphi and Bayesian networks and calculate the human error probability of flight conflict resolution [15]. [PERSON] et al. determine human error probabilities by analyzing the results of a real-time simulation involving air traffic controllers (ATCOs) and pilots, with a focus on communication errors [16]. They also analyze air traffic safety from the aspect of air traffic controller behavior and develop a human reliability assessment tool for air traffic safety management [17]. [PERSON] et al. apply a Markov chain model to predict and verify differentstates of ATC automation software [18]. [PERSON] studies the influence of the equipment operation environment and internal and external risk factors on the reliability of air traffic control equipment based on a Bayesian network [19]. To date, the study of the reliability of transport networks has focused on road transport networks [20; 21; 22; 23; 24; 25]. Such studies mainly evaluate the reliability of the networks from the perspectives of connectivity reliability, travel-time reliability, and capacity reliability. By contrast, little research has been conducted on the reliability of air traffic networks. With the rapid development of the aviation industry, air traffic is becoming increasingly complex, resulting in a significant decline in system stability. Low reliability seriously threatens operational safety and transportation efficiency. At present, most research on air traffic planning and management assumes that the flight time of a route is a fixed value without considering the influence of stochastic factors on the air traffic system [26]. In fact, due to the high uncertainty of the air traffic system, flight time and other air traffic indicators are continuously changing, seriously affecting the reliability of air traffic operation and transportation efficiency. Therefore, the reliability analysis of air traffic systems is a key problem to be solved. It is meaningful to apply the general research idea of the reliability of road transport networks to the reliability of air transport networks. Because of the differences between air traffic operation and road traffic operation, it is not reasonable to calculate the connectivity reliability, the travel-time reliability, and the capacity reliability using the calculation methods proposed in the available literature. For example, an aircraft seldom changes its flight path randomly. If there is a traffic jam in a flight segment, the flights generally implement a ground delay program or air-holding policy. Thus, we cannot calculate the capacity reliability based on dynamic traffic assignment. There are two main tasks in our study. The first task is to calculate reliability indexes. From the perspective of a complex system, the structure is the internal composition of the system, reflecting the integrity of the system from the inside; the function is the external behavior of the system, reflecting the integrity of the system from the outside. Thus, it is reasonable to establish reliability indexes based on the structure and function of the air traffic network. In this work, we propose three indexes, i.e., connectivity reliability, travel-time reliability, and capacity reliability.