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INNOVATSION TEXNOLOGIYALAR Maxsus son, 2023-yil, dekabr 
ISSN 2181-4732 
30 
In this article, we will review some of the applications of CNT to model the process of 
regulating air traffic with an increase in the intensity of flights. We will focus on three main aspects: 
the network topology of the ATM system, the network resilience to disruptions and failures, and the 
network optimization for performance improvement [1, 2]. 
Network topology of the ATM system. 
The ATM system can be represented as a network of 
nodes and links, where nodes are entities that provide or consume air traffic services, such as airports, 
air traffic control (ATC) agencies, or aircraft, and links are connections that enable the exchange of 
information or coordination between nodes, such as flight routes, radio frequencies, or data links. The 
network topology of the ATM system reflects its structure and organization, as well as its operational 
characteristics and constraints. 
One example of applying CNT to analyze the network topology of the ATM system is the work 
by Zanin A.L. (2013), who studied the European ATM network using data from EUROCONTROL. 
They constructed a network where nodes were airports and links were flights between them. They 
calculated various network metrics, such as degree distribution, clustering coefficient, average path 
length, and assortativity coefficient. They found that the European ATM network had a scale-free 
structure, meaning that it followed a power-law degree distribution, where a few nodes had a very 
high number of connections (hubs), while most nodes had a low number of connections. They also 
found that the network had a high clustering coefficient, meaning that nodes tended to form groups 
or communities with dense connections among them. Moreover, they found that the network had a 
low average path length, meaning that a small number of hops or intermediate nodes could reach any 
two nodes. Finally, they found that the network had a negative assortativity coefficient, meaning that 
nodes tended to connect with nodes that had a different degree than them [2, 3]. 
The analysis of the network topology of the ATM system can provide insights into its 
functionality and efficiency. For instance, hubs can facilitate the connectivity and accessibility of the 
network, but they can also create congestion and delays. Communities can reflect regional or 
operational similarities or differences among nodes, but they can also create fragmentation or 
isolation. Path length can indicate the speed and reliability of information or coordination flows in 
the network, but it can also depend on external factors such as weather or regulations. Assortativity 
can indicate the diversity or homogeneity of node interactions in the network, but it can also affect 
its robustness or vulnerability [3]. 
Network resilience to disruptions and failures. 
The ATM system is subject to various types of 
disruptions and failures that can affect its normal operation and performance. These can be caused by 
natural phenomena (such as storms or volcanic eruptions), technical malfunctions (such as equipment 
breakdowns or cyberattacks), human errors (such as miscommunication or miscoordination), or 
intentional actions (such as strikes or terrorism). Disruptions and failures can have different impacts 
on different parts of the network depending on their severity, location, duration, frequency, and 
propagation. 
One example of applying CNT to assess the network resilience to disruptions and failures is the 
work by Wang et al. (2016), who studied the Chinese ATM network using data from CAAC. They 
constructed a network where nodes were ATC agencies and links were flight routes between them. 
They simulated two types of attacks on the network: random failures, where nodes were removed 
randomly from the network; and targeted attacks, where nodes were removed according to their 
centrality measures (such as degree centrality or betweenness centrality). They measured the impact 
of these attacks on the network using metrics such as size of giant component (the largest connected 
subnetwork), average path length (the average number of hops between any two nodes), efficiency 
(the inverse of average path length), diameter (the maximum number of hops between any two nodes), 
and robustness (the ratio of size of giant component before and after the attack) [4]. 
They found that the Chinese ATM network was resilient to random failures, meaning that it 
could maintain its connectivity and functionality even after a large fraction of nodes were removed. 
However, they found that the network was vulnerable to targeted attacks, meaning that it could lose 
its connectivity and functionality after a small fraction of nodes were removed. They also found that 

INNOVATSION TEXNOLOGIYALAR Maxsus son, 2023-yil, dekabr 
ISSN 2181-4732 
31 
the network had different levels of vulnerability depending on the centrality measure used to select 
the nodes for removal. For instance, the network was more vulnerable to attacks based on 
betweenness centrality than on degree centrality, because betweenness centrality captured the 
importance of nodes as bridges or bottlenecks in the network. 
The evaluation of the network resilience to disruptions and failures can provide guidance for 
designing and implementing contingency plans and recovery strategies for the ATM system. For 
instance, random failures can be mitigated by increasing the redundancy and diversity of the network, 
while targeted attacks can be prevented by enhancing the security and protection of the network. 
Moreover, different types of disruptions and failures can require different types of responses 
depending on their impact on different parts of the network [4, 5]. 
Network optimization for performance improvement. 
The ATM system aims to achieve high 
levels of performance in terms of safety, capacity, efficiency, predictability, environment, and cost-
efficiency. These performance areas are interrelated and often conflicting, meaning that improving 
one area can compromise another area. Therefore, there is a need to find optimal solutions that can 
balance and harmonize these performance areas according to the objectives and preferences of the 
stakeholders involved in the ATM system. 
One example of applying CNT to optimize the network performance is the work by Zhang et 
al. (2019), who studied the US ATM network using data from FAA. They constructed a network 
where nodes were airports and links were flights between them. They proposed a multi-objective 
optimization model that considered three performance indicators: flight delay (the difference between 
actual and scheduled arrival times), flight distance (the length of flight routes), and flight fuel 
consumption (the amount of fuel consumed by flights). They used a genetic algorithm to find Pareto-
optimal solutions that minimized these indicators simultaneously. They compared these solutions 
with the actual flight data and evaluated their potential benefits [5, 6]. 
They found that their optimization model could reduce flight delay by 19.8%, flight distance 
by 2.4%, and flight fuel consumption by 2.6%, compared with the actual flight data. They also found 
that their optimization model could generate different trade-offs among these indicators depending 
on the weights assigned to them. For instance, they found that reducing flight delay had a positive 
effect on reducing flight fuel consumption, but a negative effect on increasing flight distance. 

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