，

College of Air Traffic Management，Civil Aviation University of China，Tianjin 300300，P.R.China

Abstract: To ensure flight safety，the complex network method is used to study the influence and invulnerability of air traffic cyber physical system（CPS）nodes. According to the rules of air traffic management，the logical coupling relationship between routes and sectors is analyzed，an air traffic CPS network model is constructed，and the indicators of node influence and invulnerability are established. The K-shell algorithm is improved to identify node influence，and the invulnerability is analyzed under random and selective attacks. Taking Airspace in Eastern China as an example，its influential nodes are sorted by degree，namely，K-shell，the improved K-shell （IKS） and betweenness centrality. The invulnerability of air traffic CPS under different attacks is analyzed. Results show that IKS can effectively identify the influential nodes in the air traffic CPS network，and IKS and betweenness centrality are the two key indicators that affect the invulnerability of air traffic CPS.

Key words：complex network；air traffic cyber physical system；improved K-shell algorithm；influential node ranking；invulnerability

0 Introduction

In recent years，the rapid development of the air transport industry has increasingly worsened the problem of flight delays，which has not only affect?ed the economic benefits of aviation but also imposed hidden safety risks. On May 19，2016，a computer failure caused a temporary closure of the airspace in Stockholm，Sweden. As a consequence，airplanes from the local airport failed to take off on time. On August 10，2019，3 023 flights were can?celed in Eastern China due to typhoon“Lichma”. It can be seen that when an emergency，such as equip?ment failure or adverse weather，causes air traffic control（ATC）positions or waypoints to fail，the entire air traffic system would not be able to operate normally. Therefore，alleviating flight delays and promoting high-quality development of civil aviation have become a major issue in the future.

Air traffic management，as a highly complex task，is of great importance to the overall order and safety of the air traffic system［1］. The air traffic man?agement system integrates the communication net?work and physical environment to realize the func?tions of controlling and directing flights，which is characterized by a typical cyber physical system（CPS）. The deep integration of the network and en?vironment forms a multi-dimensional heterogeneous complex system that can achieve real-time sense，dynamic control as well as information service. This system gradually evolves into a physical air traffic in?formation system（air traffic CPS）with frequent in?teraction of traffic flow and information flow. In this study，an air traffic CPS model is constructed.Its in?fluential nodes are identified and the invulnerability is analyzed. We provide insight into the safe opera?tion of the air traffic management system.

In recent years，the identification of key nodes in aeronautical complex networks has attracted gen?eral interest. In 2014，Lordan et al.［2］used a mediacentric adaptive strategy to identify the key airport nodes in global aviation networks. In 2017，Pan et al.［3］evaluated the key nodes in the ATC navigation network and sorted the importance of navigation equipment of Chengdu control area in the south?west. In 2018，Wen et al.［4］proposed an aviation network node importance evaluation method based on the improved node deletion method and proved that potential key-airports in China and America can be discovered by the method. The studies above have analyzed the network characteristics from the aspects of airports，routes and sectors in the air traf?fic network，but have not taken into account the in?tegrity of air traffic systems or the relationship be?tween systems.

This problem has been addressed in some litera?ture.In 2013，Sampigethaya et al.［5］proposed a nov?el CPS framework to understand the cyber layer and cyber-physical interactions in aviation to study their impacts on each other. In 2016，Roy et al.［6］estab?lished an evaluation model based on CPS to analyze the degree of threat to the air traffic management system caused by the interruption of the information network under attack. In 2017，Ren et al.［7］de?scribed how flight operations control（FOC）and air navigation service provider（ANSP）in the aviation system transit to CPS in detail. Although these stud?ies have laid the foundation for future research on air traffic CPS，they have only offered a simple descrip?tion of the aviation system from the perspective of CPS，while the unified modeling theory has not been proposed so far.

Destruction of a few influential nodes is likely to cause the entire network to fail. Studies have shown that such destruction in power grid CPS can paralyze the entire power system［8］. For air traffic CPS，adverse weather，severe epidemics，military activities，equipment failures，and other events may lead to the closure of the sectors managed by failed ATC positions or congestion of waypoints. Conse?quently，the air traffic CPS information network cannot operate smoothly，thus inducing extensive flight delays and safety hazards.

In this paper，the complex network theory is used to build an air traffic CPC model. The interac?tion between cyber and physical systems is de?scribed scientifically and reasonably，and the nodes in the air traffic CPS are sorted to identify the influ?ential nodes. Different strategies are used to attack the network to analyze its invulnerability. The re?sults provide a theoretical basis for the future scien?tific management of air traffic and can improve air traffic operation safety.

1 Air Traffic CPS Model

It is proved that CPS can model systems with coupled relationships［9］. The rising complex net?work theory also provides an approach to studying structural functions of coupled networks.

In this paper，the topological abstraction of the air traffic CPS is obtained based on complex net?work theory. An air traffic CPS network model is established combining the current air traffic manage?ment rules［10］and the logical connection between air route and ATC sectors，as shown in Fig.1. The air traffic CPS network consists of two interactive and mutual-influencing parts：The physical network，which is the air route network，and the cyber net?work，which is the air traffic control network. Way?points and ATC positions are abstracted into nodes of the two networks respectively and are linked ac?cording to their relationships—ATC positions ob?serve the changes of waypoints status and control the operation of waypoints.

Adjacency matrix {αij}N×Nand {βij}N×Nare used to represent the connection ofNnodes in ATC network and air route network，respectively. When there is a connected edge between nodeiandj，αij=αji=1，βij=βji=1，otherwise，αij=αji=0，βij=βji=0.

Fig.2 explains the coupling relationship be?tween ATC network and air route network. Air traf?fic controllers and pilots consider aircraft as physical entities，and air traffic information perception and communication control are deeply integrated through controller-pilot data link communication（CPDLC）. Air traffic controllers receive informa?tion such as the aircraft status，the traffic situation，the weather conditions，and the information sensed by radar，ADS-B，weather monitoring station or other equipment from the ATC center. Controllers analyze and process the information and issue con?trol instructions to pilots. Pilots give feedback to the corresponding control instructions，change the air?craft state，therefore enable to smooth traffic flow.

Fig.1 Air traffic CPS

Fig.2 Coupling relationship of air traffic CPS

1.1 Physical network

The physical network of air traffic CPS is the air route network，scilicet the traffic flow network.Waypoints（compulsory reporting points and naviga?tion stations）and airports in the airspace sector con?trolled by each ATC position are considered as nodes. If the navigation station and the airport are at the same position，only keep the airport and use the segment between nodes as the edge. The function of the air traffic system is to ensure the safe and effi?cient operation of air traffic. The process is mainly implemented in the air route network. To facilitate research，the following procedures are performed.

（1）The physical network is undirected，and for those parallel routes，only one direction is re?served.

（2）Delete waypoints that do not change the route direction or connection.

（3）When constructing the air route network，the pilot and aircraft are considered as a unified whole.

（4）Neglect temporary and international air routes，and delete the isolated border points.

1.2 Cyber network

The air traffic CPS cyber system is the ATC network with ATC positions as nodes and flight handover relations as edges. The aircraft reports its current operating status to the corresponding ATC positions in the air route network and follows the in?structions given by the ATC positions［11］. For con?venience，this research makes the following assump?tions.

（1）Merge the high and low sectors in the air?space，and each ATC position is responsible only for the flight handover of the corresponding sector.

（2）The information network is undirected.

（3）When constructing the air traffic control net?work，the ATC position and the sector controlled by it are considered as a unified whole.

2 Indicators of Air Traffic CPS Model

Evaluating node influence is vital for improving the invulnerability of complex networks［12］. Identify?ing and sorting influential nodes in air traffic CPS provide a basis for attack simulation in the later in?vulnerability research. Protecting critical nodes and their connected edges prevents the network from los?ing its robustness in case of damage［13］，which helps to manage sectors scientifically and alleviate air traf?fic congestion. The performance of the CPS is close?ly bound up with the nodes that provide various ser?vices for the whole system［14］. Studying the invulner?ability of the air traffic CPS，observing the node characteristics with poor invulnerability and protect?ing the sectors where the node is located can effec?tively avoid continuous attacks on the same node，and reduce losses through traffic flow prediction and control sectors. To analyze the node influence and CPS network invulnerability better，the indicators of influence and invulnerability are defined in this paper.

2.1 Characteristic indicators of node influ?ence

Node influence refers to the ability of a node to directly or indirectly affect the network structure or other nodes in the air traffic CPS network. The quantitative description of the node influence in the network helps us better analyze the network charac?teristics. However，many factors need to be consid?ered such as the attributes of the nodes themselves and the influence of the connecting edges between nodes［15］. The definitions and symbols of the charac?teristic indicators of node influence are shown in Ta?ble 1.

Table 1 Indicators of air traffic CPS

In the previous research on unweighted net?works，the connected edges between nodes were mostly regarded to have the same influence，but if two respect nodes are connected to many nodes，the information flow or traffic flow spreads more widely between the two nodes，and the connecting edge be?tween the two nodes is more influential. Therefore，we use flow as edge weight to represent the influ?ence of edges. At the same time，node weight is tak?en into consideration，and the edge influence coeffi?cient is established as the parameter for identifying the influence of the edge. Next，the original K-shell algorithm is used to obtain the node’s K-shell level，and edge weights and edge influence coefficients are combined to obtain node weight. The greater the node weight is，the greater the influence is. The im?proved K-shell（IKS）remedies the defect that the original K-shell algorithm cannot accurately mea?sure the influence of nodes when there are many identical values as they will be judged to have the same influence［16］，therefore it functions better in ranking influential nodes. The calculation process is shown in Fig.3.

Fig.3 Flow chart of IKS

In this paper，the degree of air traffic CPS and the K-shell level of the nodes are calculated，and the edge weights and edge influence coefficients are cal?culated afterward to get the node weights so that the nodes can be sorted accordingly.

2.2 Characteristic indicators of invulnerability

Invulnerability refers to the characteristics of a network to maintain and restore its functions to a certain degree when its structure is damaged［17］. Dur?ing operation，if the air traffic CPS is affected by ad?verse weather，major epidemics，military activities，equipment failure or other events，its invulnerability will drop to a certain value，some nodes and their connected edges will fail，the network will get dam?aged or even break down，and ATC operations would not be able to carry out normally either. This will lead to large-scale air route congestion and flight delays. Once a flight delay occurs，it will dis?rupt the original parking stand allocation，runway scheduling，and the order of flight arrivals and de?partures. Various tasks affect each other，thereby in?creasing the complexity of civil aviation resource scheduling and resulting in huge civil aviation securi?ty risk in the end. Besides，flight delays will detain a large number of stranded passengers at the airport，which will affect security and control of the airport.

To study the invulnerability，attacks on the net?work are simulated. For showing strong uncertain?ty，adverse weather，equipment failure and other ef?fects are considered as random attacks. While the damages caused by communication failure resulting from military activities or terrorist attacks are rela?tively subjective，so they are considered as selective attacks.

Network efficiency and the relative value of the maximum connected subgraph are used to evaluate the structural damage of the air traffic CPS. The def?initions and symbols of these indicators are shown in Table 2.

The coupling invulnerability of the air traffic CPS network is studied according to the coupling re?lationship between the air traffic control network and air route network. The simulation attack，as shown in Fig.4，consists of four steps.

Table 2 Indicators of invulnerability of air traffic CPS

Step 1Choose the ATC positions in the air traffic CPS network for invulnerability research.The coupling failure rule of the ATC network and the air route network is set as follows. ATC posi?tions in the ATC network cannot transmit informa?tion when failed. When all the corresponding way?points become invalid，the failed waypoints and their connected air routes are removed. The cou?pling invulnerability of the air traffic CPS is studied by observing the changes of invulnerability indica?tors under different attacks.

Step 2Sort the ATC positions randomly us?ing Python. Then sort the ATC positions in the air traffic CPS network in the descending order by de?gree，MKS and betweenness centrality.

Step 3Remove the ATC positions according to the order in Step 2 to simulate attacks on the net?work. The ATC positions cannot work properly so that the sectors under their management are closed，all the waypoints in the sector become invalidated，and the structure and capacity of the air route net?work are also severely affected. Then the network invulnerability is obtained under degree-first，IKSfirst and betweenness-centrality-first attacks.

Step 4Observe the changes in invulnerability indicators，network efficiency and relative value of the maximum connected subgraph to analyze the in?vulnerability of the air traffic CPS and learn about the ability of the control network to maintain its structure after attack.

Fig.4 Flow chart of attack simulation on the network

3 Empirical Analysis

The airspace under the jurisdiction of the East?ern China Air Traffic Management Bureau，one of the busiest airspaces in China，is used to establish the Eastern China Air Traffic CPS model. The actu?al radar and ADS-B data are processed based on TrackDig（a three-dimensional high-speed flight da?ta mining software）to restore the track in the map.Then the geographic coordinates of sectors and way?points corresponding to each ATC position in East?ern China are imported into ArcGIS（a geographic information system software）to finish the mapping.The information layer（air traffic control network），as shown in Fig.5（a），is made up of 33 ATC posi?tions as nodes and 69 edges. The physical layer（air route network） has 171 waypoints and 261 air routes，as shown in Fig.5（b）.

Fig.5 Air traffic CPS network of Eastern China

3.1 Ranking and analysis of influential nodes in air traffic control network

Based on the traffic statistics of the airspace un?der the jurisdiction of the Eastern China Air Traffic Management Bureau of China，the ATC positions of the control network are calculated using the IKS algorithm to obtain the weighted influence of each ATC position. Great influence means that this ATC position has flight transfer relationship with many adjacent positions. The top 15 IKS nodes of the air traffic control network are taken as examples，and sorted from large to small by IKS，degree，K-shell and betweenness centrality. The sorting result is shown in Table 3.

Through comparison，it can be seen that some of the top 10 ATC positions are the same among the sorting results identified by different methods. The ATC positions with great influence according to the IKS algorithm are also at the highest level of the Kshell algorithm，and the top 10 ATC positions are highly consistent with those ranked by degree. This result further illustrates the effectiveness of IKS. Al?so，No.19 ATC position has the most influence ac?cording to all the methods except closeness centrali?ty. It can be seen that there is information transmis?sion between No.19 ATC position and many other surrounding positions. This means that No.19 ATC position has an impact on its surrounding positions，and it is the central hub of the air traffic CPS throughout Eastern China.

Table 3 Top 15 influential nodes in the air traffic control network of Eastern China

3.2 Ranking and analysis of influential nodes in air route network

As a scale-free network［18］，the air route net?work has severe heterogeneity in the connection be?tween nodes. The typical feature is that most way?points in the network are connected to only a few nodes，and there are only a few waypoints connect?ed to a large number of nodes. Generally speaking，there is a distribution relation of traffic flow between this kind of node and other surrounding waypoints，which has a greater influence on the surrounding ar?ea. Ordinary influence recognition methods can also identify these waypoints，but it is difficult to distin?guish the influence of most nodes in the air route net?work. To prove the effectiveness of the IKS algo?rithm，the node influence of the airway network is also calculated. The top 15 IKS nodes in the air route network are taken as examples，sorted from large to small，and compared with other algo?rithms，as shown in Table 4.

Table 4 Top 15 influential nodes in the air route net?work of Eastern China

The comparison in Table 4 shows that IKS has a significant effect on identifying the influence nodes of the Eastern China Air Traffic CPS route net?work. A total of 171 waypoints are divided into 114 layers sorted by IKS，and the influence of most nodes in the network can be identified. In the air route network，the sorting of the top 10 influential nodes is highly close to the result of degree. Al?though the influential nodes are in the second and the third layers of the original K-shell algorithm，the highest level of the original K-shell algorithm after decomposition is only three because the connections between air route network nodes are not dense.This result also shows that this method cannot effec?tively distinguish the influence of scale-free net?works with many nodes. Different from the identifi?cation of influential nodes in the air traffic control network，the centrality of the air route network dif?fers greatly from the IKS sorting. This is because the betweenness centrality describes the influence of the ability of the node itself as an intermediary. An?other reason is that the connectivity between way?points is relatively poor，so most nodes cannot play an intermediary role. Consequently，the results are not accurate.

3.3 Invulnerability analysis of air traffic CPS

According to the coupling relationship of the two layers of air traffic CPS network，when the ATC network is affected，the ATC positions can?not function properly which leads to the closure of sectors，and therefore the waypoints inside fail and the structure of air route network are changed. We learn how air traffic CPS works by attacking the nodes in air traffic control network and observing the changes in air route network.

The specific relationship between ATC sectors and the waypoints under their control is described in Table 5.

Table 5 Waypoints controlled by different ATC positions

Thirty-three ATC positions are sorted by the degree，IKS，betweenness centrality and in ran?dom，then removed in turn to simulate degree-first，IKS-first，and betweenness-centrality-first and ran?dom attacks on the network. The waypoints con?trolled by failed ATC positions are removed as well. Therefore，the structure of air route network is changed. Fig.6 shows the comparison of the invul?nerability indicators of the air route network of East?ern China Air Traffic CPS using four attack meth?ods. When the top seven ATC positions are at?tacked，the two indicators，network efficiency and the relative value of the maximum connected sub?graphs，decline at a similar speed. If continuing to attack other ATC positions，there is sufficient evi?dence to show that random attacks have less dam?age to the air route network than other attack meth?ods. This is because the Eastern China Air Traffic CPS network has better invulnerability against ran?dom attacks than selective attacks. From Fig.6（b），it can be seen that air route network collapses fastest under the betweenness-centrality-first attack. Com?bining Figs.6（a）and（b），it is clear that when No.11 ATC position fails，the two invulnerability indicators of the air route network hardly change and gradually approach the lowest value，which means the betweenness centrality has most impact on the invulnerability of air route networks.

Fig.6 Changes of invulnerability indicators of air route network under four attack methods

ATC positions with greater IKS have greater degrees too. Therefore，given a similar sorting，the invulnerabilities of the air route network are similar at the onset of IKS-first attack and degree-first at?tack. The difference between IKS-first and degreefirst attack is that the two indicators of ATC posi?tions under IKS-first attack reach a stable level first，and then decline，while the indicators under degree-first attack change in the opposite way.

In a nutshell，the air traffic CPS network has the best invulnerability under random attacks，and the invulnerability under selective attacks is poor.The invulnerability indicators of the ATC network fluctuate sharply under IKS-first attack. The struc?ture and traffic capacity of the air route network get damaged fastest under betweenness-centrality-first attack. In conclusion，IKS and betweenness centrali?ty are two important indicators that affect network invulnerability.

4 Conclusions

（1）Air traffic CPS network is a multi-dimen?sional and heterogeneous complex network integrat?ing the air route network and air traffic control net?work. This paper builds an air traffic CPS network model and proposes characteristics indicators of node influence and invulnerability，thus providing a new approach to ensuring the safe operation of the air traffic system.

（2）The IKS algorithm can get more accurate results than other methods in identifying the influ?ence of air traffic CPS nodes. Its effectiveness is ver?ified by the airspace of Eastern China. The greater the influence of the air traffic control network node is，the greater the influence of waypoints in the rele?vant sectors for the ATC position is.

（3）Different attack strategies are used to ana?lyze and study the invulnerability of air traffic CPS network. The results show that the invulnerability is better under random attacks than that under selec?tive attacks. Also，the invulnerability indicators of the air route network fluctuate sharply when the net?work is attacked according to the IKS sorting order，and the traffic capacity of the air route network de?creases fastest when the selective attack is per?formed according to the betweenness centrality.