## 4 Controller Workload Prediction and Assessment Method  
Air traffic complexity is an accurate and clear description of the air traffic situation, an explanation of the control difficulty in the case of special situations in the airspace, and the ability to make a reasonable description of the controller's subjective workload. Analyzed from the point of view of the system structure, the microstructure between the nodes in the system determines the macrostructure and functions of the system. The microstructure between each aircraft node and the controller node in the sector determines the complexity of the overall network, and the position and velocity relationships between the aircraft nodes are the basic constituents of the microstructure [12]. In previous studies, it was found that topological metrics such as node node intensity and the clustering coefficient can reflect the complexity of air traffic well [18]. Therefore, the node node intensity and clustering coefficients of network topology metrics are chosen to reflect the looming effect between the aircraft posture controllability index, and to calculate the network complexity. Among them, the looming effect between aircraft refers to the convergence posture of the aircraft, which is expressed by the relative proximity of the aircraft in time and space perspectives. In the interdependent network model constructed in this paper, the proximity effect is reflected by the values of the edge weights of the connected edges. Equation (7) is used for calculating the proximity effect. \[P_{(i,j)}=\omega_{ij}=\exp(-\frac{L_{0}}{V}) \tag{7}\]  
where \(P_{(i,j)}\) is the looming effect; \(L_{0}\) is the shortest distance between aircraft B in the direction of velocity \(V\) and the intersection C of the flight protection zone of aircraft A; and \(V\) is the relative velocity of the aircraft. The situation controllability index reflects the ease of conflict situation deployment by controllers for aircraft speed, heading and altitude adjustment. In this paper, the weighted clustering coefficients in the model are chosen for expression. Equation (8) is used to calculate the situation controllability index. \[I_{(i)}=c(i) =\frac{1}{s_{i}(k_{i}-1)}\sum_{m,n}\frac{w_{im}+w_{in}}{2}a_{im}a_ {in}a_{mn} \tag{8}\]  
Based on Equations (7) and (8), we can obtain Equation (9). Equation (9) is used for the calculation of the inter-aircraft complexity. \[C_{(ij)}=\left|\left[aP_{(i,j)},\beta(I_{(i)}+I_{(i)})\right]\right| \tag{9}\]  
where \(\alpha\) and \(\beta\) are the adjustment factors, which denote the influence weights of looming effect and posture controllability with complexity, respectively. For the convenience of calculation, the values of the adjustment factors are set as \(\alpha=1\) and \(\beta=1\). Therefore, the calculation of the complexity of the system can be considered as the summation of the complexity between the two pairs of aircraft in the system. Equation (10) is used for calculating the complexity of the system. \[C_{N}=\frac{1}{n(n-1)}{\sum_{i\
eq j}C_{(i,j)}} \tag{10}\]  
where \(N\) is the code of each different sector in the system, \(n\) is the number of aircraft in the sector, and \(C_{N}\) is the overall complexity value of the sector. According to the definition of the complexity value and the model of the interdependent network constructed in this paper, the complexity value of the nodes that do not satisfy the conditions of the connected edge construction in the model should be infinitely close to zero, which can be regarded as negligible. Therefore, in this model, the complexity value of the sector is the complexity of the conflicting nodes. Since the complexity can quantitatively reflect the air traffic situation in the sector, the controller workload can be evaluated by the complexity value of the sector. Equation (11) is used to calculate the controller workload.