## 3 Sector Capacity Evaluation Method Based on the DNN Algorithm  
### Route-Availability Model  
The route-availability model is first used to identify the flights that need to be rerouted due to bad weather in the sector. When the aircraft enters the control sector, rerouting, returning, and forced landing will occur due to the weather. Resolving conflicts between the rerouted aircraft requires the controller to issue multiple instructions to adjust flight plans, which will increase the workload of the controller. In addition, the capacity of the sector changes. The main task in this section is to statistically calculate the number of rerouted aircraft under different types of bad weather conditions so that the corresponding sector capacities can be calculated. According to the theory of maximum flow and minimum cut, when the directions of the traffic flow in a plane are the same, the maximum flow that can pass in that plane is not based on the average value, but instead determined by the flow that can pass through the narrowest place in the plane, that is, the plane bottleneck. Therefore, according to the theory, it can be assumed that route \(L\) is connected to \(K\) rectangular regions at altitude level \(I\), and the blocking probability of route \(I\) at this altitude is determined by the rectangle with the largest blocking value among the \(K\) rectangular regions [20]. Thus, the blocking probability of route \(I\) at altitude level \(I\) can be obtained as  
\[q^{Li}=\underset{1\leq D\leq k}{\max}q^{Li}_{D} \tag{10}\]  
where \(q^{Li}\) is the blocking probability of route \(L\) at altitude level \(i\). If there are m available altitude levels on route \(L\), the blocking probability of route \(L\) under the influence of bad weather can be expressed as  
\[q^{L}=\sum\limits_{i=1}^{M}q^{Li}/M \tag{11}\] \[=\sum\limits_{i=1}^{M}\left(\underset{1\leq D\leq k}{\max}q^{Li}_ {D}\right)/M\] \[=\sum\limits_{i=1}^{M}\underset{1\leq D\leq k}{\max}\left[\sum \limits_{n=1}^{32}\left(\frac{\mu^{Li}_{Dn}}{d^{Li}_{Dn}\times 5.36}\right) \right]/M\]  
where \(q^{L}\) is the blocking probability of route \(L\). The availability of route \(L\) in bad weather is expressed by \(RA^{r}\):  
\[RA^{r}=1-q^{L} \tag{12}\] \[=1-\sum\limits_{i=1}^{M}\underset{1\leq D\leq k}{\max}\left[\sum \limits_{n=1}^{32}\left(\frac{\mu^{Li}_{Dn}}{d^{Li}_{Dn}\times 5.36}\right) \right]/M\]  
In order to facilitate the subsequent calculations and enhance the visibility of the available capacity of the route, different types of bad weather are classified into grades 1, 2, and 3, and the fuzzy mathematics method is used to classify them. Fuzzy mathematics is a mathematical method used to investigate certain types of uncertain quantities. There is no clear numerical boundary to define the grade that each weather type belongs to, which makes the fuzzy mathematics method inherently suitable for solving this problem. Fuzzy subsets are set up according to the following requirements: Let \(U\) be the universe of discourse, called mapping \(\mu_{\widetilde{A}}:U\rightarrow\left[0,1\right],\)\(a\mapsto\mu_{\widetilde{A}}(a)\in\left[0,1\right],\) and determine a fuzzy subset of \(u\) where \(\mu_{\widetilde{A}}(a)\) is called the membership degree \(\widetilde{A}\) of a pair. When \(\mu_{\widetilde{A}}(a)\) is closer to 0, it is less likely that a belongs to \(a\), while when \(\mu_{\widetilde{A}}(a)\) is closer to 1, it is more likely that a belongs to \(a\); \(\mu_{\widetilde{A}}(a)=0.5\) represents the most-fuzzy condition, also known as the fuzzy point. Fuzzy subset \(\widetilde{A}\) is uniquely determined by the membership function \(\mu_{\widetilde{A}}\), so they are considered to be equivalent. For simplicity, \(\widetilde{A}\) and \(\mu_{\widetilde{A}}\) are usually represented by \(a\). The Zadeh representation of fuzzy subsets is used:  
\[A=\frac{A(a_{1})}{a_{1}}+\frac{A(a_{2})}{a_{2}}+\ldots+\frac{A(a_{n})}{a_{n}} \tag{13}\]  
where \(\frac{A(a_{i})}{a_{i}}\) means that the membership of \(a_{i}\) in fuzzy set \(a\) is \(A(a_{i})\).