# Collaborative Allocation Method of En-Route Network Resources Based on Stackelberg Game Model
## 5 Experiment Analysis  
The hardware and software configuration of the computer used for the experiment analysis is as follows: the operating system is Windows 11 (64-bit); the processor is Intel (R) Core (TM) i7-1165G7; the CPU frequency is 2.80 GHz; the onboard memory is 16.0 GB; and the programming language is Python 3.11. The actual operational and simulated data of an en-route sector in Shanghai Flight Information Region (FIR) in the eastern region of China in April 2019 are used for analysis. Congestion is more likely to occur on the A599 and H24 high-altitude en-routes in the  
Figure 3: Allocation situations of each flight for the initial allocation plan. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & & **Estimated** & **Estimated** & **Estimated** & **Estimated** & **Earliest** \\
**Flight** & **Airlines** & **Time to** & **Time to** & **Time to** & **Time to** & **Time to** & **Entry** \\
**Number** & & **Ener** & **Enter** & **Enter** & **Enter** & **Enter** & **Time** \\  & & **FCA001** & **FCA002** & **FCA003** & **FCA004** & & \\ \hline \(f_{11}\) & C & 17:45:34 & 17:30:34 & 17:40:34 & 17:25:34 & 17:25:34 \\ \(f_{12}\) & A & 17:33:03 & 17:48:03 & 17:28:03 & 17:43:03 & 17:28:03 \\ \(f_{13}\) & B & 17:36:58 & 17:51:58 & 17:31:58 & 17:46:58 & 17:31:58 \\ \(f_{14}\) & A & 17:32:01 & 17:47:01 & 17:37:01 & 17:52:01 & 17:32:01 \\ \(f_{15}\) & C & 17:38:53 & 17:53:53 & 17:33:53 & 17:48:53 & 17:33:53 \\ \(f_{16}\) & C & 17:35:50 & 17:50:50 & 17:40:50 & 17:55:50 & 17:35:50 \\ \(f_{17}\) & B & 17:43:12 & 17:58:12 & 17:38:12 & 17:53:12 & 17:38:12 \\ \(f_{18}\) & C & 18:00:33 & 17:45:33 & 18:15:33 & 17:50:33 & 17:45:33 \\ \(f_{19}\) & C & 18:02:28 & 17:47:28 & 18:07:28 & 17:52:28 & 17:47:28 \\ \(f_{20}\) & C & 17:49:15 & 18:04:15 & 17:54:15 & 18:09:15 & 17:49:15 \\ \hline \hline \end{tabular} Note: Airlines A, B, and C, respectively, correspond to Juneya Airlines, Shenzhen Airlines, and Eastern Airlines. Based on the above situational information, the initial allocation of en-route resources is conducted with the objectives of efficiency and fairness. A multi-objective optimization algorithm is used to allocate 20 flights from different airlines to the available time slots to obtain feasible allocation plans. Then, the Pareto front is calculated based on the obtained allocation plans, and the objective function values of these plans are compared with the results of the allocation plans obtained by the commonly used Ration-by-Schedule (RBS) algorithm [25] to obtain six superior allocation plans that completely dominate the RBS method in the Pareto optimal solution set. The specific allocation details of these six plans are shown in Figure 3, while the efficiency and fairness indicator values of each plan, that is the total delay cost and fairness loss degree, are shown in Figure 4, which are calculated for each scenario based on the model constructed in this paper. In Figure 3, the allocated trajectory of each flight and the time order of entering the trajectory is used to represent the specific situation of each allocation, the specific position of each flight point on the timeline do not directly correspond to the actual time slot situation, and the relative interval size of each flight within the same trajectory option represents the length of the interval time between the allocated time slots.  
\end{table} 
Table 2: _Cont._According to the specific allocation information of the obtained plans, the delay costs of each airline under each plan can be calculated. The calculation results are shown in Figure 5, where Juneyao Airlines, Shenzhen Airlines, and Eastern Airlines, respectively, correspond to the airlines A, B, and C.  
After obtaining the above initial allocation plan information, the first stage of the Stackelberg game is completed. The preliminary allocation plan is used as the guiding information by the ATC to pass to the airlines, and then, the game between the airlines is the second stage of the Stackelberg game.