# Collaborative Allocation Method of En-Route Network Resources Based on Stackelberg Game Model
## 5 Experiment Analysis
Based on the flight information in Table 2 and the preliminary allocation plan information in Table 3, it can be seen that there are three airlines participating in the game, and each airline has six different options. According to the game model between airlines established earlier, the probability of Juneyao Airlines choosing each option is calculated first. The calculation results are shown in Figure 6. From the game results of Juneyao Airlines shown in Figure 6, it can be seen that when Juneyao Airlines chooses plan 4, the probability of other airlines (that is the set of airlines participating in the game excluding Juneyao Airlines) choosing a plan other than plan 4 is relatively small. Combining specific allocation information, it can be known that this is because when all flights of Juneyao Airlines choose plan 4, the other airlines will be more likely to conflict with the flight time of Juneyao Airlines when making their choices among other plans, so the probability of  
Figure 4: Efficiency and fairness statistics of the initial allocation plan. Figure 5: Delay costs of each airline. choosing other plans in this case is very small, which is in line with the actual situation. At the same time, this also has a reverse influence on the choosing inclination towards plan 4 of Juneyao Airlines, resulting in a lower probability of choosing option 3 for Juneyao Airlines. Similarly, it can be seen that when Juneyao Airlines chooses option 1, it has the least influence on the other airlines' choices of plans. Other airlines have a higher probability of choosing each plan, which in turn makes Juneyao Airlines more inclined to choose option 1. Furthermore, when analyzing the game results combined with the delay costs for Juneyao Airlines in each option shown in Table 3, it is found that the probabilities of airlines choosing each plan do not necessarily have a linear relationship with their own delay situations. This is because when the airline chooses the plan with the least delay for itself, it is equivalent to taking the first advantageous time, and then opportunities for other airlines to choose will be reduced. As a result, in such a situation, the opportunities for other airlines to make their choices are reduced, which in turn affects the airline's own choice of the plan. Similar to the game process of Juneyao Airlines, the game process between Shenzhen Airlines and Eastern Airlines is conducted in turn. The probabilities of each airline choosing each plan are calculated, and the results are shown in Figures 7 and 8. From the probability information shown in the figure, it can be seen that Shenzhen Airlines prefers choosing option 4, while Eastern Airlines prefers choosing option 3. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Airlines**} & **Maximum** & **Selected** & **Delay Cost** & **Selected** \\  & **Probability** & **Optimal Plan** & **under Optimal** & **Suboptimal** \\  & & & **Plan** & **Plan** \\ \hline Juneyao Airlines & 0.346 & Plan 1 & 80.3 & Plan 2 \\ Shenzhen Airlines & 0.363 & Plan 4 & 104.3 & Plan 1 \\ Eastern Airlines & 0.358 & Plan 3 & 90.2 & Plan 1 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Optimal options for each airline. Figure 6: Probability of Juneyao Airlines choosing each plan. After the above game process, the selection tendency of each airline is obtained, and the specific choosing situation is shown in Table 3. The maximum probability is the average of the probabilities of the other airlines choosing each option while one airline chooses its optimal option. From the results, it can be seen that the optimal plan for each airline is different. Then, the next step of the game will be played, that is, all airlines will feedback their selection tendency of the plans to the ATC side. Based on the choice preference of each airline, ATC will make the decision on the final allocation plan. The third stage of the game is an information exchange between ATC and the airlines.