## 7 Results and Discussion  
The input parameters for each case study are shown in Table 7, and the distance matrix shown in Table 4 is used as a cost function. The UAM speeds are also set as variables, with a maximum of 240 km/h and a minimum of 210 km/h. The waiting time is assumed to satisfy the customer requirements of 3 to 5 min. The cases are shown in Table 8. The route selection results for the two cases are shown in Figures 9 and 10, respectively, and the details of the scheduling, mission times and corridors are given in Appendix A. Figures 9 and 10 show the time-space network of vertiports and the operation time horizons for the given vertiport network and numbers of UAMs. Red color lines the results of vehicle that depart from Gimpo, black lines show the results of vehicle that depart from Seoul Bus Express Terminal, green lines show the results of vehicle that depart from Incheon, Megnat lines show the results of vehicle that depart from Jamsil, and the blue lines shows the results of vehicle that depart from Yongsan vertiport.  
second vehicle waits for 5 min before travelling to Incheon. For the vehicles at Gimpo, the waiting time is only 3 min, whereas the vehicles at Incheon vertiport wait for 5 and 3 min, as shown in the figure (marked ICN). The overall route selection schedule also shows that there is no overlap between the time stamps at each depot, which satisfies our problem definition. The speeds used to travel between vertiports are shown in Appendix A. The speed variable only has values between the upper bound of 240 km/h and the lower bound of 210 km/h. However, owing to the waiting time variables, dynamic scheduling is also achieved while selecting the optimum route between vertiports.  
When there are three vehicles at each vertiport, as shown in Figure 10, the first, second and third vehicles select different routes. By increasing the number of vehicles, our formulation of the route selection constraint in Equation (5) is satisfied, in addition to optimising the flight schedule, which forces the vehicles to select different routes with the variables of 0 and 1. However, the formulation still follows the FIFO rule for dynamic AADS.  
Dynamic scheduling was also achieved through the mission selection module, which was used to calculate the mission flight time and speed based on the arrival and departure locations and the variables representing the departure and arrival times in the point-to-point problem formulation; these are related to the mission flight time of each UAM and the waiting time at each depot. The mission flight time between each departure and arrival point was relatively short for Jamsil, Seoul Bus Terminal and Yongsan because the travel distances between these locations are short, and the cruising speed of the UAM is quite high, resulting in short mission flight times. In all the cases examined here, different routes were selected for all the vehicles, with different flight missions, and almost all departure and arrival scheduling was calculated based on the mission time and waiting time. Hence, a solution to the point-to-point network problem with dynamic scheduling was achieved for UAM operation management by applying our proposed new formulation of the point-to-point problem.