## 4 Capacity Analysis for Each Topology  
### Theoretical Background  
For UAM operation, a vertiport will be newly built in a limited space in a downtown area or integrated with existing infrastructure. Therefore, it is necessary to consider a layout that can operate as many aircraft as possible in a limited space, so we compared the three layouts reviewed in the previous section under the same conditions to evaluate capacity.  
The operating procedure of the aircraft in the vertiport is shown in Figure 23. While the simultaneous operating distance of AC 150/5390-2C was applied, the capacity analysis code was written with the assumption that the vertiport is empty at t = 0. To accommodate  
Figure 21: Pier topologies for the Gimpo Airport parking lot that comply with the FAA’s new regulations: (**a**) current parking space; (**b**) expanded parking space.  
Figure 22: Pier topologies for the Gimpo Airport parking lot that comply with the EASA’s new regulations: (**a**) current parking space; (**b**) expanded parking space.  
the maximum number of aircraft, arrival is prioritized over departure in the TLOF pad. For the safe operation of the vertiport, there can be only one aircraft at the node where the TLOF pad and gate are connected. For example, when an aircraft is arriving at a vertiport with one TLOF pad, step 5 cannot be performed.  
Figure 24 shows the possible departure/arrival integer pairs. The section 4 is the number of times the vertiport can accommodate the arrival of aircraft and is created to be as much as the number of aircraft arrivals that fill the gate in the initial state. Sections 4 and 4 are linear by giving priority to arrival where departure or arrival is possible. Sections 5 and 6 are free-operation sections, and in section 5, departures can occur without reducing the number of arrivals. The free-operation section may vary depending on the number of prearranged aircraft, arrival time, departure time, turnaround time, etc. [7]. Section 4 is a section in which the sum of feasible departures and arrivals in the vertiport is maximum and can be created as a single point or as a line by decreasing arrivals and increasing departures. Therefore, an integer pair in this section means the maximum capacity of the vertiport. Section 6 is created when there is an aircraft prepared in advance, i.e., when an arrival is blocked and a departure occurs.  
Figure 24: Integer pairs of departures and arrivals: section 4 is the number of accommodated aircraft when the vertiport is empty; 4 and 4 are the priority arrival sections; 4 and 4 are the free-operation sections; section 4 has the maximum of feasible departure and arrival; and section 4 is the section with prepared departure aircraft.  
Figure 23: Operation process on a vertiport. 4 is arrival, 4 is taxing to gate, 4 is gate, 4 is taxing to TLOF pad, 5 is departure.  
In this study, the capacity was analyzed using Matlab and the departure/arrival integer pair was expressed while satisfying Equations (1)-(4) for \(n\) gates and time \(t\). Figure 25 shows the operation procedure of each aircraft at one to four gates of a vertiport with one TLOF pad and four gates.  
The TLOF pad utilization rate is the time ratio for arrival, taxi-in, taxi-out, and departure in the total time as shown in Figure 25. The gate utilization rate is calculated as the average of the time ratio of the taxi-in, taxi-out, and turnaround time on each gate in the total time, and then calculated again as an average for all gates when the capacity reaches the max-throughput in Equation (5). In the case of gate utilization, even if the turnaround of the aircraft is completed, there could be a waiting time for departure that is due to priority on arrival, and this congestion time is also counted. The gate holding time increases when the equal sign is satisfied in Equation (4) and is calculated using Equation (6). Table 3 summarizes the variables used in the equations.  
\[\sum_{n=1}^{N_{\textit{t}\textit{t}\textit{f}}}N_{\textit{arr}}(t,\ n)-\sum_{n