## 3 Problem Description and Multiple Operation Procedures Design for U-Shaped Area
### Partition-shared Operation Procedure  
Under the partition-shared operation procedure, the apron U-shaped area can be divided into three zones: \"outer\", \"middle\", and \"inner\", and two access in the U-shaped area are being used as one access. For a specific partition, intersection taxiing of arrival and departure aircraft is not allowed (e.g., the paths of aircraft A and B in Figure 3), thus ensuring that aircraft operations meet the airport's lateral safety separation regulations. Under the partition-shared operation procedure, the specific aircraft operation rules need to be classified according to the physical structure of the U-shaped area and the aircraft interaction relationship. Figure 4a-c show the aircraft operation rules for different types of arrival and departure activities in different physical structure areas under the partition-shared operation procedure. Figure 4: Partition-Shared Operation Procedure. Blue arrows indicate the aircraft operation path. (**a**) shows a scenario where there is a simultaneous pushing back of departure aircraft A and B in the outer and inner sectors (aircraft C and D are waiting to pushback or enter the U-shaped area); (**b**) shows a scenario where there are simultaneous departure aircraft B and A pushing back from the outer and middle areas respectively (aircraft C and D are waiting to pushback or enter the U-shaped area); (**c**) shows a scenario where there are simultaneous departure aircraft B and A from the inner and middle areas respectively (aircraft C and D are waiting to pushback or enter the U-shaped area). Figure 3: Intersection Taxing Diagram of Arrival and Departure Aircraft. The intersection taxiing of departure aircraft A and arrival aircraft B is not allowed. Figure 2: Exclusive Operation Procedure. (**a**) Departure: the departing aircraft A in the U-shaped area is pushing out, and the arrival air-craft C must wait outside the U-shaped area and the following departing aircraft B must wait in the stand until aircraft A leaves the U-shaped area; (**b**) Arrival: departing aircraft B within the U-shaped area must queue up in order to await push-back instructions and arrival aircraft C must wait outside the U-shaped area until aircraft A parks on stand. Figure 4a shows a scenario where there is a simultaneous pushing back of departure aircraft in the outer and inner sectors. Under the partition-shared operation procedure, only one aircraft A in the outer area and one aircraft B in the inner areas are allowed to be pushed back simultaneously at a time. Departure aircraft C in the middle area and other aircraft D that need to enter the U-shaped area must wait at the stand or outside the U-shaped area entrance until aircraft B from the inner area has left the U-shaped area. Figure 4b shows a scenario where there are simultaneous-departure aircraft pushing back from the outer and middle areas, respectively. Under the partition-shared operation procedure, if there is a demand for aircraft to push back in the middle and the outer area at the same time, the priority is to push aircraft A in the middle area with extension into the inner area, and then push aircraft B in the outer area after aircraft A in the middle area reaches the designated position in the inner area, and then launch the two aircraft A and B with reference to the scenario of aircraft push back in the outer area and the inner area at the same time. The departure aircraft C in the inner area and other aircraft D that need to enter the U-shaped area must wait at the stand or outside the U-shaped area entrance until aircraft A has left the U-shaped area. Figure 4c shows a scenario where there are simultaneous departure aircraft from the inner and middle areas, respectively. Under the partition-shared operating procedure, if there is a simultaneous aircraft push-back demand in the inner and middle areas, priority to push back will be given to aircraft A in the middle area and then pull forward the aircraft A to the outer area.