# Airport Field Path Optimization Method Based on Conflict Hotspot Avoidance Mechanism
## 2 Modelling
### Hotspot Avoidance Mechanisms  
A hotspot avoidance mechanism is designed for critical conflict hotspot areas \(HS=\{HS_{1},HS_{2},\cdots\}\), where the likelihood of conflict is high. The core of the mechanism is to determine the priority of aircraft in different operating environments, and then allow aircraft with a high priority to pass through the hotspot area first and continue taxiing on the pre-planned path, while aircraft with a low priority will use other resolution strategies. When a potential conflict occurs in a hotspot area, the following principles are used to determine the priority of aircraft:  
(1) Priority judgment for inbound and outbound: In a certain period, if there are inbound and outbound aircraft occupying the hotspot area one after another and there is a potential taxiing conflict, the inbound aircraft will be allowed to continue taxiing in the hotspot area on the original taxiing path, and the outbound aircraft will either slow down and wait for it, or change to a suboptimal alternative taxiing path as shown in Figure 1a, to avoid the potential taxiing conflict.  
(2) Taxiing time priority judgment: In a certain period, if there are inbound and outbound aircraft occupying the conflict hotspot area successively and there is a potential taxiing conflict, the aircraft with a longer taxiing time will be allowed to continue taxiing on the original taxiing path passing through the hotspot area, whereas the aircraft with shorter taxing time will decelerate and wait for the alternative taxing path or change to a suboptimal alternative taxing path, as shown in Figure 1b, to optimize the field resource utilization.  
(3) Aircraft priority judgement: In a certain period, there are more aircraft occupying the hotspot area one after another; therefore, the time is subdivided into several time slots, so that the aircraft in the first time slot will continue to taxi on the original taxing path passing through the hotspot area, and the aircraft in the neighboring time slow down and wait for or choose the suboptimal alternative taxing path, as shown in Figure 1c, to avoid the conflict of taxing.  
For the two options for conflict resolution--decelerate and wait, and replan the suboptimal alternative path--it is necessary to evaluate the waiting time for both and select the solution with the smaller waiting time. The time to decelerate and wait is \(\Delta t\), and the time to replan the suboptimal alternative path over the original plan is \(\Delta c/v\), where \(\Delta c\) is the increased glide distance of the replanned path. To select the less costly solution to resolve the conflict, the conflict resolution process is shown in Figure 2. In the conflict resolution process, deadlocks or livelocks may occur. In order to avoid the phenomenon of a deadlock (waiting in a loop) or livelock (priority keeps changing but cannot be unlocked) that occur in the hotspot avoidance process, this paper introduces a waiting directed graph monitoring mechanism into the scheduling module. The system treats all the waiting aircrafts as vertices in real time, and constructs directed edges according to the relationship of letting them go first and then moving them later, and once the directed loop is detected, it is considered that a potential deadlock occurs. Firstly, the local unlocking strategy is executed, and the flight with the longest waiting time in the ring exchanges priority with its predecessor; if the ring is not broken by two consecutive local unlockings, the global unlocking is triggered, and a set of new alternative paths without the ring are generated to replace the original conflicting paths at one time [32] This is a detailed description of the Swap Aircraft Priority, Resolve Conflicts section of Figure 2.  
Figure 1: Aircraft prioritization schematic.