# Reservation-Based 3D Intersection Traffic Control System for Autonomous Unmanned Aerial Vehicles
## 4 UAV's Behavior in the Approaching Area
### Entering the Intersection as Scheduled  
When \(UAV_{B}\) is in the queueing zone and there is no UAV ahead in the queueing zone, \(UAV_{B}\) must adjust its speed such that it can enter the intersection at the scheduled time. The time it will spend from \(t_{j}\) until it enters the intersection, \(t_{B,j}^{inter}\), must be equal to \(t_{B,j}^{sched}\), the time it is scheduled to enter the intersection from \(t_{j}\). The value of \(t_{B,j}^{inter}\) depends on the speed of \(UAV_{B}\) in the queueing zone and acceleration zone. In short, \(UAV_{B}\) uses a constant rate from \(t_{j+1}\) until it reaches the exit of the queueing zone, \(r_{B,j+1}^{pre}\) where \(r_{min}\leq r_{B,j+1}^{pre}\leq\ r_{max}\). Afterwards, it may spend some time waiting at the entrance of the acceleration zone. After it enters the acceleration zone, it accelerates at rate \(r_{max}\) until its speed reaches \(s_{max}\). Then, it maintains its speed at \(s_{max}\) until it reaches the intersection. To be more specific, the different scenarios on how \(UAV_{B}\) will behave at the queueing zone and acceleration zone based on \(r_{B,j+1}^{qz}\) are listed below. * Scenarios for which \(r_{B,j+1}^{qz}\) is less than zero
* Scenario 1: \(UAV_{B}\) slows down at rate \(r_{B,j+1}^{qz}\) from \(t_{j+1}\) until it reaches the entrance of the acceleration zone. It reaches the entrance of acceleration zone with speed equal to zero. Then, it waits for some time before it enters the acceleration zone. In the acceleration zone, it accelerates at rate \(r_{max}\) until its speed reaches \(s_{max}\). Then, it maintains its speed until it enters the intersection. * Scenario 2: \(UAV_{B}\) slows down at rate \(r_{B,j+1}^{qz}\) from \(t_{j+1}\) until it reaches the entrance of the acceleration zone with speed equal to zero. Then, it immediately enters the acceleration zone and then accelerates at rate \(r_{max}\) until its speed reaches \(s_{max}\). Then, it maintains its speed until it enters the intersection. * Scenario 3: \(UAV_{B}\) slows down at rate \(r_{B,j+1}^{qz}\) from \(t_{j+1}\) until it reaches the entrance of the acceleration zone. It reaches the entrance of acceleration zone with speed greater than zero. Then, it enters the acceleration zone and accelerates at rate \(r_{max}\) until its speed reaches \(s_{max}\). Then, it maintains its speed until it enters the intersection. * Scenarios for which \(r_{B,j+1}^{qz}\) is equal to zero
* Scenario 4: \(UAV_{B}\) maintains its speed in the queueing zone, which is less than \(s_{max}\). Then, it enters the acceleration zone and accelerates at rate \(r_{max}\) until its speed reaches \(s_{max}\). Then, it maintains its speed until it enters the intersection. * Scenario 5: \(UAV_{B}\) maintains its speed in the queueing zone, which is equal to \(s_{max}\). Then, it enters the acceleration zone and maintains its speed until it enters the intersection. * Scenarios for which \(r_{B,j+1}^{qz}\) is greater than zero
* Scenario 6: \(UAV_{B}\) accelerates at rate \(r_{B,j+1}^{qz}\) from \(t_{j+1}\) until it reaches the entrance of the acceleration zone. It reaches the entrance of the acceleration zone with speed less than \(s_{max}\). In the acceleration zone, it accelerates at rate \(r_{max}\) until its speed reaches \(s_{max}\). Then, it maintains its speed until it enters the intersection. * Scenario 7: \(UAV_{B}\) accelerates in the queueing zone at rate \(r_{B,j+1}^{qz}\) from \(t_{j+1}\) until it reaches the entrance of the acceleration zone with speed equal to \(s_{max}\). Then, it maintains its speed until it enters the intersection. * Let \(t_{B,j}^{qz}\) be the time \(UAV_{B}\) will spend in the queueing zone from \(t_{j}\). Let \(t_{B}^{wait}\) be the time it will spend waiting at the entrance of the acceleration zone. Let \(t_{B}^{qz}\) be the time it will spend in the acceleration zone.