# Reservation-Based 3D Intersection Traffic Control System for Autonomous Unmanned Aerial Vehicles
## 2 Related Work
* It enters the acceleration zone such that it can enter the intersection as scheduled. Details on the length of the zones in the approaching area are described as follows:
* Reservation zone  
A UAV must send its reservation request to the intersection manager as soon as it enters this zone. After it has sent its request, it should receive its schedule before it enters the next zone. Since the intersection manager processes the requests every \(k\Delta t\), up to one \(k\Delta t\) can be spent before its request can be processed and another \(k\Delta t\) is needed for the scheduling. Hence, it will wait up to \(2k\Delta t\) before it receives its schedule. If the UAV moves at the fastest speed possible, \(s_{max}\), then it will travel up to \(2k\Delta t\)s\({}_{max}\) before it receives its request. Thus, to make sure that a UAV traveling at \(s_{max}\) will receive its schedule before it enters the next zone, the length of the reservation zone, \(l_{rz}\), should be at least  
\[l_{rz}\geq 2k\Delta t_{max} \tag{1}\]
* Queueing zone  
After the reservation zone, UAVs will enter the queueing zone. It is expected that a UAV has already been scheduled by the time it enters this zone. In this zone, it must adjust its speed to be able to enter the intersection as scheduled. It will either maintain its speed, speed up, slow down, or stop and wait for some time before entering the next zone, the acceleration zone. Assume a UAV entered this zone at the speed of \(s_{max}\), there is no UAV ahead, and it must stop for some time before it enters the next zone to be able to follow its schedule. Then, it will travel a distance of  
\[d_{stop}=\frac{{s_{max}}^{2}}{-2\ r_{min}} \tag{2}\]  
where \(r_{min}\) is the fastest possible negative acceleration rate of all UAVs. Thus, to make sure that the UAV can stop before it reaches the entrance of the acceleration zone, the length of the queueing zone, \(l_{qz}\) must be at least  
\[l_{qz}\geq\frac{{s_{max}}^{2}}{-2\ r_{min}} \tag{3}\]In case a UAV did not receive a response by the time it enters the queueing zone, then it is assumed that the message is lost. When this happens, it will resend a new request message while slowing down to stop at entrance of the acceleration zone. Then, it waits for its new schedule and will enter the acceleration zone as scheduled. Since this UAV causes the UAVs behind it to stop, the UAVs behind must also send requests again. * Acceleration zone  
A UAV can enter the acceleration zone only when it can enter the intersection at the scheduled time. If a UAV's speed is not in the allowed speed range when it enters this zone, then it must adjust its speed until it reaches the allowed minimum speed in the intersection. Assume a UAV stopped before the entrance of the acceleration zone, then to be able to reach the speed requirement before it enters the intersection, the length of the acceleration zone, \(l_{az}\), must be at least  
\[l_{az}\geq\frac{{s_{max}}^{2}}{2\,r_{max}} \tag{4}\]  
where \(r_{max}\) is the fastest possible positive acceleration rate of all UAVs.