# Reservation-Based 3D Intersection Traffic Control System for Autonomous Unmanned Aerial Vehicles
## 8 Simulation Results
### Comparison of Our Proposed System with the 2D Optimal Static Traffic Light Intersection System
\begin{table}
\begin{tabular}{l} \hline \hline
**Intersection Parameters** \\ \hline \(s_{min}=15\) m/s \\ \(s_{max}=15\) m/s \\ UAV diameter \(=3\) m \\ Lane width \(=5\) m \\ 3 lanes per way \\ Intersection size \(=30\) m \(\times\) 30 m \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Intersection parameters used in traffic light system and in our proposed system. Figure 24: Traffic phases of the traffic light system of (**a**) Scenario 1: when all UAVs move straight and (**b**) Scenario 2: when UAVs can turn left, move straight, or turn right. are UAVs ahead, its queueing delay is the delay of the UAV ahead plus the time it will take to reach the entrance of the intersection. In our scheduling scheme, when traffic is low, UAVs can enter the intersection without stopping if there is no conflict with the paths of the UAVs in the intersection. As shown in the figure, even when traffic is high, our system performs better than traffic light system on this scenario. The average number of UAVs in the intersection on this scenario are shown in Figure 26. As shown in the figure, the number of UAVs in the intersection using our system is always greater than the traffic light. The difference in the number of UAVs in the intersection is between one to three UAVs. The maximum of average number of UAVs in the intersection is 33 UAVs for the traffic light and 36 UAVs for our system. \begin{table}
\begin{tabular}{l} \hline \hline
**Intersection Parameters** \\ \hline \(ar_{min}=-3.5\,\mathrm{m/s^{2}}\) \\ \(ar_{max}=4\,\mathrm{m/s^{2}}\) \\ \(l_{rz}=150\,\mathrm{m}\) \\ \(l_{lqz}=33\,\mathrm{m}\) \\ \(l_{az}=29\,\mathrm{m}\) \\ Cell size = 1 m \\ \(\Delta t=0.05\,\mathrm{s}\) \\ \(k\Delta t=5\,\mathrm{s}\) \\ GA population size per generation = 100 \\ GA termination = 80 generations \\ GA mutation rate = 10\% \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Parameters used in our proposed system. Figure 25: Average queueing delay of the UAVs using 2D optimal static traffic light and using our proposed system in 2D intersection on Scenario 1. To understand better how both system works, we obtained the number of UAVs in the intersection every 1 s for the traffic light system and every 0.2 s in our system. The results are shown in Figure 27. We ran five simulations for each system. The arrival rate is 200 UAVs per minute per direction in each simulation. We started obtaining the number of UAVs for 25 s after the simulation has been running for 2 min, which is when the simulation is already in a steady state. We can see from the figure that in the traffic light system, there are at maximum 60 UAVs in the intersection. The number of UAVs mostly remained at 60 UAVs. Then, it decreased when the traffic light turned yellow, and the number of UAVs started to increase again to 60 UAVs after the light of the next phase turned green. In our system, the number of UAVs in the intersection changes between 19 UAVs and 60 UAVs. This graph reflects the average number of UAVs when arrival rate is 200 UAVs, as shown in Figure 26.  
Figure 26: Average number of UAVs in the intersection using 2D optimal static traffic light and using our proposed system in 2D intersection on Scenario 1.  
time duration of 5 s and a yellow time duration of 5 s. Since there are four phases in this scenario, a UAV at the start of a queue can wait up to 30 s before it can enter the intersection on this arrival rate. As shown in Figure 28, our system performs better than traffic light system on low and medium traffic for the same reason with Scenario 1. However, when the arrival rate is greater than 40 UAVs per direction per minute, the delay of the UAVs in the left most lanes contribute to the increase in the average delay of the UAVs. The UAVs turning left experience greater delay than the straight moving UAVs since the trajectories of left turning UAVs experience more conflicts in the intersection. Similar trends will be observed when the arrival rate is higher than 50 UAVs per minute.