# Structured Urban Airspace Capacity Analysis: Four Drone Delivery Cases
## 4 Monte Carlo Simulations  
In this section, we conduct Monte Carlo (MC) simulations with two different outer loop algorithms (the FCFS and LCFS algorithms) that are based on the proposed flight planning algorithm for four drone delivery operation types. We investigate how the different operation types' performance and safety behave with regard to the different flight planning algorithms and the number of sUASs in the high-density VLL urban airspace using the suggested four metrics. It aims to provide an approach for choosing between resolution strategies for urban airspace management by regulators, policymakers, and urban airspace designers. The representative operation being considered in this study is drone delivery, especially last-mile delivery and first-mile delivery. Last-mile delivery is defined as the movement of items from transportation hubs (which are retailers in this study) to final delivery destinations, typically personal residences. First-mile delivery refers to the movement of goods from sellers to courier services who will take these goods to their final users. A scenario for the simulations is based on the town 'Oldbrook', which is one of the well-planned towns in Milton Keynes in the United Kingdom. Two-dimensional infrastructure data of the town is obtained from Google Earth Pro. The scenario has an area size of 0.98 km\({}^{2}\) as shown in Figure 7. Similar to the en-route airspace for commercial aircraft, in this route network, we construct two layers of nodes that are set above the roads at heights of 15 m and 25 m as shown in Figures 8 and 9 for eastbound and westbound routes, respectively. We assume that each layer consists of 70 points (3 retail points (red pins) and 67 service points (green pins)) and 107 directed routes as shown in Figures 8 and 9. All sUASs are of the same type as shown in Table 4. The sUAS type can be later changed and varied based on the missions and operators. For the separation between sUASs, it is assumed that the time-based minimum vertical and horizontal separation requirement during the flight is 5 s. No hovering manoeuvres are allowed for any sUASs. Figure 8: Eastbound at 15 m, 3 retail points (E68, E69, E70) and 67 service points (E1\(\sim\)E67) and 107 directed routes, (Oldbrook, Milton Keynes, United Kingdom). Figure 7: Oldbrook, Milton Keynes, United Kingdom (from Google Earth Pro). Green pins (1\(\sim\)67) and red pins (67\(\sim\)70) represents retail points and service points respectively. We conduct 100 MC simulations for each outer loop algorithm (FCFS and LCFS algorithms) by increasing the number of sUASs from 5 to 50 with 5 s interval for the four drone delivery operation types (1-to-\(\mathcal{M}\), \(\mathcal{M}\)-to-1, \(\mathcal{N}\)-to-\(\mathcal{M}\), \(\mathcal{M}\)-to-\(\mathcal{N}\)) as shown in Table 5. At each simulation a service point and a retail point for each sUAS are randomly chosen except for the 1-to-\(\mathcal{M}\) and \(\mathcal{M}\)-to-1 cases in which there is the single retail point E68 and W68, respectively. Once the route network and each sUAS' retail point and service point are given, which are the input of Algorithm 1, the algorithm generates each sUAS' flight plan as described in Section 3. From the output of the algorithm, we obtain \(M_{tf}\) (total flight time), \(M_{mct}\) (mission completion time), \(M_{tfd}\) (total flight distance), and \(M_{cnf}\) (normalised number of conflicts). Both the FCFS and LCFS algorithm results quantify the route network-based urban airspace based on the four metrics. For each operation type, we analyse both results, and suggest one of the two outer loop algorithms that is more appropriate for the operation type. \begin{table}
\begin{tabular}{c c} \hline \hline  & **Small UAS** \\ \hline Speed Range (km/h) & [5; 6; 7; 8; 9; 10; 11; 12; 13; 14; 15; 16; 17; 18; 19; 20; 21; 22; 23; 24; 25] \\ Endurance (s) & 900 \\ Separation (s) & 5 \\ Max Weight (kg) & 25 (FAA Part 107) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: sUAS specification.