## 4 Performance Evaluation
### Analytical Results of the Linear Programming Equations in the Ideal Scenario  
In this section, we first use the linear programming equations formulated in Section 3 to calculate analytical results of the objective function, i.e., Equation (10) for the aggregate event communication time, as the performance benchmark in the _ideal_ scenario. For solving the optimal result of Equation (10), information, like locations, numbers of sub-events, etc. of all events must be known in advance. Hence we assume that the number of all events and their sub-events are given using default values in Table 3. They happened at the same time and their locations are fixed. Here, we compare analytical optimal results of Equation (10), which are denoted as the OPT scheme below, and simulation results of the aggregate event communication time of EAUD and EAMUD. These analytical optimal results are solved by the JAVA API, provided by CPLEX [30], on Eclipse.  
Figure 9 illustrates the average ratio of the event link communication time with respect to the number of UAVs in the ideal scenario. As the number of UAV raises, the probability that the GCS can dispatch UAVs to serve all sub-events of the same parent event becomes higher, which increases average ratio of the event link communication time accordingly for all schemes until the number of UAVs is high enough, i.e., larger than 240, to satisfy all UAV requirements in the event queue. When the number of UAVs is smaller than 240, OPT achieves the highest ratio of the event link communication time, then EAUD and EAMUD follow. This is because OPT can dispatch as more UAVs as possible to events having the highest event link communication time among all given events, according to four constraints of Equation (10). In this ideal scenario without considering UAV handovers and dispatch exceptions, EAUD and EAMUD achieve the same event link communication time, which are a little lower than those of OPT.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Item** & **Value** \\ \hline Simulation time & 172,800 s \\ Event duration (\(T_{ce}\)) & 57,600 s \\ The number of total road segments (\(N_{rs}\)) & 245 \\ UAV flying speed (\(S_{u}\)) & 10 m/s \\ UAV communication range (\(d^{02 tu}\)) & 300 m \\ U2U carrier frequency (\(f_{1}\)) & 1 GHz \\ U2V carrier frequency (\(f_{2}\)) & 5.9 GHz \\ The unit energy consumed on flying (\(E_{u}^{Fly}\)) & 115/s \\ Charge current (\(I_{chur}\)) & 3 A \\ Charge current voltage (\(V_{chur}\)) & 4.2 V \\ SNR threshold (\(SNR_{\text{HU2U}}\)) & 2 dB \\ Noise powers of U2V and U2U (\(N_{\text{LI2V}}\), \(N_{\text{LI2V}}\)) & \(-80\) dBm \\ Required transmission powers of U2V and U2U (\(P_{t\text{LI2V}}\), \(P_{t\text{LI2V}}\)) & 27 dBm \\ UAV dispatch energy threshold (\(E^{DTH}\)) & 50, 62.5, 75, 87.5 (default), 100\% \\ Number of UAVs & 20, 40, 80 (default), 160, 240, 320, 400 \\ Event percentage (\(EP\)) & 20, 30 (default), 40, 50, 60 \% \\ UAV battery capacity (\(E^{Max}\)) & 251,748 ] \\ \hline \hline \end{tabular}
\end{table}
Table 3: Simulation parameters.  
Figure 9: The average ratio of the event link communication time vs the number of UAVs in the ideal scenario.  
Figure 10 exhibits the relation between the average ratio of the event link communication time and the event percentage. As the event percentage grows, all events and their corresponding sub-events in the event queue of GCS increase accordingly. Hence, the probability for dispatching a UAV to serve a sub-event is getting lower under a fixed number of UAVs, which in turn degrades the average ratio of the event link communication time of each scheme. Among these three schemes, OPT can choose a better event to dispatch UAVs when the event percentage, i.e., the number of events and sub-events, raises, such that it can achieve the highest ratio of the event link communication time. In summary, EAUD and EAMUD approximate performance behaviors and results of OPT with respect to the number of UAVs and the event percentage in the ideal scenario.