## 4 Simulation Study
### Effect of the Number of Surveillance Cameras  
In this section, we evaluate how the number of surveillance cameras affects the performance of the surveillance system. Figure 5 shows the change in performance \(T_{suc}\), \(T_{fail}^{out}\), and \(T_{fail}^{dir}\) as the number of surveillance cameras is increased from 10 to 500, with the number of pedestrians fixed at 10.  
\(T_{suc}\) refers to the duration of the successful detection of pedestrians within the coverage area, and \(T_{suc}\) consistently increases from 6.6 to 259.0 s as the number of surveillance  
\begin{table}
\begin{tabular}{l l c} \hline \hline
**Category** & **Description** & **Value** \\ \hline \multirow{8}{*}{Surveillance camera} & number of surveillance cameras & 10–500 \\  & focal length (mm) & 2.8 \\  & sensor width (mm) & 4.8 \\  & sensor height (mm) & 3.6 \\  & image width in pixel (pixels) & 1920 \\  & image height in pixel (pixels) & 1080 \\  & viewing angle in horizontal domain (degree) & semi\(-\)random \\  & viewing angle in vertical domain (degree) & \(-\)45 \\  & installation height (m) & 5 \\  & maximum target height (m) & 3 \\ \hline \multirow{4}{*}{Pedestrian} & number of pedestrians & 100 \\  & width of pedestrians (m) & 0.9 \\  & height of pedestrians (m) & 1.7 \\  & moving speed of pedestrians (m/s) & 1.7 \\ \hline \multirow{4}{*}{Road} & road width (m) & 10 \\  & road interval (m) & 25 \\  & number of road interval & 5 \\ \hline Simulator & unit time (ms) & 100 \\  & simulation time (s) & 600 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Default configurations in simulation scenarios.  
cameras is increased from 10 to 500. This indicates a positive correlation between the number of cameras and the successful detection time.  
\(T_{fail}^{out}\) refers to the duration of time for which the pedestrians are outside of the effective detection area. As the number of cameras increases from 10 to 500, the \(T_{fail}^{out}\) values decrease from 593.4 to 340.1 s, indicating the improved performance of the surveillance system.  
From this observation of \(T_{suc}\) and \(T_{fail}^{out}\), it is clear that pedestrians can be detected more frequently as the number of surveillance cameras increases. However, even when the number of cameras is increased from 10 to 500, which is 50 times the initial number, pedestrians are still not detected for 340 s, which represents 56% of the total simulated time of 600 s. This suggests that merely equating the number of cameras to increase the surveillance coverage could be inefficient in terms of cost and performance improvement.  
The time for which pedestrians are within range but undetected due to incorrect camera directions is referred to as \(T_{fail}^{dir}\). In Figure 5, as the number of surveillance cameras increased from 10 to 250, the values of \(T_{fail}^{dir}\) increased from 41.8 to 377.1 s but ceased to increase when the number of cameras exceeded 260.  
It is important to note that \(T_{fail}^{dir}\) is a partial representation of \(T_{fail}^{out}\), signifying that some pedestrians who were initially undetected could be detected with a proper camera direction. For instance, if there were 100 surveillance cameras, \(T_{fail}^{out}\) and \(T_{fail}^{dir}\) would be 524.5 s and 288.3 s, respectively. By correctly controlling the camera direction, the time it takes to detect pedestrians could be reduced by 288.3 s, a performance improvement of roughly 55%. In a separate scenario with 500 surveillance cameras, \(T_{fail}^{out}\) and \(T_{fail}^{dir}\) are 340.9 and 332.9 s, respectively. This suggests that controlling the camera orientation could decrease the duration that pedestrians went undetected for by 97.7%.