## 4 Simulation Study
### Effect of the Camera Sensor Dimension  
In the present subsection, we have delved into the impact of the camera sensor size on surveillance camera system functioning. The dimensions of the sensors of surveillance cameras are conventionally \((L_{suc},L_{sh})\) = (3.2 mm, 2.4 mm), (4.8 mm, 3.6 mm), (5.76 mm, 4.29 mm), and (6.4 mm, 4.8 mm), horizontally and vertically. The average detection time performance \(T_{suc}\) for various sensor sizes is illustrated in Figure 7a. Our observation reveals that with an increase in the number of cameras, \(T_{suc}\) escalates roughly 72-fold from 0.22 s to 15.90 s for the smallest sensor size (\((L_{suc},L_{sh})\) = (3.2 mm, 2.4 mm)), but this was significantly lower in comparison to the increase from 8.15 s to 257.12 s for \((L_{suc},L_{sh})\) = (4.8 mm, 3.6 mm).  
In essence, it is important to note that an increase in the density of surveillance cameras and the number of cameras deployed does not necessarily guarantee an improvement in performance, especially if the size of the camera's sensor is small and the surveillance area is subsequently limited. This is due to the fact that the size of the sensor is directly proportional to the coverage area of each camera.  
On the contrary, when the size of the camera sensor is at its largest, with dimensions of \((L_{sw},L_{sh})\) = (6.4 mm, 4.8 mm), there is a significant improvement in the average detection time, increasing from 56.57 s to 553.58 s. In other words, with the highest density of surveillance cameras, \(N_{cam}\) = 500, a pedestrian can be detected 92% of the time.  
Hence, it can be inferred that the coverage provided by every surveillance camera, covering a wider area owing to the larger sensor size, yields a noteworthy enhancement in the detection time \(T_{suc}\). Consequently, this leads to more productive surveillance and an improved public safety service approach.  
However, as depicted in Figure 7b, it is evident that the performance in terms of surveillance resolution per millisecond can potentially fall with larger camera sensor dimensions. For instance, the sensor with the most diminutive dimensions, \((L_{suc},L_{sh})\) = (3.2 mm, 2.4 mm), exhibits the lowest \(T_{suc}\) performance. Nevertheless, the surveillance resolution per millisecond performance records an average of 242.65 kilopixels/ms.  
Conversely, the \(T_{suc}\) performance of the sensor with the highest values of \((L_{sw},L_{sh})\) = (6.4 mm, 4.8 mm) is superior. However, even when considering the highest surveillance resolution value per millisecond (i.e., 55.85 kilopixels/ms when \(N_{cam}\) was 500), it only attains a quarter of the performance of \((L_{sw},L_{sh})\) = (3.2 mm, 2.4 mm).  
In other words, if the surveillance resolution provided is inadequate for target identification or if a closer observation of the target is necessary, then configuring the system with a surveillance camera with a sensor size of \((L_{sw},L_{sh})\) (6.4 mm, 4.8 mm) may not suffice.  
In conclusion, when contemplating the trade-off between detection time and surveillance resolution per ms, and given that only one sensor needs to be mounted on the surveillance camera, it may be feasible to mount a sensor with \((L_{sw},L_{sh})\) = (4.8 mm, 3.6 mm), for which both performance metrics are moderate. However, suppose multiple sensors with different specifications can be installed on a single surveillance camera. In this case, it might be more effective to select the appropriate sensor in accordance with the requirements of detection time and surveillance resolution per ms.