## 5 Numerical Analysis
### Scenario A--Analysis of Cloud Resources Variation  
The results of detecting cloud resource capabilities fluctuation are shown in Figure 4. It's important to note that the fog in this instance was localized. The MRT reflects the system's responsiveness. The MRT tends to be smaller as resources increase; however, this trend is not always visible. The findings for MRT are shown in Figure 4a. Smaller MRTs were obtained in situations with fewer resources. However, the findings for 10 and 15 nodes were extremely comparable. The MRT becomes substantially greater owing to \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Type** & **Element** & **Value** & **Queue Size** & **\# of Nodes** \\ \hline \multirow{6}{*}{Processing} & Sensors & 0.1–1.0 [10 points]j/ms & X & X \\  & Gateway & 8.3 (ms) & 8 & 5 \\  & Cloud & 20.3 (ms) & 16 & 5, 10, 15 \\  & Fog & 40 (ms) & 16 & 5, 10, 15 \\  & Family Members & 15.5 (ms) & 8 & 5 \\  & Emergency & 12.5 (ms) & 8 & 5 \\ \hline \multirow{3}{*}{Transmission} & T01 & 4.5 (ms) & X & X \\  & T02 & 2.5 (ms) & X & X \\  & T03 & 4.5 (ms) & X & X \\  & T04 & 4.5 (ms) & X & X \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Model configuration parameters for numerical analysis. Figure 3: Overview of the four evaluated scenarios. Color green indicates that the request will be transmitted to that target whereas color red means the opposite. AR only when resources are reduced to five nodes. The proximity of MRT to 10 and 15 shows that using just 10 compute nodes may be more beneficial and cost-effective. AR has a greater influence on fewer resources (five nodes). The MRT exhibits a minimal significant rise as the workload grows for 10 and 15 nodes. This suggests that between 10 and 15 nodes are sufficient to fulfill the moderately high demand of up to 1.0 j/ms with an MRT of 50 to 60 ms. The slowdown of MRT growth owing to AR is a tendency that can be seen in all three situations. From AR = 0.5 j/ms, the MRT growth tends to plateau. This AR = [0.5 j/ms-1.0 j/ms] range can be utilized to  
Figure 4: Analysis results varying the arrival rate of new requests. provide infrastructure customers with an MRT that is not reliant on AR. With 15 nodes, the average would be around 55 milliseconds. For 15, 10, and 5 nodes, the MRT is 56 ms, 61 ms, and 95 ms, respectively, at the extreme point of most substantial demand (AR = 1.0 j/ms). According to one concept, a user will typically accept an MRT of 70 ms [43]. If a Service Level Agreement (SLA) with MRT is restricted to 70 ms (see the green line in the picture), it is clear that five nodes with AR more than 0.3 j/ms would not be able to meet this time constraint. Figure 4b shows the use of a gateway in the considered three scenarios. As the AR increases, the use of the gateway grows exponentially. The gateway has the same level of usage for all the cloud configurations. When the AR is equal to 0.1 j/ms, the gateway's usage is approximately 16% for the three scenarios. However, after the AR exceeds 0.6 j/ms, the gateway starts to use approximately 90% of its capacity. When the AR reaches 1.0 j/ms, the gateway uses approximately 97% of its capacity for all cloud configurations. The gateway utilization growth tends to stagnate from AR = 0.6 j/ms until reaching its maximum utilization of approximately 97%. Considering the extreme point of most significant demand (AR = 1.0 j/ms), the gateway utilization did not reach 100%. However, it becomes impossible to meet more requests at this stage of processing without data loss. Figure 4g shows the rate at which requests are dropped in the system. The increase in the drop rate is proportional to the arrival rate. The smaller the number of nodes, the higher the drop rate. Both scenarios start running with the drop rate at 0, but in AR = 0.8 j/ms, scenario A starts to perform the drop, ascending to 0.9955 at AR = 2.0 j/ms. In scenario B, the discard will only start when the system reaches AR = 1.4 j/ms and proceeds upwards to 0.7936. Figure 4c presents the cloud utilization level.