## 5 Numerical Analysis
### Scenario C--Analysis of Percentage Load Balancing Variation  
This section presents the results considering a specific routing strategy based on distribution probabilities. Such a routing strategy is provided by the queue simulation JMT tool [39] and enables us to set a specific load balancing probability to specific targets. Therefore, the router was configured in three ways, as follows:  
1. Cloud (100%) Fog (0%) [Only cloud]
2. Cloud (0%) Fog (100%) [Only fog]
3. Cloud (50%) Fog (50%) [Hybrid]  
Figure 6 presents the results addressing the percentage load balancing variation. Figure 6a presents the results considering the MRT metric. The best result was to use only the cloud isolated. The results of the \"only cloud\" (black line) configuration ranged from 50 ms to 55 ms. The \"only fog\" (blue line) configuration obtained the second-best result. The only fog configuration had a mean of 60 ms. The hybrid configuration resulted in the worst MRT, with a mean of more than 70 ms. Observing the desired SLA latency (green line), the hybrid configuration would not attend such a requirement for AR \(\geq\) 0.3 j/ms. Figure 6b shows the gateway utilization. As the AR increases, the use of the gateway grows exponentially. The gateway has the same level of usage for all configurations. When the AR is equal to 0.1 j/ms, the gateway's use is approximately 16% for the three configurations. However, after the AR exceeds 0.8 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 configurations. Figure 6c shows the utilization to the fog and cloud. The utilization increases proportionally to the AR growth. The highest utilization was when using only the fog. The more limited fog resources explain this. The second highest utilization were two configurations: the only cloud (black line) and the hybrid configuration--fog utilization (green line). The hybrid configuration's cloud utilization obtained the lowest resource utilization (blue line). Therefore, if the system designer intends to have low utilization, they must consider the hybrid configuration. In addition, as far as the cloud is more potent than the fog, the cloud's utilization will be lower, taking into account similar parameters used in this work. Figure 6d,e presents the utilization of family member and emergency components. Again, both results are shown together due to their similarities. The family member's utilization is slightly higher than the emergency component due to the service time difference. The two previous configurations (A and B) significantly differed between the utilization levels. However, the only cloud configuration and the hybrid one had the same result here. The utilization of the \"only fog\" is lower because, in this case, the drop rate is higher (see Figure 6g), and fewer jobs pass by the output components. In any case, none of the three utilizations achieved the 100% level. Figure 6f presents the system number of jobs in the system. The number of jobs increases proportionally to the AR growth. The number of jobs in the \"only cloud\" configuration is lower than the hybrid one. This fact can be explained because the \"only cloud\"  
Figure 6: Results changing the arrival rate with distinct load balancing distributions. has obtained the lowest MRT result (see Figure 6a), meaning that fewer jobs remain inside the system. The \"only fog\" system number of jobs was lower than the hybrid one as well. However, this is caused by the high drop rate of the \"only fog\" configuration (Figure 6g). Therefore, the drop rate of the \"only fog\" is higher than the other two configurations, indicating that the fog resources are less efficient considering AR higher than \(0.3\,\mathrm{j}/\mathrm{ms}\). The drop rate of the only cloud and the hybrid are the same because even with only 50% of the cloud, the resources are enough to meet the demand. Finally, Figure 6h presents system power.