## 5 Numerical Analysis
### Scenario A--Analysis of Cloud Resources Variation
Again, utilization grows according to the AR. However, unlike the previous utilization, here, the lines are not overlapping. Changing the number of resources in the cloud directly impacts cloud utilization. With more nodes, cloud utilization is lower. At the starting point (AR = 0.1), the cloud utilization has similar values for 10 and 15 nodes. However, when the AR reaches 1.0 j/ms, the result for 10 nodes approaches five nodes. If the demand is deficient, five nodes are enough to avoid overloading the system, but five and 10 nodes will not be enough if the demand is high. Only after 15 nodes will utilization remain at 62%. Another critical observation is regarding the curves of growth stagnation. For five nodes, stagnation occurs from AR = 0.3 j/ms. For 10 and 15 nodes, stagnation occurs from AR = 0.7 j/ms. Figure 4d,e show the use of the components Family Member and Emergency, respectively. The results were very similar, so the interpretation can be grouped. Again, the usage proportionally increases the AR. Unlike the use of the cloud, the greater the nodes number, the greater the utilization. When the number of resources in the cloud increases, more requests will pass. As the number of resources of such output components (Family Member and Emergency) does not change, such components are directly proportional to the number of nodes in the cloud. Initially, it is not possible to notice a difference in the utilization of the three scenarios. Only from AR = 0.2 j/ms does the utilization present different values. However, this distinction only becomes noticeable concerning 10 and 15 nodes when AR reaches 0.5 j/ms. When the AR reaches 1.0 j/ms, the utilization is approximately 37% (5 nodes), 71% (10 nodes), and 78% (15 nodes). Even with the AR equal to 1.0 j/ms, the user does not reach 100% due to the cloud's dependence. Figure 4f shows the jobs number in the system. The jobs number within the system increases as the AR increases, as jobs are queued for resource constraints. A slightly different result from the other two scenarios is considering five nodes. When the AR is lower, the system's number is higher for five nodes than the other scenarios. When the AR becomes higher (\(>\)0.6 j/ms), the number of jobs in the system is lower for five nodes than in the other scenarios. Therefore, when the capacity is shallow and the workload is very high, data drop occurs, which results in fewer jobs within the system. It is worth  
menting that even with a very high arrival rate (1.0 j/ms), there are not very high numbers of accumulation of jobs in the system, with an average of 32 jobs. Figure 4g shows the rate at which requests are discarded in the system. The increase in the discard rate is directly proportional to the arrival rate. The smaller the number of nodes, the higher the discard rate. Initially, with AR = 0.1 j/ms and AR = 0.2 j/ms, all scenarios have a rate of 0 discards. However, afterward, the result of the three scenarios is at odds. Only the scenarios with 10 and 15 nodes remained similar. In the worst case (five nodes), the maximum drop rate peak was 0.8 j/ms. This value may seem low but is equivalent to 2,880,000 jobs lost in just one hour. Figure 4h presents an analysis to find the system's ideal operational point, called system power. As previously mentioned, system power is obtained by dividing the throughput by the MRT. The system power increases proportionally to the increase in AR when the number of resources is higher (10 and 15 nodes). When the number of resources is lower, the power decreases slightly with AR increase. To understand this result, one must observe the MRT (Figure 4a). The MRT increases significantly as a function of RA. However, for 10 and 15 nodes, the MRT hardly changes. Therefore, as the system power is inversely proportional to the MRT, the system power decreases if the MRT increases. The increase in the system power to 10 and 15 nodes is conditioned to the throughput. Each of the three scenarios has its respective maximum system power points.