## 5 Discussion  
Based on the results of the synthetic dataset, it is observed that the proposed FPD approach is superior to FCFS-EDF, SJF-EDF, and Random-EDF with respect to almost all performance measures. For the number of VMs, DoI, and cost, it showed inferior results relative to those of the compared approaches. However, when it is considered that the proposed approach was able to succeed under the main constraints of the problem, viz., high-priority SLA and makespan, the inferior results in non-primary performance measures may be overlooked. Furthermore, it is observed that the rise in cost of the proposed approach is an order of magnitude lower than the increase in the number of VMs utilized compared to the other approaches. Considering the results for the metric of time spent under SLA violation, if it is used to compute a financial penalty, then the differences in the cost of proposed approach compared to the other approaches will be reduced even further, if not entirely inverted. For the GoCJ dataset, the proposed approach was found to still meet one of the primary constraints of completing high-priority SLA tasks at any cost. The proposed approach provided worse results for some measures, especially those that concern low-priority tasks. However for the requirements of this study, the primary focus is on high-priority tasks. The makespan, although more than that for the compared approaches, was offset by the lower cost achieved compared to the other techniques. The proposed approach also demonstrated the ability to reduce the number of VMs compared to the other approaches and was still able to meet its constraints. The number of VMs being reduced for the second dataset is explained by the long-tailed distribution of task lengths followed by the GoCJ dataset, which means that most of the tasks contained in it were small in length [38]. On the other hand, all task lengths were equally likely in the synthetic dataset. This means that the total task length in the GoCJ dataset was shorter than that for the synthetic dataset. The proposed approach was designed to determine the number of VMs after taking the task length of individual tasks and, by extension, the combined task lengths of all the tasks into account. This resulted in it using a lower number of VMs for the GoCJ dataset compared to the synthetic dataset. The compared heuristic approaches, on the other hand, were not capable of making informed decision about the number of VMs to use, hence they were restricted to using the same number of VMs for the two datasets. In order to justify that the superiority of the proposed FPD approach compared to FCFS-EDF, SJF-EDF, and Random-EDF, a weighted ranking system was used. For each performance measure, the best performing approach out of the four was given a score of 4, the next to best approach was given a score of 3, and so on, with the approach coming last getting a score of 1. The performance measures concerning high-priority tasks were multiplied by a weight of 2, while all other measures were multiplied by a weight of 1. For each approach, the average of its scores over the 12 performance measures was used to give it a final rank. The final scores of the approaches according to this method for both datasets are summarized in Table 4. In the table, it can be seen that the proposed approach obtains the highest score for both datasets and is, thus, superior to all the compared approaches. The ability of the presented two-phase fuzzy controller-based approach to determine the number of VMs to rent based on the properties of the input task set gives it an advantage compared to the usual task scheduling approaches in the literature that are not able to determine the number of VMs that will be needed. The scalability of public clouds means that this ability in a task scheduling approach is vital to making full use of public clouds.