# Cost and Time Economical Planning Algorithm for Scientific Workflows in Cloud Computing
## 5 Results and Discussion  
The results obtained by the POTC algorithm--along with the ELSH, MOPT, PEFT, and BDHEFT and their performance--are presented in this section. For the purpose of the experiment, two sets of workflow applications called 'Epigenomics' and 'Montage' were taken, and they represented the workflow real-world problems of genomics and astronomical Image Mosaic Engine. Firstly, the comparison metrics termed scheduling length ratio (SLR), for the proposed and existing algorithms were described. Schedule Length Ratio (SLR):  
This is one of the main measures of makespan (schedule length) of its output schedule. Schedule length ratio:  
\[\frac{\text{Makespan}}{\sum_{n\in RP_{MIN}}\min_{p_{j}\in T}\ \{CC(i,j)\}} \tag{17}\]  
where _Makespan_[21] is the total implementation time, and \(RP_{MIN}\) signifies the minimum of the critical path. The denominator is the totality of all implementation costs of the tasks on the minimum critical path. Since the denominator is the lower bound, the schedule length ratio cannot be smaller than one. The performance of all three algorithms has been evaluated with some of the scientific workflows, namely Montage and Epigenomics. The total count of the tasks in each workflow is taken as Epigenomics: 30, 50, 100, 1000, and Montage: 30, 50, 100, and 1000. The simulation environment consists of a heterogeneous \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Task** & \(Rank_{POCM}\) & \(Rank_{oct}\) & \(Rank_{uc}\) \\ \hline T1 & 263.2 & 84.3 & 183.8 \\ \hline T2 & 161.7 & 53.3 & 120.9 \\ \hline T3 & 168.6 & 44 & 112.6 \\ \hline T4 & 143.6 & 62.3 & 116.6 \\ \hline T5 & 150.9 & 31 & 139.59 \\ \hline T6 & 165.3 & 54.6 & 125.9 \\ \hline T7 & 78.3 & 23.3 & 58.6 \\ \hline T8 & 106.9 & 31.3 & 94.6 \\ \hline T9 & 69.6 & 14.33 & 48.2 \\ \hline T10 & 22.6 & 0 & 22.6 \\ \hline \hline \end{tabular} Note: The Rank for \(Rank_{POCM}\) is calculated based on the formula mentioned in Equations (11) and (12). \(Rank_{oct}\) is calculated from [12], and \(Rank_{uc}\) is calculated from [21].  
\end{table} 
Table 1: The rank obtained through the POCM, OCT, and upward rank for Figure 3.  
system with 20 virtual machines. The target system is generated based on 'Workflowsim', which is a Java framework. Epigenomics: The average SLR results for Epigenomics are shown in Figure 4. The performance of the proposed algorithm using Epigenomics is shown in Figure 4. The average SLR shows 3.2% for 30 tasks, 3.29% for 50 tasks, 3.68% for 100 tasks, and 14.7% for 1000 tasks for the POTC algorithm. Thus, POTC for 50 tasks has improved by 6.4% over ELSH, and for 1000 tasks it has increased by 3.5%. In addition, POTC for 1000 tasks has improved by 6.9% over MOPT. Montage: Figure 5 shows the average SLR of the real-world scientific workflow application Montage. Again, the POTC algorithm has shown a better performance when compared to the ELSH, MOPT, PEFT, and BDHEFT algorithms. Thus, for 30 tasks, POTC has improved its performance by 9.4% over MOPT, for 50 tasks POTC has improved its performance by 6.1% over MOPT, for 100 tasks POTC has improved its performance by 1.9% over MOPT, and for 1000 tasks POTC has improved its performance by 3.5% over MOPT, and thus POTC gives better performance over ELSH. Moreover, for 100 tasks, POTC has improved its performance by 30.4% over BDHEFT, and for 1000 tasks POTC has improved its performance by 11.3% over BDHEFT. Thus POTC, has a better performance than BDHEFT. Depending on these outcomes, with the results for DAG with a small and large task number, the POTC algorithm surpassed ELSH, MOPT, PEFT, and BDHEFT for both the Epigenomics and Montage workflow. For a huge graph, the POTC algorithm has a better performance. Table 2 shows how the processor is selected based on the rank and cost of various processors. Speedup: The speedup for any given graph is obtained by the division of the cumulative implementation time of the tasks in the graph by the length of the schedule. In other words, it is the sequential implementation time to the parallel implementation time.