# Cost and Time Economical Planning Algorithm for Scientific Workflows in Cloud Computing
## 5 Results and Discussion
The sequential time is calculated by allocating all tasks to a single processor that reduces the implementation costs. If the total sum of the implementation costs is increased, it results in a larger speedup. Figure 6 shows the Speedup of the proposed algorithm compared with existing algorithms [27; 28]. Figure 4: Average schedule lengths ratio for the epigenome workflow. \[\text{Speedup}=\frac{\text{min}p_{j}\in P\big{\{}\sum_{i,eV}\text{CC}(i,j)\big{\}}}{ \text{Total No. of Tasks}} \tag{18}\]  
Efficiency: It is given by the ratio of speedup to the number of VMs used. \[\text{Efficiency}=\frac{\text{Speedup}}{\text{No.of processors used in each run}} \tag{19}\]  
Figure 7 shows the efficiency of the BDHEFT, PEFT, MOPT, ELSH, and POTC algorithms. It shows that the performance of PEFT is very similar to that of MOPT. Higher values of efficiency are obtained by the proposed algorithm. For every algorithm, the makespan decreases as the number of processors is increased. Successful Rate: the successful rate \((SR)\) is given as a ratio of the successful planning to the total number in the experiment. \[SR=\text{Succesful Planning}/\text{Number of total Experiments} \tag{20}\]  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Step** & **Ready List** & **Selected Task** & **EFT\_P\({}_{1}\)** & **EFT\_P\({}_{2}\)** & **EFT\_P\({}_{3}\)** & **Selected Processor** \\ \hline
1 & T1 & T1 & 24 & 23 & 38 & P2 \\ \hline
2 & T3,T6,T2,T5,T4 & T3 & 24 & 20 &  
The graph of \(SR\) as in Equation (16) is captured with around 50 runs of simulations. The BDHEFT, PEFT, MOPT, ELSH, and POTC algorithms are selected for comparison. The processors that are supported by Workflowsim have processors with varying configurations, and their time and cost parameters vary. The deadline ratio (\(K_{d}\)) and Budget ratio (\(K_{b}\)) values are considered as \(K_{d}\) {0.3, 0.5, 0.7 } and \(K_{b}\) {0.3, 0.5, 0.7 }. Some of the real-world applications, such as Epigenomics (I/O intensive workflow) and Montage (compute intensive workflow), are taken for analysis with 100 tasks, as shown in Figures 8 and 9. Montage has a high communication to computation ratio (\(CCR\)) [29; 30; 31], and epigenomics has a low communication to computation ratio (\(CCR\)). The success rate is always inversely  
Figure 6: Speedup comparison of the four algorithms. Figure 7: Efficiency comparisons of the four algorithms. proportional to \(CCR\). For Epigenomics, as shown in Figure 8, POTC has obtained a performance similar to those of MOPT and PEFT for the deadline (\(k_{d}\)) = 0.7. The obtained performance using POTC is better when compared to BDHEFT for large budgets (\(k_{b}\)). Figure 9 shows the success rate of the montage workflow. PEFT, MOPT, ELSH, and POTC show a lower performance for lower values of budget (\(k_{b}\)). The performance is similar to MOPT and ELSH for large values of the deadline (\(k_{d}\)). In order to compare the execution cost of various scientific workflows, we assume VMs of five different types with the processing speed of 1000-10,000 MIPS in a single data center. On the basis of the processing capacity, the task processing time was estimated. The cost varies between 2 and 10 units, and the time interval used in this tool is 1 h, which is similar to the Amazon cloud, which uses a pay-as-you go model. The metrics used to capture time and cost minimization are normalized schedule length (\(NSL\)) and normalized  
Figure 3.0 Success rate of the epigenomics workflow. Figure 3.1 Success rate of the montage workflow. schedule cost (\(NSC\)) [32; 33]. The \(NSL\) is defined by the ratio of the total execution time to the workflow execution time by executing them on the fastest resource. Figure 3.2  
where \(T_{f}\) is the time required to execute the workflow tasks on the fastest resource. \(NSC\) is defined by the ratio of the total cost to the workflow execution cost by executing them on the cheapest resource. Figure 3.3  
where \(T_{c}\) is the execution cost of the workflow while executing them on the cheapest resource.