## 4 Levelized Multiple Workflow Heterogeneous Earliest Finish Time
### The LMAEFT Algorithm
In this work, we have followed two approaches to allocate multiple workflows as suggested by [19], namely, the sequential approach (workflows allocated one after another) and the merging-based approach (all workflows are merged by using one pseudo entry and exit task). For performance evaluation, the LIMEFT model is compared with two other workflow allocation algorithms that have been demonstrated to be competitive in the workflow allocation domain. The baseline algorithms are as follows. DLS [18]: The DLS algorithm is a dynamic, list-based scheduling approach used for allocating tasks to processors in parallel and distributed computing environments. Its goal is to achieve efficient load balancing and minimize the overall execution time by dynamically assigning tasks to processors based on their current state and workload. Tasks in parallel and distributed systems are dynamically scheduled by DLS, which continuously optimizes task allocation for effective load balancing and shorter execution times. Tasks are prioritized according to their computational cost and dependencies. HEFT [9]: It is a list-based heuristic algorithm to schedule single workflow tasks for execution in heterogeneous computational machines. The algorithm chooses the task with the highest upward rank value at each stage and assigns it to the machine that minimizes its earliest completion time. In the experiment results, HEFT is modified to allocate multiple \begin{table}
\begin{tabular}{c c c} \hline \hline \multicolumn{1}{c}{**S. No.**} & **Parameter** & **Range** \\ \hline
1. & Processing capacity of VMs (\(\mathrm{PC_{k}}\)) & 1–1000 \\ \hline
2. & Number of VMs (K) & 4–128 \\ \hline
3. & Number of Workflows (N) & 4–128 \\ \hline
4. & Average Number of Tasks in the Workflow & 4–256 \\ \hline
5. & Task Size (Size(\(\mathrm{T_{ij}}\))) & Not Given \\ \hline
6. & Depth level (L) & 4–64 \\ \hline
7. & Initial Ready Time (\(\mathrm{RT^{1}}_{\mathrm{k}}\)) & 0–1000 \\ \hline
8. & Task communication (\(\mathrm{TC_{ipq}}\)) & 1–1000 \\ \hline
9. & Inter Machine Distance (\(\mathrm{MD_{kr}}\)) & 1–100 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Simulation parameters. workflows using sequential-based and merge-based approaches [19]. In this way, two variants of the batch mode HEFT algorithm, namely, HEFT1 and HEFT2, are designed for proper comparison. HEFT1 is a sequential-based algorithm in which a set of workflows is sequentially executed one after another, while HEFT2 is a merge-based algorithm in which a set of workflows is converted into a single workflow and then it is executed as per the standard HEFT. The experiments are performed by using the ETC simulation benchmark model. The results have been presented by a varying number of workflows in the batch, depth level, and number of VMs participating in heterogeneous cloud systems, followed by detailed observations. Four objective parameters, i.e., makespan (MS), utilization (U\({}_{\text{s}}\)), and flowtime (FT), are considered for performance evaluation. The experiments are repeated 50 times, and the mean values of the parameters are reported in this study. The performance order is determined by taking the average value of the respective parameter in various experiments conducted for the case. ### Varying the Number of Workflows

In this section, all methods that have been taken into consideration are assessed by varying the independent workflow while keeping the batch's number of tasks fixed and the system's other input parameters fixed. The simulation was run for an average of 100 datasets, and the outcomes are shown in Figure 8. Figure 8a-c shows the results for makespan, flowtime and utilization, respectively, on varying number of workflows. The other input parameters are given below for the experiments as follows:

RT1k = 0-1000, PCk = 1-1000, Tij = 256, K = 16, TCipq = 1-1000, Dkr = 1-100, L = 16 and N = 4-128, IHH. As expected, the trend of the makespan (MS) is increasing as the number of workflows is increased (N = 8 to N = 128) for all the considered models as shown in Figure 8a.