## 4 Levelized Multiple Workflow Heterogeneous Earliest Finish Time
### The LMAEFT Algorithm
This Sig. value at a 5% threshold of significance is less than 0.05. Ho1 is therefore rejected. Rejection of the null hypothesis demonstrates how drastically the makespan of LMHEFT differs from HEFT-2, DLS, and HEFT-1. The mean plot shown in Figure 15 also supports the conclusion that LMHEFT performs noticeably better on the makespan. The samples of another experiment, where the batch size, the depth levels, and the number of VMs are varied for the makespan, utilization, and flowtime, as in Section 5, have been tested similarly. Ho1 is rejected for all samples examined for makespan and flowtime, but H11 is accepted. This demonstrates that LMHEFT greatly outperforms all other scenarios regarding the makespan and flowtime for this study. The majority of experiments rejected the Ho1 in the utilization condition. Even so, certain study samples still accept Ho1. With a few exceptions, LMHEFT performs almost better than the competitors in terms \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multicolumn{5}{c}{**Test of Homogeneity of Variance**} \\ \hline  & Levene Statistic & df1 & df2 & Sig. \\ \hline \multirow{3}{*}{Based on Mean Based on Median Based on Median and with adjusted df Based on trimmed mean} & 7.410 & 3 & 20 & 0.002 \\ \cline{2-5}  & 2.791 & 3 & 20 & 0.067 \\ \cline{2-5}  & 2.791 & 3 & 10 & 0.095 \\ \cline{2-5}  & 6.226 & 3 & 20 & 0.004 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Homogeneity test for models for makespan on a varying number of workflows. Figure 14: Normal Q-Q plot for makespan of DLS. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multicolumn{5}{c}{**Rank**} & \multicolumn{3}{c}{**Test Statistics**} \\ \hline Algorithm & N & Mean Rank & Kruskal–Wallis H & 14.113 \\ \hline LMHEFT & 6 & 6.17 & df & 3 \\ \hline HEFT-1 & 6 & 16.17 & Asymp. Sig. & 0.003 \\ \hline HEFT-2 & 6 & 8.33 & & \\ \hline DLS & 6 & 19.33 & & \\ \hline Total & 24 & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Kruskal–Wallis test for makespan on a varying number of workflows. of utilization. As a result, the findings of the hypothesis testing support the hypothesis made in Sections 5.1-5.3 of the simulation study. ## 6 Conclusions

This study proposes a Levelized Multiple Workflow Heterogeneous Earliest Finish Time Strategy (LMHEFT) for optimizing the makespan for multiple workflows. In addition, the LMHEFT is capable enough since it uses simple and flexible level attributes combined with upward rank to deal with precedence constraints. These constraints determine the order in which workflow tasks are executed; therefore, dealing with them makes the scheme more capable. This research addresses the crucial challenge of efficiently allocating heterogeneous resources to multiple workflows while considering task dependencies. An experimental study has been carried out by contrasting LMHEFT with other state-of-the-art workflow allocation strategies, such as HEFT and DLS, by varying the number of workflows, the degree of parallelism in the workflows (depth levels), and the number of available VMs (hardware parallelism), to evaluate the appropriateness of each strategy in the existing body of research. According to the results of the experimental investigation, LMHEFT has the best performance among all of its competitors, significantly performing better in all of the cases under investigation. The simulation results underscore the algorithm's versatility, adaptability to varying workloads, and potential to cater to real-world scenarios

Conceptualization, M.S. ([PERSON]); Methodology, M.S. ([PERSON]) and F.A. ; Formal analysis, M.S. ([PERSON]), M.A. and F.H. ; Investigation, F.B., M.S. ([PERSON]) and F.A. ; Resources, F.B. ; Data curation, M.S. ([PERSON]) and M.A. ; Writing--original draft, M.S. ([PERSON]), F.A., M.A., F.H. and M.S. ([PERSON]); Writing--review and editing, F.B., M.S. ([PERSON]), M.A., F.H. and M.S. ([PERSON]); Visualization, M.A. and M.S. ([PERSON]); Supervision, F.B., M.S. ([PERSON]) and F.A. ; Funding acquisition, F.B.