## 4 Levelized Multiple Workflow Heterogeneous Earliest Finish Time
### The LMAEFT Algorithm
The performance order of the strategies on the makespan is LMHEFT, HEFT-1, HEFT-2, and DLS. LMHEFT performs best and DLS is worst on makespan. The average performance gain of LMHEFT over HEFT-2 and DLS is 15.51% and 85.12%, respectively. For small batches, the LMHEFT performs comparably to HEFT-2 (N = 4). However, as soon as the batch size increases, LMHEFT consistently outperforms all other algorithms on makespan for all the batches of workflows (N = 8 to N = 128). This performance gain is achieved by employing the level attribute with an upward rank for allocation, resulting in the

Figure 8: Varying the number of workflows. simultaneous execution of all parallel executable tasks across the workflows. As shown in Figure 8b, system utilization is growing as the number of workflows is increased on a fixed number of tasks and VMs for all the strategies. The performance order on flowtime is the same as in the case of makespan, i.e., LMHEFT, HEFT-2, HEFT-1, and DLS. The average gain of LMHEFT on flowtime over HEFT-2 and DLS is 11.45% and 91.35%, respectively. Again, DLS performs worst. In Figure 8c, the performance order is LMHEFT, DLS, HEFT-2, and HEFT-1. The average improvement in utilization for this case is reported at 3.57% and 40% over DLS and HEFT-1, respectively. HEFT-1 performs worst. Additionally, as the number of workflows increases, the performances of LMHEFT and DLS are recorded as comparable. ### Varying Depth Levels

In this instance, the performance of LMHEFT is evaluated by varying the depth level in the cloud system. Figure 9a-c shows the results for makespan, flowtime and utilization on varying depth levels. Here, the following input parameters are taken: \(\mathrm{RT^{1}_{k}}\) = 0-1000, \(\mathrm{PC_{k}}\) = 1-1000, \(\mathrm{T_{ij}}\) = 128, \(\mathrm{K}\) = 32, \(\mathrm{TC_{ipq}}\) = 1-3000, \(\mathrm{D_{kr}}\) = 1-100, \(\mathrm{L}\) = 8-64, and \(\mathrm{N}\) = 256. On varying the number of depth levels, the performance order is LMHEFT, HEFT-2, HEFT-1, and DLS, as shown in Figure 9a. In this case, the behavior of the strategies on the makespan is the same as the behavior of the makespan in Section 5.2. LMHEFT is again the best, with the DLS performance being the worst. The improvement in makespan for this case is reported at 41.19% and 86.73% over HEFT-2 and DLS. As we can see in Figure 9b, the performance order on flowtime is the same as for makespan. The average performance gain on flowtime for this case is reported at 37.39% and 60.77% over HEFT2 and DLS, respectively. On the other hand, for utilization, the performance order is DLS, LMHEFT, HEFT-2, and HEFT-1, as presented in Figure 9c. LMHEFT is lagging behind DLS with 11%. However, LMHEFT is still better than HEFT-2 and HEFT-1, with an average gain of 3.44% and 33.52%, respectively. Figure 9: Varying the number of depth levels. ### Varying Virtual Machines

This section estimates each strategy under consideration by varying the number of VMs. Figure 10a-c shows the results for makespan, flowtime, and utilization, respectively, on varying number of virtual machines. The remaining parameters are as follows: RT1k = 0-1000, PCk = 1-1000, Tij = 512, K = 8-128, TCipq = 1-100, Dkr = 1-100, L = 16, and N = 64. As we see in Figure 10a, every strategy has a declining trend when the VMs are increased. Additionally, the performance order of the considered strategies on the varying number of virtual machines is LMHEFT, HEFT-2, HEFT-1, and DLS. HEFT-2 is the runner-up, lagging behind LMHEFT, and DLS performs worst. The improvement in makespan for this case is reported over HEFT-2 and DLS at 13.74% and 80.24%, respectively. As suggested by Figure 10b, the performance order is also the same as in earlier cases. For this case, the performance gain on flowtime over HEFT-2 and DLS is reported at 31.30% and 77.10%, respectively. Utilization also shows a decreasing trend when varying the number of VMs as shown in Figure 10c. Utilization performance is in the following order: HEFT-2, LMHEFT, HEFT-1, and DLS. DLS performs poorly, and HEFT-2 is the best.