## 4 Results and Discussion
### Synthetic Workflows

Table 7: Performance evaluation of the prediction model. which presents a marginal increase equal to zero. This is the best choice compared to the other candidate stage (s\({}_{6}\)), whose execution time would be increased by 12,496.36 milliseconds by the assignment of \(t_{17}\), with a degradation of the overall makespan. At the end of the process, a consolidation step is exploited for optimizing throughput and execution time, by merging two stages with zero out-degree with some tailing stages, so as to avoid the sequential execution of the two stages in favor of a parallel one. Figure 5 shows disk occupancy throughout the execution. As a consequence of memory saturation, the execution of full-parallel resulted in a huge amount of disk writes, while IIWM achieved a null disk usage since no swapping occurred thanks to intelligent task scheduling. Thus, this translates into better use of in-memory computing. These results can be clearly seen also in Table 9, which shows the scheduling plan produced by the IIWM scheduler, together with some statistics about the execution times  
Figure 5: Disk usage over time for full-parallel and the IIWM. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Iteration** & **State** & **Stages** \\ \hline \multirow{2}{*}{It. 0} & \(\mathcal{T}^{0}_{free}=\{t_{0}\}\) & \multirow{2}{*}{\(s_{0}=\{t_{0}\}\)} \\  & Create \(s_{0}\) and assign \(t_{0}\) & \\  & Unlock \(\{t_{1},t_{2},t_{3}\}\) & \\ \hline \multirow{2}{*}{It. 1} & \(\mathcal{T}^{1}_{free}=\{t_{1},t_{3},t_{2}\}\) & \multirow{2}{*}{\(s_{0}=\{t_{0}\}\), \(s_{1}=\{t_{1}\}\)} \\  & Create \(s_{1}\) and assign \(t_{1}\) & \\  & Unlock \(\{t_{4}\}\) & \\ \hline \multirow{2}{*}{It. 2} & \(\mathcal{T}^{2}_{free}=\{t_{3},t_{4},t_{2}\}\) & \multirow{2}{*}{\(s_{0}=\{t_{0}\},s_{1}=\{t_{1}\}\),} \\  & Create \(s_{2}\) and assign \(t_{3}\) & \\  & Unlock \(\{t_{7},t_{8},t_{9},t_{10}\}\) & \\ \hline \multirow{2}{*}{It. 3} & \(\mathcal{T}^{3}_{free}=\{t_{7},t_{4},t_{10},t_{2},t_{8},t_{9}\}\) & \multirow{2}{*}{\(s_{0}=\{t_{0}\},s_{1}=\{t_{1}\}\),} \\  & Create \(s_{3}\) and assign \(t_{7}\) & \\ \hline \multirow{2}{*}{It. 4} & \(\mathcal{T}^{4}_{free}=\{t_{4},t_{10},t_{2},t_{8},t_{9}\}\) & \multirow{2}{*}{\(s_{0}=\{t_{0}\},s_{1}=\{t_{1}\}\),} \\  & \(\mathcal{S}_{sel}=\{s_{2},s_{3}\}\) & \multirow{2}{*}{\(s_{0}=\{t_{0}\},s_{1}=\{t_{1}\}\),} \\  & \(\mathcal{S}_{sel}=\{s_{2},s_{3}\}\) & \\  & \(\mathcal{S}_{sel}=\{t_{3},t_{4}\},s_{3}=\{t_{7}\}\) \\  & \(\mathcal{S}_{sel}=\{0,0\}\) & \\  & Assign \(t_{4}\) to \(s_{2}\) & \\ \hline \(\ldots\) & \(\ldots\) & \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Example of execution of Algorithm 1 at the iteration level. and the use of the disk. In particular, given the curves representing disk writes over time shown in Figure 5, on-disk usage graphically represents the sum, for each disk write, of the ratio between the area under the curve identified by a write and its duration. Compared to the full-parallel strategy, the IIWM achieved better execution times and an improvement in application performance, with a boost of almost \(1.45x\) (\(p_{imp}\)) and a \(31.15\%\) reduction in time (\(m_{imp}\)) on average. With different sizes of available memory, the full-parallel approach showed higher and higher execution times and disk writes as memory decreased, while the IIWM was able to adapt the execution to available resources, as shown in Figure 6, finding a good trade-off between the maximization of the parallelism and the minimization of the memory saturation probability. At the extremes, with unlimited available memory, or at least greater than that required to run the workflow, the IIWM performs as a full concurrent strategy, producing the same scheduling of full-parallel. The second synthetic workflow consisted of the 27 tasks described by Table 10 and their dependencies, shown in Figure 7. This scenario was characterized by highly heavy tasks and very low resources, where the execution of a single task can exceed the available memory.