## 4 Results and Discussion
### Synthetic Workflows
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Node** & **Task Name** & **Task Type** & **Task Class** & **Rows** & **Columns** & **Categorical Columns** & **Dataset Size (MB)** \\ \hline \(t_{0}\) & K-Means & Estimator & Clustering & 3,918,745 & 34 & 4 & 446.55 \\ \(t_{1}\) & Decision Tree & Estimator & Classification & 4,000,000 & 27 & 0 & 257.49 \\ \(t_{2}\) & GMM & Estimator & Clustering & 2,458,285 & 28 & 0 & 145.01 \\ \(t_{3}\) & Decision Tree & Estimator & Classification & 3,000,000 & 53 & 0 & 379.09 \\ \(t_{4}\) & Decision Tree & Estimator & Classification & 4,000,000 & 129 & 0 & 1230.24 \\ \(t_{5}\) & Decision Tree & Estimator & Classification & 3,918,745 & 18 & 4 & 265.25 \\ \(t_{6}\) & Decision Tree & Estimator & Classification & 4,898,431 & 42 & 3 & 648.89 \\ \(t_{7}\) & Decision Tree & Estimator & Classification & 2,939,059 & 42 & 4 & 386.53 \\ \(t_{8}\) & K-Means & Estimator & Clustering & 2,458,285 & 56 & 0 & 278.75 \\ \(t_{9}\) & GMM & Estimator & Clustering & 3,000,000 & 53 & 0 & 379.09 \\ \(t_{10}\) & SVM & Estimator & Classification & 4,000,000 & 53 & 0 & 505.45 \\ \(t_{11}\) & K-Means & Estimator & Clustering & 2,939,059 & 42 & 4 & 386.53 \\ \(t_{12}\) & SVM & Estimator & Classification & 2,000,000 & 53 & 0 & 252.72 \\ \(t_{13}\) & K-Means & Estimator & Clustering & 1,639,424 & 9 & 2 & 93.70 \\ \(t_{14}\) & Naive Bayes & Estimator & Classification & 260,924 & 3 & 0 & 10.33 \\ \(t_{15}\) & K-Means & Estimator & Clustering & 2,000,000 & 78 & 0 & 371.93 \\ \(t_{16}\) & Decision Tree & Estimator & Classification & 3,918,745 & 26 & 4 & 379.11 \\ \(t_{17}\) & Decision Tree & Estimator & Classification & 3,918,745 & 34 & 4 & 446.55 \\ \(t_{18}\) & FPGrowth & Estimator & Association Rules & 823,593 & 180 & 180 & 697.00 \\ \(t_{19}\) & Decision Tree & Estimator & Classification & 2,939,059 & 26 & 4 & 284.33 \\ \(t_{20}\) & SVM & Estimator & Classification & 5,000,000 & 27 & 0 & 321.86 \\ \(t_{21}\) & FPGrowth & Estimator & Association Rules & 164,719 & 180 & 180 & 139.87 \\ \(t_{22}\) & GMM & Estimator & Clustering & 3,000,000 & 27 & 0 & 193.12 \\ \(t_{23}\) & K-Means & Estimator & Clustering & 4,898,431 & 26 & 4 & 473.88 \\ \(t_{24}\) & Decision Tree & Estimator & Classification & 2,000,000 & 104 & 0 & 495.90 \\ \(t_{25}\) & K-Means & Estimator & Clustering & 2,458,285 & 69 & 0 & 344.60 \\ \(t_{26}\) & FPGrowth & Estimator & Association Rules & 494,156 & 180 & 180 & 417.01 \\ \hline \hline \end{tabular}
\end{table} 
Table 10: Task and dataset descriptions (Workflow 2). Figure 7: Task dependencies (Workflow 2). Figure 8 shows the disk occupancy during the execution. As we can see, even the IIWM could not avoid data spilling, even though its disk usage was much lower considering the peak value and write duration compared to full-parallel. Finally, Table 12 shows the statistics about disk usage and execution times. Again, the IIWM achieved better results with a boost in performance of almost \(1.30\times\) (\(p_{imp}\)) with respect to a full-parallel strategy and a 23% reduction in time (\(m_{imp}\)) on average. An interesting aspect that emerged from the behavior of the IIWM scheduler, in the task-scheduling plan, was the similarity with priority-based scheduling in assigning tasks based on decreasing weights. In fact, tasks characterized by low memory occupancy may be assigned to tailing stages even if they are close to the root (e.g., in full-parallel, \(t_{1}\) is executed in the second stage, while in the IIWM, it is executed in the seventh one). Hence, in a dynamic scheduling scenario where tasks can be added at runtime, the IIWM may suffer from the starvation problem, as such tasks may experience an indefinite delay as far as new tasks with a higher memory weight are provided to the scheduler. Nevertheless, in the proposed work, we dealt with a static scheduling problem, where all tasks were known in advance and the task set was not modifiable at runtime.