# Secure Partitioning of Cloud Applications, with Cost Look-Ahead
## 7 Experimental Assessment
### Experimental Results  
We started by taking the execution time of the probabilistic model creation as \(K\) varies. The execution times include the queries to the labelling predicate and for every labelling,the probability of being in a specific labelling (random variable \(Y_{i}\)) and the probability of reaching a labelling from the starting one (random variable \(Z_{se}^{k}\)) are computed. Figure 6 shows the average execution time in seconds on a logarithmic scale (\(y\)-axis) at varying values of \(K\) of each probabilistic model (\(x\)-axis). Increasing \(K\), the execution time grows exponentially, from 55 milliseconds of \(K\) equal to 1 to over 3 min of \(K\) greater than 11. As aforementioned, for \(K\) equal to 11, 12 and 13 the labellings are the same and the difference in execution time is reduced drastically for those values of \(K\). Concerning the total execution time, we collected the data from each experiment and grouped them by \(DLimit\). The execution times were obtained by timing the ProbSKnife script after the creation of the probabilistic model. Figure 7 shows the average execution time in seconds on a logarithmic scale (\(y\)-axis) at a range of values of \(K\) of each probabilistic model (\(x\)-axis). The three lines represent the experiments as \(DLimit\) varies from four to six. In this plot, the execution time grows exponentially as \(K\) varies until \(K\) is equal to 11, being on the order of a few seconds for \(K\) equal to one and reaching over 8 h (about 28,000 s) for \(K\) equal to 13. The three highest values of \(K\) have a negligible difference in time, on the order of a few seconds. Concerning the \(DLimit\) lines, the execution time for \(DLimit\) equal to four is always the lowest, for \(DLimit\) equal to five is always the intermediate one and for \(DLimit\) equal to six is always the greatest. Figure 6: Execution times for computing labelling probabilities at varying \(K\). Figure 7: Execution times for computing expected costs at varying \(K\) and DLimit. To analyse the partitioning costs we divided the collected data by \(DLimit\) to show the future cost as \(K\) varies. For each \(DLimit\) Figures 8-10 show the future cost in work hours (\(y\)-axis) at varying values of \(K\) of each probabilistic model (\(x\)-axis). The number of domains of each partitioning is annotated in the legend as \(nd\). In the future cost calculation, the results with \(K\) equal to \(11,12\) and \(13\) have the exact same values. As aforementioned, this happens due to the data with a probability of \(1\) of maintaining the same label. We generated three plots with the future cost of a partitioning having the same colour in all the figures; for instance, the minimal partitioning [[AppManager,authenticator,db],[ApiGateway], [aiLearning],[userConfig] is always represented with a blue line. The plot with \(DLimit\) equal to four (Figure 8) represents the future cost of only the minimal partitioning. We proved in Section 5 that the solution with the minimum number of domains is unique. The future cost of such a partitioning grows linearly with \(K\), starting from 6.8 with \(K\) equal to one and arriving at a future cost of \(16.1\) with \(K\) equal to \(11,12\) and \(13\). The plot with \(DLimit\) equal to five (Figure 9) represents the future cost of four different partitionings, the minimal one with four domains and the other with five domains. Two partitionings (the blue and the orange one) have a future cost that grows linearly until \(K\) is equal to seven, then it remains stable around \(15\) h. The blue lines stay under the orange one until that \(K\), and then they switch, with the blue one being the more costly for the highest values of \(K\).