## 4 Example and Comparison Results
### The Task Dispatching Phase  
Basically, there are three cases that need to be discussed in different heterogeneous environments, and the cases are illustrated and discussed as follows, step by step. **Case 1. **\(MSV_{i}\) > \(ECT_{ij}\) of \(S_{j}\) and \(ECT_{i}\) > \(AECT_{j}\) of \(S_{j}\)  
Compare the \(MSV\) value found in the \(MSV_{i}\) calculation phase with the earliest expected completion time of other tasks. Task \(i\) can be dispatched to the appropriate server node \(j\) while \(MSV_{i}\) > \(ECT_{ij}\) of \(S_{j}\) and \(ECT_{i}\) > \(AECT_{j}\) of \(S\). Therefore, task \(d\) is dispatched to Node D while \(MSV_{i}\) > \(ECT_{ID}\) and \(ECT_{ID}\) > \(AECT_{j}\) in Tables 7 and 8. **Case 2. **\(MSV_{i}\) < \(ECT_{ij}\) of \(S_{j}\)  
Compare the \(MSV\) value found in the \(MSV_{i}\)_calculation phase_ with the earliest expected completion time of other tasks. Task \(i\) with maximum \(ECT\) can be dispatched to appropriate server node \(j\) when \(MSV_{i}\) < \(ECT_{ij}\) of server node \(j\). Therefore, task \(l\) is assigned to Node A in Table 9 because its \(ECT_{IA}\) is greater than the \(MSV\) value (43336 > 21486). \begin{table}
\begin{tabular}{c c|c|c c} \hline  & **Node C** & **Node D** & \(SV\) & \(MSV\) \\ \hline Task \(a\) & 52978 & 25328 & 27650 & - \\ Task \(b\) & 47351 & 20187 & 27164 & - \\ Task \(d\) & 54429 & 26330 & 28099 & 54429 \\ Task \(e\) & 47319 & 20348 & 26971 & - \\ Task \(f\) & 43566 & 15918 & 26971 & - \\ Task \(h\) & 44310 & 17678 & 26995 & - \\ Task \(l\) & 43986 & 16558 & 27428 & - \\ Average & - & 19562 & - & - \\ \hline \end{tabular}
\end{table} 
Table 7: Comparison of the MSV values of tasks. \begin{table}
\begin{tabular}{c c c c c} \hline  & **Node C** & **Node D** & \(SV\) & \(MSV\) \\ \hline Task \(a\) & 52978 & 25328 & 27650 & - \\ Task \(b\) & 47351 & 20187 & 27164 & - \\ Task \(d\) & 54429 & 26330 & 28099 & 54429 \\ Task \(e\) & 47319 & 20318 & 26971 & - \\ Task \(f\) & 43566 & 15918 & 27648 & - \\ Task \(g\) & 51026 & 24491 & 26995 & - \\ Task \(h\) & 44310 & 1778 & 26632 & - \\ Task \(l\) & 43986 & 16558 & 27428 & - \\ Average & - & 19562 & - & - \\ \hline \end{tabular}
\end{table} 
Table 8: Comparison of the average \(ECT\) values of tasks in Node D under Case 1. **Case 3. **\(\mathit{MSV}_{i}>\mathit{ECT}_{\mathit{ij}}\) of \(S_{j}\) and \(\mathit{EECT}_{i}<\mathit{AECT}_{j}\) of \(S_{j}\)  
Compare the MSV value found in the \(\mathit{MSV}_{i}\)_calculation phase_ with the earliest expected completion time of other tasks. Task \(i\) in Table 10 will be dispatched to server node \(j\) where the \(\mathit{ECT}_{i}\) is approximate to \(\mathit{AECT}_{j}\) and the \(\mathit{ECT}_{i}\) is larger than \(\mathit{AECT}_{j}\) under the conditions that \(\mathit{MSV}_{i}>\mathit{ECT}_{\mathit{ij}}\) and \(\mathit{EECT}_{i}<\mathit{AECT}_{j}\) of \(S_{j}\). Therefore, task \(j\) is assigned to Node B in Table 11 because \(\mathit{ECT}_{\mathit{jB}}\) is bigger than and closer to \(\mathit{AECT}_{B}\). Subsequently, the above examples can be simulated in our experiment. At first, the number of tasks is set to 50 to 100 and the computing ability of the 5 cloud server nodes is set to [500-1000] units to adapt to the high-heterogeneity environment. Besides this, the comparisons of MakeSpan and load balancing among the Suffrage, MaxSuffrage, and ACSS algorithms are simulated 50 times and the \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **Node A** & **Node B** & \(\mathit{SV}\) & \(\mathit{MSV}\) \\ \hline Task \(b\) & 60023 & 49827 & 10196 & - \\ Task \(e\) & 60374 & 49966 & 10408 & - \\ Task \(f\) & 55406 & 45186 & 10220 & - \\ Task \(h\) & 57267 & 46499 & 10768 & - \\ Task \(i\) & 51372 & 40433 & 10939 & 51372 \\ Task \(j\) & 56974 & 46493 & 10481 & - \\ Average & - & 46400 & - & - \\ \hline \hline \end{tabular}
\end{table} 
Table 10: Comparison of the average \(\mathit{ECT}\) values of tasks in Node D under Case 3.