## Appendix B Full List of the Input Parameters of VirtFogSim  
The following Table A2 reports the full list of the (settable) input parameters of the current Version 4.0 of the simulator, together with their meaning/role, measuring units, and default values used for the simulation of Section 6. \begin{table}
\begin{tabular}{c l l l} \hline \hline \multicolumn{1}{c}{**Parameter**} & \multicolumn{1}{c}{**Meaning/Role**} & \multicolumn{1}{c}{**Measuring Units**} & \multicolumn{1}{c}{**Simulated Settings**} \\ \hline \(V\) & Number of tasks of the application & & Dimensionless & \(9\leq V\leq 45\) \\  & DAG & & & \\ \(\xi\) & \(V\)-tuple row vector of the task & & & \\  & workloads & & (bit) & \begin{tabular}{l} Computing- and communi- \\ cation-intensive DAG \\ \end{tabular} \\ \(A\) & \(\begin{array}{l}(V\times V)\text{ binary (i.e., }\{0,1\})\text{ DAG}\\ adjacency matrix \\ \end{array}\) & Dimensionless & & \\ \(Da\) & \(\begin{array}{l}(V\times V)\text{ weight matrix of the}\\ \text{(directed) edges of the DAG}\\ \end{array}\) & & & \\ \(n_{M}\) & Number of the (virtual) computing & & & \\  & cores equipping the Mobile device & Dimensionless & \(n_{M}=1\) \\ \hline \(n_{F}\) & Number of the (virtual) computing & & & \\  & cores equipping the device clone at & & Dimensionless & \(n_{F}=4\) \\  & the Fog node & & & \\  & & Number of (virtual) computing cores & & \\ \(n_{C}\) & equipping the device clone at the & & Dimensionless & \(n_{C}=12\) \\  & Cloud node & & & \\ \hline \(NF_{WiFi}\) & \
\begin{tabular}{l} Average per-connection number of \\ failures of the one-way Mobile\(\rightarrow\)Fog \\ and Fog\(\rightarrow\)Mobile WiFi TCP/IP \\ connections \\ \end{tabular} & Dimensionless & \(NF_{WiFi}=1.1\) \\  & Average per-connection number of & & \\ \(NF_{CELL}\) &
\begin{tabular}{l} failures of the cellular one-way \\ Mobile\(\rightarrow\)Cloud and Cloud\(\rightarrow\)Mobile \\ TCP/IP connections \\ \end{tabular} & Dimensionless & \(NF_{CELL}=0.1\) \\ \hline \hline \end{tabular}
\end{table} 
Table A2: Input parameters of the _VirtFogSim_ simulator and their simulated settings of Section 6. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameter** & **Meaning/Role** & **Measuring Units** & **Simulated Settings** \\ \hline \hline \multirow{4}{*}{\(NF_{WD}\)} & Average per-connection number of failures of the two-way Cloud\(\leftrightarrow\)Fog & Dimensionless & \(NF_{WD}=0.01\) \\  & TCP/IP backhaul connection & & \\ \hline \multirow{4}{*}{\(f_{M}^{MAX}\)} & Per-core maximum computing frequency at the Mobile device & (bit/s) & \(f_{M}^{MAX}=12\times 10^{6}\) \\  & Per-core maximum computing frequency at the Fog clone & (bit/s) & \(f_{F}^{MAX}=12\times 10^{6}\) \\ \hline \multirow{4}{*}{\(f_{C}^{MAX}\)} & Per-core maximum computing frequency at the Cloud clone & (bit/s) & \(f_{F}^{MAX}=12\times 10^{6}\) \\  & Maximum bit rate of the WiFi-based & & \\ \cline{1-1} \multirow{4}{*}{\(R_{U}^{MAX}\)} & Maximum bit rate of the WiFi-based & & \\  & one-way Mobile\(\rightarrow\)Fog TCP/IP & (bit/s) & \(R_{U}^{MAX}=8.0\times 10^{6}\) \\  & connection & & \\ \cline{1-1} \multirow{4}{*}{\(R_{D}^{MAX}\)} & Maximum bit rate of the WiFi-based & & \\  & one-way Fog\(\rightarrow\)Mobile TCP/IP & (bit/s) & \(R_{D}^{MAX}=9.0\times 10^{6}\) \\  & connection & & \\ \cline{1-1} \multirow{4}{*}{\(B_{U}^{MAX}\)} & Maximum bit rate of the cellular connection & & \\ \cline{1-1} \multirow{4}{*}{\(B_{D}^{MAX}\)} & Maximum bit rate of the cellular & & \\  & one-way Cloud\(\rightarrow\)Mobile TCP/IP & (bit/s) & \(B_{D}^{MAX}=7.0\times 10^{6}\) \\  & connection & & \\ \cline{1-1} \cline{3-4}  & Scalar non-negative real parameter. It & & \\ \cline{1-1} \multirow{4}{*}{\(TH_{0}^{MIN}\)} & is the minimum required application throughput & (DAG/s) & \(0.333\leq TH_{0}^{MIN}\leq 3.33\) \\ \hline \multirow{4}{*}{\(\theta_{M}\)} & Binary \(\{0,1\}\)-parameter.