# A Petri Net Model for Cognitive Radio Internet of Things Networks Exploiting GSM Bands +
## 5 Numerical Results
\begin{table}
\begin{tabular}{c c c c c} \hline \hline  & \multicolumn{4}{c}{\(\mathbf{QS}=\mathbf{5}\)} \\ \hline \(\mathbf{W_{1}}\)-\(\mathbf{N_{D}}\) & \(\mathbf{1}\) & \(\mathbf{2}\) & \(\mathbf{3}\) & \(\mathbf{4}\) \\ \hline \(\mathbf{0.30}\) & \(40,993\) & \(33,162\) & \(32,564\) & \(32,487\) \\ \(\mathbf{1.00}\) & \(40,070\) & \(33,105\) & \(31,801\) & \(32,389\) \\ \(\mathbf{3.00}\) & \(39,392\) & \(32,721\) & \(32,238\) & \(31,404\) \\ \hline \multicolumn{5}{c}{\(\mathbf{QS}=\mathbf{10}\)} \\ \hline \(\mathbf{W_{1}}\)-\(\mathbf{N_{D}}\) & \(\mathbf{1}\) & \(\mathbf{2}\) & \(\mathbf{3}\) & \(\mathbf{4}\) \\ \hline \(\mathbf{0.30}\) & \(21,716\) & \(15,204\) & \(14,968\) & \(14,977\) \\ \(\mathbf{1.00}\) & \(19,080\) & \(15,162\) & \(14,463\) & \(14,866\) \\ \(\mathbf{3.00}\) & \(18,150\) & \(15,030\) & \(14,877\) & \(14,418\) \\ \hline \multicolumn{5}{c}{\(\mathbf{QS}=\mathbf{15}\)} \\ \hline \(\mathbf{W_{1}}\)-\(\mathbf{N_{D}}\) & \(\mathbf{1}\) & \(\mathbf{2}\) & \(\mathbf{3}\) & \(\mathbf{4}\) \\ \hline \(\mathbf{0.30}\) & \(14,811\) & \(9773\) & \(9669\) & \(9680\) \\ \(\mathbf{1.00}\) & \(11,986\) & \(9754\) & \(9284\) & \(9597\) \\ \(\mathbf{3.00}\) & \(11,300\) & \(9696\) & \(9634\) & \(9308\) \\ \hline \multicolumn{5}{c}{\(\mathbf{QS}=\mathbf{20}\)} \\ \hline \(\mathbf{W_{1}}\)-\(\mathbf{N_{D}}\) & \(\mathbf{1}\) & \(\mathbf{2}\) & \(\mathbf{3}\) & \(\mathbf{4}\) \\ \hline \(\mathbf{0.30}\) & \(11,621\) & \(7198\) & \(7140\) & \(7150\) \\ \(\mathbf{1.00}\) & \(8715\) & \(7186\) & \(6833\) & \(7084\) \\ \(\mathbf{3.00}\) & \(8162\) & \(7155\) & \(7123\) & \(6871\) \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Mean delay (ms). \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & \multicolumn{4}{c}{\(\mathbf{QS}=\mathbf{15}\)} \\ \hline \(\mathbf{W_{1}}\)-\(\mathbf{N_{D}}\) & \(\mathbf{1}\) & \(\mathbf{2}\) & \(\mathbf{3}\) & \(\mathbf{4}\) \\ \hline \(\mathbf{0.30}\) & \(0.042\) & \(0.307\) & \(0.343\) & \(0.346\) \\ \(\mathbf{1.00}\) & \(0.113\) & \(0.314\) & \(0.314\) & \(0.346\) \\ \(\mathbf{3.00}\) & \(0.144\) & \(0.335\) & \(0.370\) & \(0.346\) \\ \hline \multicolumn{5}{c}{\(\mathbf{QS}=\mathbf{20}\)} \\ \hline \(\mathbf{W_{1}}\)-\(\mathbf{N_{D}}\) & \(\mathbf{1}\) & \(\mathbf{2}\) & \(\mathbf{3}\) & \(\mathbf{4}\) \\ \hline \(\mathbf{0.30}\) & \(0.029\) & \(0.307\) & \(0.343\) & \(0.346\) \\ \(\mathbf{1.00}\) & \(0.103\) & \(0.314\) & \(0.314\) & \(0.346\) \\ \(\mathbf{3.00}\) & \(0.137\) & \(0.335\) & \(0.370\) & \(0.346\) \\ \hline \hline \end{tabular}
\end{table} 
Table 5: _Cont._  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline  & \multicolumn{4}{c}{\(\mathbf{QS}=\mathbf{5}\)} \\ \hline \(\mathbf{W_{1}}\)-\(\mathbf{N_{D}}\) & \(\mathbf{1}\) & \(\mathbf{2}\) & \(\mathbf{3}\) & \(\mathbf{4}\) \\ \hline \(\mathbf{0.30}\) & \(40,993\) & \(33,162\) & \(32,564\) & \(32,487\) \\ \(\mathbf{1.00}\) & \(40,070\) & \(33,105\) & \(31,801\) & \(32,389\) \\  
We derived the results above, which are described only considering one specific set of parameters in terms of PU workload for both the circuit switching and packet switching and the transponder configuration; however, the model is very flexible, and its described analysis can be performed when assuming other working conditions. For these reasons, we think that the proposed model can be considered as a good candidate for tuning SU network parameters in specific GSM/EDGE cognitive radio environments in order to obtain desired QoS levels.