# A Petri Net Model for Cognitive Radio Internet of Things Networks Exploiting GSM Bands +
## 6 Conclusions  
In this paper, we proposed a new model based on non-Markovian stochastic Petri nets to evaluate QoS performance metrics in a cognitive radio environment operating in the band of a GSM/EDGE transponder. The proposed model is able to manage different load conditions of the licensed band. Specifically, the PU model is flexible because it can capture the behavior of both the circuit switching and packet switching of the mobile devices \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & \multicolumn{4}{c}{\(\mathbf{QS=15}\)} \\ \hline \(\mathbf{W_{1}}\)-\(\mathbf{N_{D}}\) & \(\mathbf{1}\) & \(\mathbf{2}\) & \(\mathbf{3}\) & \(\mathbf{4}\) \\ \hline
0.30 & 0.553 & 0.838 & 0.847 & 0.846 \\
1.00 & 0.683 & 0.840 & 0.882 & 0.854 \\
3.00 & 0.725 & 0.845 & 0.850 & 0.880 \\ \hline \multicolumn{5}{c}{\(\mathbf{QS=20}\)} \\ \hline \(\mathbf{W_{1}}\)-\(\mathbf{N_{D}}\) & \(\mathbf{1}\) & \(\mathbf{2}\) & \(\mathbf{3}\) & \(\mathbf{4}\) \\ \hline
0.30 & 0.705 & 1.138 & 1.147 & 1.146 \\
1.00 & 0.940 & 1.140 & 1.199 & 1.156 \\
3.00 & 1.004 & 1.145 & 1.150 & 1.192 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: _Cont._ \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & \multicolumn{4}{c}{\(\mathbf{QS=5}\)} \\ \hline \(\mathbf{W_{1}}\)-\(\mathbf{N_{D}}\) & \(\mathbf{1}\) & \(\mathbf{2}\) & \(\mathbf{3}\) & \(\mathbf{4}\) \\ \hline
0.30 & 0.010 & 0.017 & 0.019 & 0.020 \\
1.00 & 0.010 & 0.017 & 0.019 & 0.020 \\
3.00 & 0.010 & 0.019 & 0.022 & 0.022 \\ \hline \multicolumn{5}{c}{\(\mathbf{QS=10}\)} \\ \hline \(\mathbf{W_{1}}\)-\(\mathbf{N_{D}}\) & \(\mathbf{1}\) & \(\mathbf{2}\) & \(\mathbf{3}\) & \(\mathbf{4}\) \\ \hline
0.30 & 0.037 & 0.055 & 0.067 & 0.068 \\
1.00 & 0.033 & 0.057 & 0.063 & 0.069 \\
3.00 & 0.032 & 0.065 & 0.080 & 0.075 \\ \hline \multicolumn{5}{c}{\(\mathbf{QS=15}\)} \\ \hline \(\mathbf{W_{1}}\)-\(\mathbf{N_{D}}\) & \(\mathbf{1}\) & \(\mathbf{2}\) & \(\mathbf{3}\) & \(\mathbf{4}\) \\ \hline
0.30 & 0.082 & 0.115 & 0.146 & 0.149 \\
1.00 & 0.063 & 0.121 & 0.133 & 0.151 \\
3.00 & 0.058 & 0.139 & 0.175 & 0.163 \\ \hline \multicolumn{5}{c}{\(\mathbf{QS=20}\)} \\ \hline \(\mathbf{W_{1}}\)-\(\mathbf{N_{D}}\) & \(\mathbf{1}\) & \(\mathbf{2}\) & \(\mathbf{3}\) & \(\mathbf{4}\) \\ \hline
0.30 & 0.145 & 0.199 & 0.256 & 0.261 \\
1.00 & 0.102 & 0.210 & 0.231 & 0.266 \\
3.00 & 0.089 & 0.243 & 0.310 & 0.286 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Jitter (ms). operating inside the cell; the number of transport channels operating in the switching circuit mode and in the packet switching mode inside the transponder can also be changed as needed. The workload of each type of source can be varied according to the operating condition of the modeled cell; the average number of arriving phone calls and its average time duration can be increased or decreased, as well as the distributions of packet arrivals and distributions of packet sizes for the packet switching traffic. The conceived cognitive radio scenario assumes a synchronized spectrum sensing with the frame structure of a GSM/EDGE transponder. The SU device is able to detect the activity status of PUs in the early portion of a single time slot and opportunistically use the spectrum in the remaining portion. The SU model is flexible as well, both in terms of the distribution of packet arrivals and the distribution of packet size of the generated workload. Moreover, it is able to capture the interactions with PUs, and it is able to take into account possible spectrum sensing mistakes. Numerical results were obtained by modeling the specific scenario of a transponder with three transport channels operating in the switching circuit mode only (to serve phone call traffic implementing discontinuous transmission) and with four transport channels operating in both the packet switching and circuit switching modes. The SU workload follows a typical profile of an IoT device characterized by a Poisson arrival process of consistently sized IUs.