# Dynamic Spectrum Access for Internet of Things Service in Cognitive Radio-Enabled LPWANs
## 6 Results and Discussions  
In this dynamic spectrum access model are heterogeneous types of traffics and their traffic characteristics. In this section, the numerical analysis results are presented in order to illustrate the performance characteristics of a dynamic spectrum access strategy for a system with \(M=13\), \(m=3\), \(c_{1}=4\), \(r=7\) as shown in Figure 3. In Figure 6, we can see the blocking probability for PU callswhen the PU traffic load \(\rho_{1}\) (\(=\lambda_{1}/\mu_{1}\)) varies from \(\lambda_{1}\) = 0.0006 to 0.006 under \(\mu_{1}\) = 0.006 and 0.008, respectively. Meanwhile, the CU traffic load \(\rho_{2}\) (\(=\lambda_{2}/\mu_{2}\)) is kept constant at 0.01 with \(\lambda_{2}\) = 0.2 and \(\mu_{2}\) = 20. From the dynamic spectrum access strategy shown in Figure 3, it can be seen that the blocking probability for PU calls only depends on \(\lambda_{1}\) and \(\mu_{1}\) since the PU traffic is independent of CU traffic. Simulation is also performed together in order to verify the correctness of the mathematical analysis for the proposed dynamic spectrum access strategy. In Figure 6, the blocking probability for PU calls in the simulation is a little higher than that of the mathematical analysis overall. Before \(\lambda_{1}\) reaches 0.001, however, the blocking probability in the simulation is much lower than that of the mathematical analysis, and soon it becomes higher than the analysis result at around \(\lambda_{1}\) = 0.0012. In Figure 6, the difference between the simulation and the analysis of the blocking probability for PU calls is kept at a similar rate as \(\lambda_{1}\) increases to 0.006. Hence, the mathematical analysis can be verified with a similar upward tendency in distance. Figure 6 also shows that the blocking probability under \(\mu_{1}\) = 0.006 is 13% more than under \(\mu_{1}\) = 0.008 in both the simulation and the analysis as \(\lambda_{1}\) increases to 0.006. Figure 7 shows the mean dwell time for CU calls when the PU traffic load \(\rho_{1}\) varies from \(\lambda_{1}\) = 0.0006 to 0.006 with \(\mu_{1}\) = 0.006. Meanwhile, the CU traffic load \(\rho_{2}\) is kept constant at 0.01, 0.1, and 0.99 (\(\approx\) 1.0) with \(\lambda_{2}\) = 0.2. Now we can consider the effect of the channel bandwidth ratio \(m\) on the mean dwell time of CU calls. In this example, CU call attempts can be overflowed into PU spectrum channels or can be queued in the CUQ when enough channels are not available. Under the heavy PU traffic, therefore, an arriving PU request makes \(m\) CU calls preempted, and then these CU calls can be queued unless they fail to move onto available channels. Consequently, the longer the time spent in the CU queue, the more the mean dwell time for CU calls increases. In Figure 7, however, we can see that the CU mean dwell time is slightly reduced as PU traffic load increases. This means that the licensed spectrum channels allocated for PUs are quickly occupied under heavy PU traffic, and hence no CU calls can overflow over the licensed spectrum. Meanwhile, it is shown that the mean dwell time also increases when CU traffic load increases. Figure 7 shows the variation among the values in the mean dwell time according to different CU traffic load (\(\rho_{2}\)) at 0.01, 0.1, and 0.99 (\(\approx\) 1.0). Since CU calls often fail to get channel allocations under the heavy CU traffic in this example, the CU calls can be queued more frequently. Now we can infer the effect of the ratio (\(\mu_{2}/\mu_{1}\)) of mean service time on the mean dwell time of CU calls. In Figure 7, the spectrum performance of CU calls is better when the service time ratio (\(\mu_{2}/\mu_{1}\)) is larger even though the PU service rate (\(\mu_{1}\)) is kept constant at 0.006. On the contrary, this means that the average dwell time of CU calls increases as the spectrum channel holding time of PU calls becomes longer. This phenomenon is common in the movable boundary strategy. Figure 6: Blocking probability for PU calls.