## 5 Results  
This section presents the numerical and simulation findings of the four strategies, as stated in part 3. The study conducted in [4], as discussed in Section 2, was employed to evaluate and contrast our findings. The result figures incorporate plots from [4] for the purpose of comparison. Monte Carlo simulation (MCS) was conducted for all results, and they have been incorporated into all the figure plots. The legends of the graphs designate the plot for the scheme proposed in [4] as 'Scheme ref [4]'. The Monte Carlo simulation, abbreviated as 'MCS', is denoted solely by markers. The numerical graph displays the frequency of PU delays (d = 0, 1, 2), as represented by lines. Table 3 provides an overview of the simulation parameters used in the study to evaluate the proposed M/D/1 queueing-based CRN. Figure 2 presents the impact of the utilization factor on the mean number of packets. It measures how aggressively a resource is used and affects the system packet count. This diagram shows how utilization-factor variations affect the mean number of packets, revealing the system's behavior as the utilization factor fluctuates. In Figure 2, the analysis examines how changes in the utilization factor, which reflects resource-usage intensity in a system, affect waiting time. It shows how well the system handles demand and allocates resources based on wait times. Figure 3 describe the impact of utilization factor \(\rho_{P}\) on the average number of packets in the network. In Figure 4, we present a comprehensive comparison of the average number of packets across a spectrum of service rates, delineated by different ranges of \(\lambda_{S}\), reflecting the arrival rates of SUs. This visualization allows for a nuanced understanding of how changes in service rates impact the accumulation of packets within the network, offering insights into the system's performance under varying levels of SU activity. Additionally, Figure 5 illustrates a detailed comparison of the average number of packets within the network with regard to the service rate for primary users (PUs), with \(\lambda_{P}\) varying across different scenarios. By comparing these metrics against service rates, this figure provides valuable insights into the behavior of packet accumulation for PUs under different arrival-rate conditions, facilitating a comprehensive analysis of network dynamics and resource utilization in cognitive radio environments. \begin{table}
\begin{tabular}{l l} \hline \hline \multicolumn{1}{c}{**Parameter**} & \multicolumn{1}{c}{**Value**} \\ \hline Service Rate (\(\mu\)) & [11.00, 11.20, 11.40, 11.60] requests/sec \\ Arrival Rate (\(\lambda_{P}\)) & [19.00, 19.50, 20.00, 20.50] requests/sec \\ Arrival Rate (\(\lambda_{S}\)) & [5:10] requests/sec \\ Buffer Capacity & 50 requests \\ Priority Scheme & PU \textgreater{} SU \\ Processing Time (d) & [0, 1, 2] sec/request \\ System Stability & Stable \\ Packet Accumulation & 20 packets \\ Detection Time & 0.1 s \\ Accuracy & 95\% \\ Interference Mitigation & Frequency-hopping \\ Performance Metrics & Avg. waiting time: 2 s \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Simulation parameters used in the study. Figure 3: Impact of utilization factor \(\rho_{P}\) on the average number of packets in the network. Figure 2: Impact of utilization factor \(\rho_{S}\) on the number of packets in the network. Figure 6 shows a comparison of network-induced SU delays with respect to service rate for different values of \(\lambda_{S}\) for SUs. It represents the delays experienced by SUs at intervals within the network as the level of service provided to SUs varies while the arrival rates for SUs, \(\lambda_{S}\), also vary. Each curve represents a different value of \(\lambda_{S}\), allowing a comparative analysis of how changes in \(\lambda_{S}\) affect delays caused by different SUs at different  
Figure 4: Comparison of average numbers of packets over varying service rates for varying \(\lambda_{S}\).