# Peak Age of Information Optimization in Cell-Free Massive Random Access Networks
## 5 Simulation Results and Analysis
### Algorithm Effectiveness and Performance Comparison  
To further evaluate the effectiveness of the proposed algorithms, Figures 6-8 present a detailed comparison of the network-wide average PAoI, the group-wise PAoI, and the channel access probabilities under varying MTD distributions. Specifically, the number of MTDs in the intermediate cross-coverage group \(\mathcal{G}_{\{1,2\}}\) is varied from 10 to 80 in increments of 10, with all other parameters kept constant. Figure 5: Network-wide average PAoI versus iteration rounds. Figure 6: Network-wide average PAoI versus \(n^{\{1,2\}}\). As can be seen from Figure 6, the PAoI optimization effect of the global PSO algorithm basically coincides with that of the enumeration algorithm and can effectively approach the theoretical optimal solution. However, the average PAoI under the local PSO algorithm is only slightly higher than that of the global PSO algorithm, and the error margin does not significantly increase with the increase in the number of MTDs in group \(\mathcal{G}_{\{1,2\}}\), indicating that it can achieve performance similar to that of the global PSO and has good robustness against network topology changes. In addition to the three optimization algorithms, we present a baseline case where all groups adopt a fixed channel access probability of 0.01, regardless of network size or interference. The results clearly show that fixed access values  
Figure 8: Channel access probability of each group versus \(n^{\{1,2\}}\). Figure 7: PAoI of each group versus \(n^{\{1,2\}}\). lead to significantly higher PAoI, while all three optimization methods maintain consistently lower and more stable performance across different scenarios. As can be seen from Figure 7, as \(n^{\{1,2\}}\) gradually increases, the PAoI of \(\mathcal{G}_{\{1,2\}}\) significantly rises, while the growth of PAoI in \(\mathcal{G}_{\{1\}}\) and \(\mathcal{G}_{\{2\}}\) is more gentle. Further combined with Figure 8, it can be seen that when the PAoI of \(\mathcal{G}_{\{1,2\}}\) significantly rises, its channel access probability slowly decreases; on the contrary, the channel access probabilities of the other two groups gradually increase. This difference originates from the dynamic adjustment mechanism of the algorithm for channel access probability. As the load of \(\mathcal{G}_{\{1,2\}}\) increases, the internal transmission conflicts intensify, and at the same time, the interference intensity on \(\mathcal{G}_{\{1\}}\) and \(\mathcal{G}_{\{2\}}\) increases. To alleviate the conflicts, the algorithm gradually reduces the channel access probability of this group. However, due to the nonlinear growth of the conflict rate caused by the increase in the number of MTDs, its PAoI ultimately rises significantly. While \(\mathcal{G}_{\{1\}}\) and \(\mathcal{G}_{\{2\}}\), by moderately increasing the access probability, under the combined effect of their own loads gradually decreasing and cross-group interference being locally alleviated, achieve relatively stable performance. Because the local PSO algorithm can only obtain local topology information, although the influence of the distant group on this group is small, this influence still exists. This makes the local PSO algorithm unable to converge to the optimal solution, further causing the PAoI and channel access probability of each group to fluctuate with the change in the number of MTDs in the cross-coverage group. However, the fluctuation trends and amplitudes of the PAoI, as well as channel access probability of MTDs in the same group, are basically consistent with those of the global PSO algorithm. This indicates that the action law of the local PSO algorithm on each group of MTDs is consistent with that of the global PSO algorithm, and it will not locally change the performance of any group of MTDs or channel access behavior. Figure 9 further considers the average PAoI of the entire network for the two algorithms when the number of APs changes.