# Peak Age of Information Optimization in Cell-Free Massive Random Access Networks
## 4 Optimization of Average Peak Age of Information
### Local PSO Algorithm Based on Neighboring Topology Information  
To address the signaling overhead issue caused by the global PSO's dependency on global topology information, we propose an improved algorithm (i.e., Algorithm 2) based on local topology information. The core idea stems from the spatial decay characteristic of inter-group interference in cell-free networks: the PAoI of a group is predominantly affected by the transmission behaviors of its neighboring groups, while the impact of distant groups is negligible. By restricting optimization to the current group and its immediate neighbors, the algorithm captures the dynamics of key interference sources while significantly reducing complexity. Each group considers only its associated APs, the MTDs served by these APs, and their AP coverage relationships. Specifically, two logical groups are considered neighboring if they share at least one common AP. Based on this definition, the entire network is partitioned into local neighborhoods, and each group communicates with its neighboring groups to exchange necessary information for distributed optimization. The exchanged information includes the number of MTDs, \(n\), the channel access probability vector, \(q\), and the packet arrival rate, \(\lambda\), of each neighboring group. To further elaborate, taking a group \(\mathcal{G}_{A}\) as an example, whose neighboring groups are \(\mathcal{G}_{B}\) and \(\mathcal{G}_{C}\), when calculating the \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameters** & **Values** \\ \hline Number of particles \(K\) & 50 \\ Self-control factor \(c_{1}\) & 0.003 \\ Group control factor \(c_{2}\) & 0.8 \\ Position range \((q_{max},q_{max})\) & (0, 0.1) \\ Velocity range \((\eta_{min},\
u_{max})\) & (\(-0.002,0002\)) \\ Inertia range \((\omega_{min},\omega_{max})\) & (0.4, 2) \\ Maximum iterations \(I_{max}\) & 100 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: PSO algorithm parameter setting. successful transmission probability \(p^{A}\) of group \(\mathcal{G}_{A}\), using only the information from these three groups, according to Equation (5), \(p^{A}\) is given by  
\[p^{A}=\exp(-\frac{n^{A}\lambda q^{A}}{\lambda+p^{A}q^{A}})(1-(1-\exp(-\frac{n^{B }\lambda q^{B}}{\lambda+p^{B}q^{B}}))(1-\exp(-\frac{n^{C}\lambda q^{C}}{\lambda+ p^{C}q^{C}}))). \tag{15}\]  
The PAoI optimization is confined to these three groups:  
\[A=\frac{n^{A}A_{A}+n^{B}A_{B}+n^{C}A_{C}}{n^{A}+n^{B}+n^{C}}. \tag{16}\]  
The algorithm initializes the particle swarm at the start. During each iteration, each group determines its local optimal position. For group \(\mathcal{G}_{A}\), the information from groups \(\mathcal{G}_{B}\) and \(\mathcal{G}_{C}\) are combined. The PAoI is computed for all three groups, and the position minimizing PAoI is selected. This process is repeated for all groups to obtain the optimal channel access probability vector. When group \(\mathcal{G}_{A}\) runs the PSO under local information, the update rule becomes  
\[\mathbf{v}_{k,A}^{(i+1)}=\omega^{(i)}\cdot\mathbf{v}_{k,A}^{(i)}+c_{1}\mathbf{r}_{1,g}^{(i )}\cdot(\mathbf{b}_{k,A}^{(i)}-\mathbf{q}_{k,A}^{(i)})+c_{2}\mathbf{r}_{2,g}^{(i)}\cdot( \mathbf{d}_{A}^{(i)}-\mathbf{q}_{k,A}^{(i)}), \tag{17}\]  
where \(\mathbf{b}_{k}^{(i)}\) represents the best-experience position of the particle itself, while \(\mathbf{d}_{A}^{(i)}\) denotes the local optimal position of the group, selected from historical optima that minimize local PAoI. The inertia weight calculation and parameter settings are identical to those in Table 1.  
Compared to the global PSO framework, which depends on centralized information aggregation and coordination via a CPU, the local PSO algorithm functions in a fully distributed manner. Each group independently executes its optimization process by utilizing only topology and access information from its neighboring groups. No global network state is required, and no signaling is exchanged with a centralized controller.