## 3 Access Class Barring Configuration (ACBC) Scheme
### Methodology
Regarding the LPF method, it is immediate to see in Figure 6 that \(p_{\text{acb}}(j)\) converges toward \(\mathbb{E}\left[u(j)\right]\) at exactly \(j=M\) for \(\rho=0\), and the rate of convergence increases slightly with \(\rho\). It is also interesting to observe that the \(p_{\text{acb}}(j)\) calculated with the RLS, given \(\lambda=0.999\) and \(\delta=0.1\), shown in Figure 5b, is highly similar to that of the LPF method. On the other hand, the \(p_{\text{acb}}(j)\) calculated with the LMS presents a different behavior to both the RLS and LPF methods. For example, \(p_{\text{acb}}(M)<\mathbb{E}\left[u(j)\right]\) and converges toward \(\mathbb{E}\left[u(j)\right]\) approximately until \(j=100\). Figure 5: Ratio of idle to available resources \(u(j)\) and barring rate \(p_{\text{acb}}(j)\) calculated at the \(j\)th SIB2 for a single simulation run and \(r=54\) for the RLS algorithm with \(\lambda=\left\{0.99,0.999,1\right\}\) and (**a**) \(\delta=0.001\); (**b**) \(\delta=0.01\); (**c**) \(\delta=0.1\); and (**d**) \(\delta=1\). The horizontal line is located at \(\mathbb{E}\left[u(j)\right]\). Next, we investigate whether the difference in the response of the filters provides different benefits to our ACBC scheme. For this, we consider three key performance indicators (KPIs):  
* Success probability, defined as the probability to successfully complete the RAP. The minimum success probability considered as acceptable is 0.95. Hence, the main goal of our ACBC scheme is to guarantee that more than 95% of the UEs successfully complete the RAP. * Access delay, defined as the time elapsed since the arrival of a specific UE and the successful completion of its RAP. This KPI is assessed in terms of the 95 th percentile. That is, the delay of 95% of the UEs that successfully complete the RAP is lower than, or equal, to the reported value. * Number of preamble transmissions to successfully complete the RAP. This KPI is assessed in terms of its expected value. It is important to emphasize that the success probability under the traffic model 2 with no implemented ACB scheme is only 0.313, which is poor. In addition, the benefits of our ACBC scheme are minor when no filtering is performed and \(y(j)=u(j)\). Specifically, the success probability with \(t_{\mathrm{acb}}=1\) s and no filtering is only 0.419, which is still unacceptable. The reason for such a poor performance is that the UE arrivals and the number of successful accesses per RAO present high variations with respect to their mean value. These variations remain present in \(u(j)\) and, naturally, in \(p_{\mathrm{acb}}(j)\). On the other hand, filtering away these variations in \(u(j)\) leads to a stable \(p_{\mathrm{acb}}(j)\) that is closely related to the intensity of UE accesses in a larger time scale to that of the SIB2 period. Figure 7 shows the 95 th percentile of access delay and the expected number of preamble transmissions for the studied filtering methods. The success probability obtained with our ACBC scheme with each of the filtering methods included in Figure 7 is higher than 0.985, hence, the difference between them, in this KPI, is negligible. In contrast, the success probability under the traffic model 2 without ACB scheme is only 0.313. For benchmark purposes, Figure 7 also includes the KPIs obtained with the optimal configuration of a static ACB. The optimal configuration for the latter is defined as the combination of fixed barring parameters that leads to a success probability of 0.95 or higher with the shortest 95 th percentile of access delay. In particular, we found the optimal configuration of the static ACB to be \(p_{\mathrm{acb}}=0.31\) and \(t_{\mathrm{acb}}=1.75\) s, which yields a success probability of 0.95. Figure 6: Ratio of idle to available resources \(u(j)\) and barring rate \(p_{\mathrm{acb}}(j)\) calculated at the \(j\)th SIB2 for a single simulation run and \(r=54\) under the traffic model 1 for the (**a**) LPF with \(\rho\in\{0,1,2\}\) and (**b**) the LMS ALE algorithm.