# Dynamic RACH Partition for Massive Access of Differentiated M2M Services
## 3 System Model
### Random Access Procedures
The more competing devices there are, the more frequent the collisions are, which results in lower ASP. Thus, there is a sharp decline as \(f_{s}\) varies from 0.8 to 0.9. Therefore, setting \(f_{s}\) as 0.9 is practically meaningless in real scenarios. Consequently, our simulation is conducted in \(f_{n}=0.6+\frac{1}{3}*f_{s}\). (**d**) The baseline scheme we use for performance comparison is the original ACB scheme, since it is the currently-suggested solution for RAN overload in M2M networks by 3 GPP. Notably, the baseline ACB scheme neither divides the MTC devices into cluster groups nor partitions the preambles. ### Simulation Results

In Figure 8, we demonstrate the simulation results in terms of the overall ASP, PCP and AAD under the proposed scheme compared to the baseline ACB scheme. Figure 8a,c shows the performance \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Settings** \\ \hline Cell bandwidth & 5 MHz \\ Number of M2M devices & 30,000 \\ Attempts’ distribution & Beta distribution \\ Distribution period & 10 s \\ PRACH configuration index & 6 \\ Number of preambles for contention-based RA & 54 \\ Ra-Response WindowSize & 5 sub-frames \\ Backoff indicator & 5 ms \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Basic simulation parameters. Figure 6: The ASP _versus_ the linear correlation of \(f_{s}\) and \(f_{n}\). Figure 7: The average access delay (AAD) _versus_ the linear correlation of \(f_{s}\) and \(f_{n}\). of ASP and AAD _versus_\(f_{\rm s}\) under the proposed scheme and the baseline ACB scheme. Compared to the baseline ACB scheme, the proposed scheme yields much better performance in improving the overall access success probability, as well as reducing the average access delay. From the general trends in Figure 8a, two curves almost simultaneously climb up when \(f_{\rm s}\) varies from 0.2 to 0.8 and drop when \(f_{\rm s}\) varies from 0.8 to 0.9. Furthermore, we can observe from Figure 8a that there is a large gap between two curves when \(f_{\rm s}\) is smaller than 0.7, and the gap narrows when \(f_{\rm s}\) = 0.8. This is because when \(f_{\rm s}\) changes from 0.8 to 0.9, \(f_{\rm n}\) changes from 0.87 to 0.9, which means nearly 90% of delay-tolerant devices would compete for access. In addition, due to the huge number of delay-tolerant devices, devices competing for access do not successfully access the network more easily compared to the situations for fewer devices. The more competing devices there are, the more frequent the collisions are, which results in lower ASP in Figure 8a and longer access delay in Figure 8c. Similarly, two curves in Figure 8c drop when \(f_{\rm s}\) changes from 0.2 to 0.8, and the gap between them narrows continuously, as well a slight increase occurs in two curves when \(f_{\rm s}\) varies from 0.8 to 0.9. Obviously, the optimal value for \(f_{\rm s}\) can be adopted as 0.8 for the proposed scheme to obtain high ASP and lower AAD. Figure 8: Performance comparison between the proposed scheme and the baseline access class barring (ACB) scheme. (**a**) The ASP _versus_ the ac_barringfactor of the cluster for delay-sensitive devices; (**b**) the preamble collision probability (PCP) _versus_ the ac_barringfactor of the cluster for delay-sensitive devices; (**c**) the AAD _versus_ the ac_barringfactor of the cluster for delay-sensitive devices. Instead, the preamble collision probability of the proposed scheme performs higher PCP for about 10%, while the growth falls when \(f_{s}\) rises in Figure 8b, which is accounted for by the rise of the number of non-barred MTC devices when \(f_{s}\) is larger. Consequently, in order to visually present the trade-off between access success probability and collision probability, here we introduce a weighting factor denoted as \(\omega\) and a new indicator defined as the comprehensive parameter index (CPI).