# Dynamic RACH Partition for Massive Access of Differentiated M2M Services
## 3 System Model
### Random Access Procedures
Namely, the CPI can be expressed as:

\[CPI=\omega\cdot P_{S}+(1-\omega)\cdot P_{C} \tag{26}\]

Figure 9 depicts the three-dimensional curve, which demonstrates the variation tendency of CPI with the synchronous change of \(f_{s}\) and \(\omega\). Furthermore, Figure 9 reveals that the CPI of the proposed scheme is higher than that of the ACB scheme with the variation of weighting factor \(\omega\) when fixing the given \(f_{s}\). In comparison, Figure 10 also presents the performance of two clusters for delay-sensitive and delay-tolerant devices separately, which shows that our proposed scheme achieves higher performance without sacrificing any kinds of services. From Figure 10, we can observe that when \(f_{s}\) is larger than 0.6, the proposed scheme provides a slight effect on delay-sensitive services, while greatly improving the performance of delay-tolerant services in terms of ASP, which significantly increases the overall performance. In Figure 10a, the cluster for delay-sensitive devices yields a slightly lower ASP than when \(f_{s}\) is smaller than 0.5, which makes no difference, since \(f_{s}\) is set larger than 0.5 in a real system. Similarly, Figure 10b demonstrates that when \(f_{s}\) is larger than 0.5, the proposed scheme provides a slight effect on delay-sensitive services, while effectively reducing the AAD for delay-tolerant services, which significantly increases the overall performance. Notably, Figure 10a,b comprehensively demonstrates that the cluster for delay-tolerant devices yields more effective performance than the baseline ACB scheme. Figure 9: The comprehensive parameter index (CPI) varies with the synchronous change of \(\omega\) and \(f_{s}\) between the proposed scheme and the baseline ACB scheme. ## 7 Conclusions

In this paper, we firstly presented the RAN overload issue caused by massive devices attempting to access the eNB in the M2M communication architecture. As for the scenario where delay-sensitive and delay-tolerant devices coexist, we then proposed a mechanism for access control to jointly guarantee the RAN overload requesting from differentiated services. Based on the loading condition for attempts to access from two kinds of devices, our proposed scheme dynamically allocates the preambles to

Figure 10: Performance comparison between two clusters for delay-sensitive and delay-tolerant devices and the baseline ACB scheme. (**a**) The ASP _versus_\(f_{\rm s}\) between two clusters and the baseline ACB scheme; (**b**) the AAD _versus_\(f_{\rm s}\) between two clusters and the baseline ACB scheme. respectively accommodate both sides. In our work, the core is to devise an optimal preamble partition for both sides in order to realize the maximum access success probability during each slot. We then theoretically analyzed the performance from three aspects and provided different forms of the analysis results. In addition, computer simulations are conducted to demonstrate that our proposed scheme has performance superiority over the baseline ACB scheme in terms of overall access success probability and access success delay. The research work reported in this paper is supported by the National Natural Science Foundation of China under the Grant No. 61461136001, the Specialized Research Fund for the Doctoral Program of Higher Education under Grant No. 20110201120014, and the Fundamental Research Funds for the Central Universities. [PERSON] conceived of the study, proposed the idea, coordinated the research and corrected the manuscript. [PERSON] designed the specific scheme and drafted the manuscript. [PERSON] participated in the manuscript's design and provided valuable suggestions. [PERSON] participated in the coordination of the research and searched for funding to support the work. [PERSON] and [PERSON] proofread the manuscript. All authors read and approved the final manuscript. The authors declare no conflict of interest.