# Dynamic RACH Partition for Massive Access of Differentiated M2M Services
## 3 System Model
### Random Access Procedures
### Categories of M2M Devices

According to the comprehensive research [36], in the real scene where delay-sensitive and delay-tolerant devices coexist, although the occurrence of delay-sensitive devices, such as the hospital e-care, is very rare, the delay-sensitive devices are strict with delay, and they need instant processing. For the application in hospital e-care, the maximum tolerant delay is five milliseconds, since in a real system, the data become useless after that. On the other hand, delay-tolerant devices, such as smart grids [11], can tolerate several seconds or even minutes, and a great majority of devices is subject to this category. ## 4 Resource Partition Scheme for M2M Networks

The proposed scheme solves the RAN overload problem in the scenarios of the co-existence of delay-sensitive and delay-tolerant devices. In general, the proposed scheme comprehensively takes the resource allocation and the access control into account for the scenarios where two types of services co-exist in M2M networks. Specifically, the proposed architecture is composed of several main moves: firstly, in order to effectively provide quality of service (QoS) for two types of MTC devices mentioned above, we consider that MTC devices are classified into two clusters on the basis of delay requirements. Secondly, the vital conceptual design is achieved by dynamically adjusting the preamble partition between two given clusters. Thirdly, devices from two clusters adopt the ACB mechanism to access the network, respectively. According to the proposed principle discussed above, as depicted in Figure 3, this paper presents the implementations at length afterwards. Figure 3: The diagram of the conceptual design. ### Clustered Structure

Due to the lower incidence of delay-sensitive services [37], the delay-sensitive devices utilize the preamble resources occasionally, which results in smaller traffic loads comparing to the delay-tolerant ones. Considering this, we divide those devices that are attempting to access the network into two clusters according to their requirements of delay. In the actual implementation of our scheme, we pre-categorize the attempting devices into two clusters. In other words, once the total number of devices is given, the devices would be automatically divided into two clusters. ### Dynamic Adjustment of Preamble Partition

After dividing the attempting devices into two clusters, the eNB dynamically determines the RA preamble partition between two clusters before accessing the network. We propose a feasible scheme to obtain the preamble partition. To formulate such a random access problem, we pre-define the variables as follows. In a certain RA slot, we denote \(A_{s}\) as the number of delay-sensitive devices, \(A_{n}\) as the number of delay-tolerant ones and \(A_{i}\) as the total number of the active MTC devices. Namely, \(A_{s}+A_{n}=A_{i}\). Then, we define the preamble partition as:

\[\beta=\frac{M_{s}}{M_{n}} \tag{1}\]

where \(M_{s}\) and \(M_{n}\) respectively represent the preambles allocated for delay-sensitive and delay-tolerant devices. According to the configuration of RACH, we know:

\[M_{s}+M_{n}=c \tag{2}\]

Connecting Equation (1) with Equation (2) where \(c=54\), we solve:

\[M_{s}=\frac{c\beta}{1+\beta} \tag{3}\]

\[M_{n}=\frac{c}{1+\beta} \tag{4}\]

Moreover, we denote \(f_{s}\) and \(f_{n}\) as the ac_barringfactors of two clusters, since we adopt the ACB scheme to access the network discussed in Section 4.3. Since every MTC device selects the preamble randomly from the available resources pool, so collisions would occur if at least one MTC device transmits the same preamble. Moreover, according to [35], the contention-based RA procedure adopts a slotted-aloha as the access protocol, where the number of preambles available is analogous to the number of slots. In this way, the access success probability could be calculated by:

\[P_{s}=e^{-\frac{N}{P}} \tag{5}\]

where \(N\) is the total number of devices and \(P\) is the number of preambles available within an RA slot.