## 1 Introduction  
With the rapid development of the Internet of Things (IoT) [1], one of the major drivers of cellular networks is machine-to-machine (M2M) communication [2; 3]. M2M communications, also known as machine-type communications (MTC), means the communications of machine devices without human intervention [4]. Many devices may be triggered almost simultaneously and attempt to access the base station through the Random Access Channel (RACH). M2M communications, as a critical part of the development of the IoT, are crucial to efficient data transmission from machine devices to networks for various IoT applications such as smart metering, health-care, smart home appliances, surveillance, security and logistics tracking [5; 6; 7].  
M2M services have great market potential because of their wide range of applications. Recent market reports forecast that in 2020, 50 billion of machine devices are expected to be deployed and connected to the network to serve the IoT [8]. It should be noted that compared to traditional human-to-human (H2H) communications, M2M communications have many different characteristics. A typical feature of M2M services is that they consume little bandwidth with subtle impact on Radio Access Network (RANs) [9]. Nevertheless, such kinds of communications generally involve an extremely large number of MTC devices to support various applications. Therefore, a critical challenge of MTC is how to tackle the network degradation caused by small data transmissions and vast heterogeneous applications.  
The traditional cellular network, which is originally engineered for H2H communications, has been considered unsuitable to handle the unique characteristics of M2M applications [10; 11]. It needs to be specifically adapted to match the Quality of Service (QoS) requirements of M2M applications. In order to facilitate M2M communications through existing cellular networks such as Long Term Evolution-Advanced (LTE-A) [12], the Third Generation Partnership Project (3 GPP) organization has initiated related study items and working groups. Considering the characteristics of high density, intermittent transmission and battery powered for M2M communications, one of the major problem of M2M communications is congestion vulnerability. When a massive number of MTC devices attempt to access the eNodeB simultaneously, it will inevitably cause severe network congestion due to the limited number of Physical Random Access Channel (PRACH) resources in a single cell system [13]. The network congestion and overloading will inevitably increase delays, cause packet loss and even lead to the service interruption of H2H communications [10].  
Due to diverse application scenarios, QoS requirements in M2M communications exhibit a relatively wider range [14]. Therefore, another valuable research issue is how to meet the growing diversity of QoS requirement for MTC devices. When we measure QoS requirements for various M2M services, delay requirement is a major concern. Some M2M applications, such as smart grid and fire alarm, have very stringent delay requirements [15]. It is likely to cause incalculable loss of property and a threat to life security if we cannot effectively meet the QoS requirements of these services. Providing effective access policies for such devices is one of the research focuses.  
The remainder of this paper is organized as follows: in Section 2, we explain preliminaries on the related works and the random access procedure in LTE-A system. In Section 3, we introduce the clustered structure and the conceptual design of our proposed scheme in detail. In Section 4, we introduce the analytical model and the derivation of performance parameters. In Section 5, the performance of our scheme is evaluated by comparing our proposed scheme with typical traditional schemes. The paper is concluded in Section 6.