Performance Optimization for Massive Random Access of mMTC in Cellular Networks with Preamble Retransmission Limit

As one of the three main application scenarios of 5 G cellular system, massive Machine-Type Communications (mMTC) has been regarded as the key solution to facilitate the IoT paradigm. One major bottleneck for accommodating mMTC is the severe congestion at the cellular random access channel when plenty of Machine-Type Devices (MTDs) send access requests concurrently while the preamble resources are limited. To remedy this issue, limiting the number of retransmissions and dropping access requests after the limit is reached can be an effective approach. Yet, the effect of the preamble retransmission limit K on the optimal access performance of mMTC in cellular networks remains largely unexploited, which motivates the study in this paper. Specifically, in this paper, we start by characterizing the network steady-state points based on the limiting probability of successful transmission of access requests. We then obtain explicit expressions of the access throughput and the mean access delay of successfully-transmitted access requests as functions of K and the number of preambles M. The maximum access throughput and the corresponding optimal backoff window size are further derived. It is shown that the maximum access throughput is independent of K, while the mean access delay can be significantly reduced with a small K, yet, at the expense of increased request dropping ratio. In addition, to improve both the throughput and delay performance, the analysis shows that more preambles should be allocated but the performance gain becomes marginal when M is large. Therewith, an algorithm is proposed for determining the least number of preambles M^\ast that maximizes the access throughput and the preamble resource utilization ratio. Numerical results show that a smaller preamble retransmission limit K can further reduce M^\ast.