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 $M^\ast$ .

中文翻译：

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具有前导重传限制的蜂窝网络中mMTC大规模随机接入的性能优化

作为5G蜂窝系统的三大应用场景之一，海量机器类通信（mMTC）被视为推动物联网范式的关键解决方案。适应 mMTC 的一个主要瓶颈是当大量机器类型设备 (MTD) 同时发送访问请求而前导资源有限时，蜂窝随机访问信道的严重拥塞。为了解决这个问题，限制重传次数并在达到限制后丢弃访问请求可能是一种有效的方法。然而，前导重传限制的影响$K$关于 mMTC 在蜂窝网络中的最佳接入性能的研究在很大程度上仍未得到利用，这激发了本文的研究。具体来说，在本文中，我们首先根据访问请求成功传输的限制概率来表征网络稳态点。然后我们获得访问吞吐量和成功传输的访问请求的平均访问延迟的显式表达式作为$K$ 和前导码的数量 百万美元 . 进一步推导出最大访问吞吐量和相应的最佳退避窗口大小。结果表明，最大访问吞吐量与$K$ ，而平均访问延迟可以显着减少 $K$ ，然而，以增加请求丢弃率为代价。此外，为了提高吞吐量和延迟性能，分析表明应该分配更多的前导码，但性能增益在以下情况下变得微不足道百万美元很大。因此，提出了一种用于确定最少前导数的算法$M^\ast$最大化接入吞吐量和前导资源利用率。数值结果表明，较小的前导重传限制$K$ 可以进一步减少 $M^\ast$ .