NarrowBand-Internet of Things (NB-IoT) is a new 3GPP radio access technology designed to provide better coverage for Low Power Wide Area (LPWA) networks. To provide reliable connections with extended coverage, a repetition transmission scheme and up to three Coverage Enhancement (CE) groups are introduced into NB-IoT during both Random Access CHannel (RACH) procedure and data transmission procedure, where each CE group is configured with different repetition values and transmission resources. To characterize the RACH performance of the NB-IoT network with three CE groups, this paper develops a novel traffic-aware spatio-temporal model to analyze the RACH success probability, where both the preamble transmission outage and the collision events of each CE group jointly determine the traffic evolution and the RACH success probability. Based on this analytical model, we derive the analytical expression for the RACH success probability of a randomly chosen IoT device in each CE group over multiple time slots with different RACH schemes, including baseline, back-off (BO), access class barring (ACB), and hybrid ACB and BO schemes (ACB&BO). Our results have shown that the RACH success probabilities of the devices in three CE groups outperform that of a single CE group network but not for all the groups, which is affected by the choice of the categorizing parameters.This mathematical model and analytical framework can be applied to evaluate the performance of multiple group users of other networks with spatial separations.
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