Massive Internet of Things (mIoT) has provided an auspicious opportunity to build powerful and ubiquitous connections that face a plethora of new challenges, where cellular networks are potential solutions due to their high scalability, reliability, and efficiency. The random access channel (RACH) procedure is the first step of connection establishment between IoT devices and base stations in the cellular-based mIoT network, where modeling the interactions between static properties of the physical layer network and dynamic properties of queue evolving in each IoT device are challenging. To tackle this, we provide a novel traffic-aware spatio-temporal model to analyze RACH in cellular-based mIoT networks, where the physical layer network is modeled and analyzed based on stochastic geometry in the spatial domain, and the queue evolution is analyzed based on probability theory in the time domain. For performance evaluation, we derive the exact expressions for the preamble transmission success probabilities of a randomly chosen IoT device with different RACH schemes in each time slot, which offer insights into the effectiveness of each RACH scheme. Our derived analytical results are verified by the realistic simulations capturing the evolution of packets in each IoT device. This mathematical model and the analytical framework can be applied to evaluate the performance of other types of RACH schemes in the cellular-based networks by simply integrating its preamble transmission principle.
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