  Massive Internet of Things (mIoT) has provided an auspicious opportunity to
build powerful and ubiquitous connections that faces 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 (BSs) in the cellular-based mIoT network, where modelling the
interactions between static properties of 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 modelled 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
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 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.
