  The Internet of Things (IoT) is large-scale by nature. This is not only
manifested by the large number of connected devices, but also by the high
volumes of traffic that must be accommodated. Cellular networks are indeed a
natural candidate for the data tsunami the IoT is expected to generate in
conjunction with legacy human-type traffic. However, the random access process
for scheduling request represents a major bottleneck to support IoT via LTE
cellular networks. Accordingly, this paper develops a mathematical framework to
model and study the random access channel (RACH) scalability to accommodate IoT
traffic. The developed model is based on stochastic geometry and discrete time
Markov chains (DTMC) to account for different access strategies and possible
sources of inter-cell and intra-cell interferences. To this end, the developed
model is utilized to assess and compare three different access strategies,
which incorporate a combination of transmission persistency, back-off, and
power ramping. The analysis and the results showcased herewith clearly
illustrate the vulnerability of the random access procedure as the IoT
intensity grows. Finally, the paper offers insights into effective scenarios
for each transmission strategy in terms of IoT intensity and RACH detection
thresholds.
