  This paper studies data aggregation in large-scale regularly deployed
Internet of Things (IoT) networks, where devices generate synchronized
time-triggered traffic (e.g., measurements or updates). The data granularity,
in terms of information content and temporal resolution, is parameterized by
the sizes of the generated packets and the duty cycle of packet generation. The
generated data packets at the devices are aggregated through static terrestrial
gateways. Universal frequency reuse is adopted across all gateways and
randomized scheduling is utilized for the IoT devices associated with each
gateway. Such network model finds applications in environmental sensing,
precision agriculture, and geological seismic sensing to name a few. To this
end, we develop a novel spatiotemporal mathematical model to characterize the
interplay between data granularity, transmission reliability, and delay. The
developed model accounts for several IoT design parameters, which include
packet sizes, generation duty cycle, devices and gateways spatial densities,
transmission rate adaptation, power control, and antenna directivity. For
tractable analysis, we propose two accurate approximations, based on the
Poisson point process, to characterize the
signal-to-interference-plus-noise-ratio (SINR) based transmission reliability.
For the delay analysis, we propose a phase-type arrival/departure (PH/PH/1)
queueing model that accounts for packet generation, transmission scheduling,
and rate-sensitive SINR-based packet departure. The developed model is utilized
to obtain the optimal transmission rate for the IoT devices that minimizes
delay. The numerical results delineate the joint feasibility range of packet
sizes and inter-arrival times for data aggregation and reveal significant gains
when deploying directional antennas.
