  LoRaWAN is a Low Power Wide Area Network technology featuring long
transmission ranges and a simple MAC layer, which can support sensor data
collection, control applications and reliable services thanks to the
flexibility offered by a large set of configurable system parameters. However,
the impact of such parameters settings on the system's performance is often
difficult to predict, depending on several factors. To ease this task, in this
paper, we provide a mathematical model to estimate the performance of a LoRaWAN
gateway serving a set of devices that may or may not employ confirmed traffic.
The model features a set of parameters that can be adjusted to investigate
different gateway and end-device configurations, making it possible to carry
out a systematic analysis of various trade-offs. The results given by the
proposed model are validated through realistic ns-3 simulations that confirm
the ability of the model to predict the system performance with high accuracy,
and assess the impact of the assumptions made in the model for tractability.
