  In this paper we present a simple, stochastic-geometric model of a wireless
access network exploiting the LoRA (Long Range) protocol, which is a
non-expensive technology allowing for long-range, single-hop connectivity for
the Internet of Things. We assume a space-time Poisson model of packets
transmitted by LoRA nodes to a fixed base station. Following previous studies
of the impact of interference, we assume that a given packet is successfully
received when no interfering packet arrives with similar power before the given
packet payload phase. This is as a consequence of LoRa using different
transmission rates for different link budgets (transmissions with smaller
received powers use larger spreading factors) and LoRa intra-technology
interference treatment. Using our model, we study the scaling of the packet
reception probabilities per link budget as a function of the spatial density of
nodes and their rate of transmissions. We consider both the parameter values
recommended by the LoRa provider, as well as proposing LoRa tuning to improve
the equality of performance for all link budgets. We also consider spatially
non-homogeneous distributions of LoRa nodes. We show also how a fair comparison
to non-slotted Aloha can be made within the same framework.
