  LoRaWAN is a promising low power long range wireless communications
technology for the Internet of Things. An important feature of LoRaWAN gateways
is related to so-called capture effect: under some conditions the gateway may
correctly receive a frame even if it overlaps with other ones. In this paper,
we develop a pioneering mathematical model of a LoRaWAN network which allows
finding network capacity and transmission reliability taking into account the
capture effect.
