generations of wireless networks [@noma; @jsacS]. In literature, non-orthogonal access has been mainly employed in order to increase the network throughput [@reem], reliability [@url], battery lifetime [@gf], and reduce access delay [@reem] in serving non-IoT traffic. In [@miao2016MAC], grant-free access to uplink radio resources of cellular networks has been analyzed for intra-group communications of IoT devices. In [@gf], a novel receiver for grant-free radio access IoT networks has been designed, which benefits from oscillator imperfection of cheap IoT devices for contention resolution. In [@2d], outage probability in grant-free access has been studied by assuming a constant received power from all contending devices, which is not the case in practice regarding the limited transmit-power of IoT devices, as well as lack of channel state information at the device-side for power control. The success probability in grant-free radio access has been also analyzed in [@sic; @mey] by assuming a Poisson point process (PPP) distribution of IoT devices.

One sees the research on grant-free radio access has been mainly focused on success probability analysis in homogeneous scenarios, and there is lack of research on performance analysis of large-scale IoT networks with multi-type IoT devices with heterogeneous communications characteristics. Furthermore, when it comes to 