the distribution of devices in wide-area IoT networks, PPP has been mainly used. However, this assumption may lead to inaccurate results [@math; @pcp] due to the cell ranges that can go up to tens of kilometers [@mag_all] and hot-spots. In hot-spots, e.g. buildings and shopping centers, a high density of IoT devices exist; while outside them, a low density of devices exists. Then, a Poisson cluster process (PCP), which takes the correlation between locations of devices into account, suits well for the distribution process of devices in LPWA IoT networks [@math; @pcp].

Contributions
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Here, we address an important problem, not tackled previously: network design in coexistence scenarios with grant-free radio access. Enabling IoT connectivity requires deployment of access points (APs) and allocation of frequency resources, which increase the network costs. On the other hand, the experienced delay, consumed energy, and success of IoT applications have strong couplings with reliability of data transfer, which is a function of provisioned network resources. This tradeoff is investigated in this work. The main contributions of this work include:

-   Provide a rigorous analytical model of reliability for heterogeneous LPWA IoT networks in terms of provisioned resources, e.g. density of the APs, and characteristics 