$P_i, n_i,\lambda_{a}, W$                           Default: 21 dBm, 1, 5.5[e]{}-8, 100 KHz
  $\ell_{\max},\mathcal Q$                            1, 0

  : Simulation Parameters []{data-label="sim"}

Performance Evaluation {#simsec}
======================

In order to investigate usefulness of our findings in IoT-network planning and operation control, here we implement a MATLAB simulator for a heterogeneous IoT network. In our simulator, 2 types of IoT devices have been considered, that differ in the distribution processes describing locations of their respective nodes, and communications’ parameters such as transmit power. Motivations for this setup are the coexistence of IoT technologies over the public ISM spectrum, e.g. SigFox and LoRa [@int2], and the coexistence of different IoT services over cellular networks, which are sharing a set of uplink resources, as described in [@gf31]. For type $i$, the distribution process of locations is characterized by PCP$(\lambda_i,\upsilon_i,f(x))$, where $\lambda_i$ is the density of cluster points (in Km$^{-2}$), $\upsilon_i=200$ is the average number of nodes in each cluster, and distribution of cluster nodes around the cluster center, i.e. $f(x)$, is modeled by a normal distribution with standard deviation of 100 meters. The reliability constraint is described as $\text{p}_{\text s}(i,d_{\text{eg}})$, where $d_{\text{eg}}=\sqrt{{1}/{(\pi\lambda_{\text a})}}$ is equivalent to the cell-edge communication distance in the case of grid deployment of APs. 