The packet arrival at each node follows a PPP with rate $\frac{1}{T_i}$. The default values of other parameters can be found in Table \[sim\].

First, we investigate tightness of the derived analytical expressions. By considering an IoT network comprising of two IoT types with different distributions and transmit powers, Fig. \[val\] represents probability of success in packet transmission for type-1 as a function of distance from the AP. One sees that the analytical model matches well with the simulation results. We have further depicted the contributions of noise, interferences from the same and other clusters of type-1 devices, as well as interference from type-2 devices. Regarding the fact that transmit power of type-2 devices is 4 dB higher than type-1 devices in this figure, it is clear that interference from type-2 traffic (plus-marked curve) is the most limiting factor.

![Validation of analytical and simulation results. Device distribution: $K$=$2$, $\lambda_1$=0.19, $ \lambda_2$=3.8, $\upsilon_1$=1200, $\upsilon_2$=30, $P_1$=21 dBm, and $P_2$=25 dBm. []{data-label="val"}](Figs/Sim/fig_cov.eps){width="3.5in"}

[0.5]{} ![Optimized operation control ($K=2, \lambda_2$=2.4, $\lambda_1$=2.4 in Sc1 and $\lambda_1$=1.2 in Sc2). In circle-marked curves, $n_1=1$ and $P_1$ is varying. In plus-marked curves, $P_1=126$ mW and $n_1$ is varying. []{data-label="oo"}](Figs/Sim/opt_oper2.eps "fig:"){width="3.5in"}

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Fig. \[oo\] represents the interplay among success 