power-law path-loss model to calculate the path-loss between an IoT device and its RRH in mIoT slices and utilize a truncated channel inversion power control scheme to eliminate the ’near-far’ effect. In the power-law path-loss model, the IoT device transmit power decays at the rate of $r^{-{\varphi}}$ with $r$ representing the propagation distance and $\varphi$ denoting the path-loss exponent. In the power control scheme, IoT devices associated with the same RRH compensate for the path-loss to maintain the average received signal power at the RRH equal to a threshold $\rho_o$. Without loss of generality, the cutoff threshold $\rho_o$ is set to be the same for all RRHs. Owing to the channel deep fading, severe co-channel interference, and insufficient transmit power, an IoT device may experience uplink preamble transmission outage. The following definition describes the definition of the probability that a randomly selected IoT device can successfully transmit a chosen preamble to its corresponding RRH.

\[mydef:preamble\_trans\_suc\_prob\] At minislot $t$, for a randomly selected active IoT device in slice $s \in \mathcal{S}^I$, its RA success probability is defined as $$\label{eq:preamble_trans_suc_prob}
    P_{s}{(t)} = {\mathbb P}\{r_s(t) \ge \gamma_s^{th}\}, \forall s \in {\mathcal{S}^I}$$ where $r_s(t) = a{\log _2}(1 + SIN{R_s}(t))$ denotes the achieved preamble transfer 