rate at the IoT device’s associated RRH and $SIN{R_s}(t)$ is the signal-to-interference-plus-noise ratio (SINR).

Then, for any active IoT device in $s$, its QoS requirement is given by $$\label{eq:mMTC_QoS}
    P_s(t)  \ge {\pi _s}, \forall s \in {\mathcal{S}^I}$$ where $\pi_s$ denotes a threshold of the required RA success probability.

This definition shows that the QoS requirement of each active IoT device in $s$ should be satisfied if the slice request of $s$ is accepted. The definition also states that $P_{s}{(t)}$ is correlated with the non-empty probability $P_{ne,s}{(t)}$. Recall that the RA success probability of an IoT device impacts its non-empty probability, we can know that the RA success probability and the non-empty probability are intertwined. Additionally, $SIN{R_s}(t)$ is a function of complicated co-channel interference. Thus, it is hard to obtain the closed-form expression of $P_{s}{(t)}$.

Without any loss in generality, we perform the analysis of RA success probability on an RRH located at the origin. According to Slivnyak’s theorem [@haenggi2012stochastic], the analysis holds for a generic RRH located at a generic location. For a randomly selected IoT device with non-empty queue in $s \in \mathcal{S}^I$, the theoretical preamble transfer rate experienced at the RRH located at the origin can take the 