as follows.

\[def:IoT\_slice\_definition\] A mIoT slice request is defined as a tuple $\{\lambda_s^I, \gamma_s^{th}, N_{a,s}\}$ for any slice $s \in {\mathcal S}^I$, where $\gamma_s^{th}$ is the requirement of data transfer rate from an IoT device in $s$ to its associated RRH, $N_{a,s}$ denotes the number of accumulated packets in a queue of an IoT device in $s$.

In this paper, all mIoT slice requests are always accepted by the RAN slicing coordinator. IoT devices with the same data transfer rate are assigned to the similar slice. For an IoT device in $s$, if it has the opportunity to send its endogenous arrival packets to the corresponding RRH, then it will randomly select a preamble (e.g., orthogonal Zadoff¨CChu sequences) from a BBU-maintained preamble pool and transmit the preamble to the RRH at the data rate $\gamma_s^{th}$. Just like the literature [@soorki2017stochastic; @gharbieh2017spatiotemporal], if the RRH can successfully decode the preamble, then a connection between the IoT device and the RRH are considered to be set up although the whole connection establishment process usually follows an RA four-step procedure [@grau2019preamble]. In other word, the RA success probability is regarded as the probability of successfully transmitting a preamble in this paper. Next, we 