## 3 System Model and Assumptions
### 5G C-RAN Architecture Model and Resource Allocation
Therefore, the number of RBs available for data transmission is equal to the total number of RBs minus the reserved RBs of control transmission and signaling overhead, represented as \(R-R_{con}\). Table 3 describes the equations used to calculate the number of virtually reserved RBs for the slices. Table 4 describes the parameters and notation of the system. In our network model, the RBs were divided into three virtual partitions: \(R_{1}\), \(R_{2}\), and \(R_{3}\). The \(R_{1}\) RBs were allocated to URLLC slices, \(R_{2}\) RBs were allocated to eMBB slices, and \(R_{3}\) RBs were allocated to mMTC slices, where \(R_{1}+R_{2}+R_{3}=R\). The resource allocation for each slice was dynamically predefined according to the slice priority ratio. \begin{table}
\begin{tabular}{c c} \hline \hline
**Symbol** & **Description** \\ \hline \hline Number of virtual reserved RBs for all user of the URLLC slice & \(R_{v}^{1}=P_{URLLC}\times R\) \\ \hline Number of virtual reserved RBs for all user of the eMBB slice. & \(R_{v}^{2}=P_{eMBB}\times R\) \\ \hline Number of virtual reserved RBs for all user of the mMTC slice. & \(R_{v}^{3}=P_{mMTC}\times R\) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Description of symbols and notations. \begin{table}
\begin{tabular}{c c} \hline \hline
**Description** & **Equation** \\ \hline \hline Number of virtual reserved RBs for all user of the URLLC slice & \(R_{v}^{1}=P_{URLLC}\times R\) \\ \hline Number of virtual reserved RBs for all user of the eMBB slice. & \(R_{v}^{2}=P_{eMBB}\times R\) \\ \hline Number of virtual reserved RBs for all user of the mMTC slice. & \(R_{v}^{3}=P_{mMTC}\times R\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Equations for calculating the number of virtually reserved RBs. In our network model, users were categorized into three slices denoted by i slice type (where URLLC slice \(i=1\), eMBB slice \(i=2\), and mMTC slice \(i=3\)). Therefore, we used three types of slice requests. We assumed that URLLC slice requests would have the highest priority, which is calculated using a priority ratio denoted as \(P_{URLLC}\). The eMBB slice requests were assumed to be mid-priority, as determined by a priority ratio denoted as \(P_{eMBB}\). The mMTC slice requests were assumed to have the lowest priority, which was calculated using a priority ratio denoted as \(P_{mMTC}\) Where \(0<P_{URLLC}<1\), \(0<P_{eMBB}<1\), and \(0<P_{mMTC}<1\), respectively. We assumed that all the slice requests would follow a Poisson arrival process with mean rates of \(\lambda_{i}\) (\(\lambda_{1}\), \(\lambda_{2}\), and \(\lambda_{3}\), respectively) [24]. The system arrival rate was calculated as follows:  
\[\lambda=\sum_{i=1}^{i=3}\lambda_{i} \tag{1}\]  
There were three queues for the aggregated slice requests where each slice request \(i\) has its own slice queue (\(Q_{i}\)). The queuing time limit of each slice request was denoted as \(MTD_{i}\), which was dependent on the slice QoS requirements. Each slice's request \(i\) had a negative exponential service time (connection time) with mean rates of \(1/\mu_{i}\). The generated load of each slice requests type \(i\), denoted as \(\rho^{i}\), is given by:  
\[\rho^{i}=\mu_{i}^{-1}\lambda_{i} \tag{2}\]  
The total traffic intensity for the system, denoted by \(\rho\), is given by:  
\[\rho=\sum_{i=1}^{i=3}\mu_{i}^{-1}\lambda_{i} \tag{3}\]  
An important feature in our network model is the call admission control (CAC), which decides whether to accept or reject a new call request based on the number of current RBs. The CAC denies a call request if the available RBs are insufficient for the proposed request. It controls the number of users in each slice of the 5G C-RAN to guarantee the QoS requirements of the slices [11]. The CAC first determines the total number of currently active RBs (the total current cell load), denoted as \(R_{c}\), and the required number of RBs (new load increment) from request \(i\) denoted as \(\Delta R_{i}\).