## 3 System Model and Assumptions  
### 5G C-RAN Architecture Model and Resource Allocation  
This study considers radio resource allocation for network slices in the 5G C-RAN system model. Figure 1 illustrates the components of the 5G C-RAN architecture. We consider an enabled SDN/NFV 5G C-RAN where the NFV deploys a virtual BBU (vBBU) pool, shared by the three slices, in which each slice can be assigned several vBBUs based on its QoS requirements [29; 30]. The virtual centralized BBU pool can then allocate shared resources based on the dynamic traffic flows associated with each slice. We assumed a centralized C-RAN architecture with a single RRU serving three different 5G slices (uRLLC, eMBB, and mMTC) [5]. Resource allocation is implemented using new 5G radio frames that use orthogonal frequency-division multiplexing (OFDM) on both the uplink and downlink to achieve high-bandwidth channels. According to 3 GPP standards, the 5G NR uses two frequency ranges: frequency range 1 (FR1) and frequency range 2 (FR2). FR1, also known as sub-6 GHz, supports the lower- and middle-frequency bands, ranging from 450 MHz to 7.125 \(\times\) 103 MHz. It is responsible for transporting typical cellular communications traffic. FR2, also known as millimeter waves, supports higher frequency bands ranging from 24.25 GHz to 52.6 GHz and offers extremely high data rates over a short range [31]. The 5G NR uses flexible numerology, described by the parameter \(\mu\) (as defined in 3 GPP Release 15), to support a wide range of services with different QoS requirements [32]. Figure 2 shows the frame structure of the 5G NR. We considered a 5G NR radio frame with a 10-ms duration consisting of 10 each one 1-ms subframes. Each subframe is comprised of \(2^{\mu}\) slots, each with a slot length of \(1/2^{\mu}\) ms and 14 OFDM symbols [31; 33]. Table 2 shows the different numerologies of 5G NR. The number of slots in a subframe increases as the value of \(\mu\) increases, leading to a higher total number of symbols that can be sent in each amount of time. The OFDM subcarrier spacing scales to \(2^{\mu}\times 15\) kHz with different values of \(\mu=1\), 2, 3, 4 to accommodate a wide range of services with different QoS requirements. The subcarrier spacing in the sub-6 GHz band is 15 kHz, 30 kHz, and 60 kHz, whereas millimeter-wave spacing is 60 kHz and 120 kHz, with 240 kHz reserved for signaling channels. As the subcarrier spacing increases, the slot size, and the symbol duration decrease, which is useful for services with lower latency requirements [31; 33]. \begin{table}
\begin{tabular}{c c c c} \hline \(\mu\) & **Num. of Slots in a Subframe** & **Slot Time Length** & **Subcarrier Spacing** \\ \hline
0 & 1 & 1 ms & 15 kHz \\ \hline
1 & 2 & 0.5 ms & 30 kHz \\ \hline
2 & 4 & 0.25 ms & 60 kHz \\ \hline
3 & 8 & 0.125 ms & 120 kHz \\ \hline \end{tabular}
\end{table} 
Table 2: 5G NR flexible numerology [31]. Figure 1: 5G C-RAN architecture with different types of slices (e.g., URLLC, eMBB, and mMTC traffic). Figure 2: 5G NR Frame structure [31]. The resource grid is a frequency representation of radio transmission resources that maps to a single subframe in the time domain and a whole carrier bandwidth in the frequency domain. It has many transmission resources, known as resource blocks (RBs). Each RB consists of 12 subcarriers with a frequency range of 180 kHz. The RB consists of resource elements (REs), which are the smallest units of the resource grid, and each RE is defined in the frequency domain by one subcarrier [31; 34]. Resource allocation to a slice involves assigning an integer number of resource blocks with a minimum allocation of one RB. The transmission rate assigned to each slice was determined according to the number of RBs allocated. We assumed a system with a full transmission bandwidth of 20 MHz and 100 RBs. Some of the total RBs were reserved for control and signaling overhead; these are denoted by \(R_{con}\).