# Multiservice Loss Models in Single or Multi-Cluster C-RAN Supporting Quasi-Random Traffic
## 2 The f-MC-SC Model  
### The Analytical Model  
Consider Figure 1 which presents the adopted C-RAN architecture where the centralized V-BBU and the RRHs are separated. There are \(W\) RRHs of capacity \(C\) RRUs which form a single cluster, justifying the abbreviation SC in the name of the model. The V-BBU can provide \(T\) CRUs to those calls that will be accepted in the system under consideration. The \(w\)-th RRH (\(w=1,\ldots,W\)) accommodates calls that may have different RUs requirements. Calls with the same RUs requirements are grouped in the same service class. Thus, calls arriving to the \(w\)-th RRH are grouped into \(S_{w}\) service classes. A call of service class \(s\) (\(s=1,\ldots,S_{w}\)) arrives to the \(w\)-th RRH according to a quasi-random process with arrival rate \(\lambda_{w,s}=(N_{w,s}-n_{w,s})v_{w,s}\), where \(N_{w,s}\) is the finite population of MUs, that use service class \(s\) and can be served by the \(w\)-th RRH, \(n_{w,s}\) is the number of in-service calls of service class \(s\) calls in the \(w\)-th RRH, and \(v_{w,s}\) is the mean call arrival rate per idle MU of service class \(s\) in the \(w\)-th RRH. An incoming call of service class \(s\) that arrives to the \(w\)-th RRH requires \(b^{r}_{w,s}\) RRUs and \(b^{c}_{w,s}\) CRUs, and we assume that \(b^{r}_{w,s}=b^{c}_{w,s}\in\mathbb{N}\). For the \(w\)-th RRH to accept an arriving service class \(s\) call, the CAC consists of two conditions: one stating that there should be enough spare RRUs in the (serving) \(w\)-th RRH, and the other stating that there should be \begin{table}
\begin{tabular}{l l} \hline \hline  & BBU & Baseband units \\ BF & Brute force \\ CAC & Call admission control \\ CBP & Call blocking probabilities \\ CC & Call congestion \\ CPRI & Common public radio interface \\ C-RAN & Cloud radio access network \\ CRUs & Computational resource units \\ f-MC-MC & Finite multi-class-multi-cluster \\ f-MC-SC & Finite multi-class-single-cluster \\ f-SC-MC & Finite single-class-multi-cluster \\ f-SC-SC & Finite single-class-single-cluster \\ MUs & Mobile users \\ NFV & Network function virtualization \\ PFS & Product form solution \\ o.d. & Occupancy distribution \\ QoE & Quality of experience \\ QoS & Quality of service \\ RRH & Remote radio head \\ RRUs & Radio resource units \\ RUs & Resource units \\ TC & Time congestion \\ V-BBU & Virtualized BBU \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Abbreviations list. enough spare CRUs in the V-BBU. That is, the \(w\)-th RRH accepts an incoming service class \(s\) call if the occupied RRUs are not more than \(C-b_{w,s}^{t}\) and the occupied CRUs in the V-BBU are not more than \(T-b_{w,s}^{c}\). If the incoming call is accepted, it remains in the \(w\)-th RRH for a generally distributed service time with mean value \(\mu_{w,s}^{-1}\). In the opposite case, the call is blocked and lost. Having defined the service time of a call, the offered traffic load per idle service class \(s\) MU (in erl), in the \(w\)-th RRH, is \(\alpha_{w,s,\text{idle}}=v_{w,s}/\mu_{w,s}\). Let \(n_{w,s}\geq 0\) be the in-service service class \(s\) calls in the \(w\)-th RRH. Then, the steady-state vector \(\mathbf{n}=(n_{1,1},\ldots,n_{1,S_{1}},\ldots,n_{w,1},\ldots,n_{w,s},\ldots,n_{w,S _{w}},\ldots,n_{W,1},\ldots,n_{W,S_{W}})\) expresses all in-service calls of all service classes in the system.