# Multiservice Loss Models in Single or Multi-Cluster C-RAN Supporting Quasi-Random Traffic
## 1 Introduction  
The cloud radio access network (C-RAN) architecture is considered to be a promising and, at the same time, cost-effective solution to face the increasing wireless traffic as well as the soaring demand for enhanced data rate and decreased latency [1, 2]. In the C-RAN, a base station is separated into two different parts: (a) the radio frequency components and the antenna which form the so-called remote radio head (RRH) that is in charge of the signal's transmission/reception (e.g., modulation, analog-to-digital and digital-to-analog conversion, as well as power amplification) and (b) the baseband unit (BBU) which is in charge of the baseband signal processing and the communication with the core network. To guarantee, via the C-RAN architecture, quality of service (QoS) to the mobile users (MUs), it is necessary to deploy, in remote sites, many RRHs of certain radio resource units (RRUs) and at the same time form a pool of BBUs, often located in a cloud data center. Such a pooling reduces the baseband processors as well as the power consumption and the overall operators' capital/operational expenditures [3, 4]. Among other advantages of BBU pooling, we mention the possibility of many operators sharing the same BBU pool as well as the more convenient BBU addition/upgrade compared to traditional RAN [5, 6]. To benefit from network function virtualization (NFV) [7], we adopt the case of virtualizedBBU computational resources (V-BBU) connected to the RRHs assuming a large capacity and low-latency fronthaul, under the common public radio interface (CPRI) [8]. Various important C-RAN architectural aspects have been studied during the last years, including (a) capacity demands and possible functional splits of the fronthaul network [9; 10; 11], (b) security and/or privacy challenges [12; 13], (c) cost and/or energy-saving issues [14; 15; 16; 17], and (d) network slicing issues [18; 19; 20]. At the same time, very few papers exist in the literature (to the best of our knowledge) that investigate call admission control (CAC) and propose efficient formulas for the call blocking probabilities (CBP) computation [21; 22; 23; 24; 25; 26; 27; 28]. Such CBP formulas are always desirable by telecom companies as they are not computationally complex and therefore can be considered when networks should be dimensioned. In [21], a cluster of RRHs is studied where all RRHs have the same RRUs capacity. Calls have the same resource requirements and therefore they form a single service class while their arrival process in the RRHs is Poisson. More specifically, a call requires two different resource units (RUs): a computational one (we name it CRU) from the V-BBU and a RRU from the (serving) RRH. If these RUs are available, then the call is serviced for a service time which can be generally distributed. Otherwise, the call is blocked and lost. This single-class-single-cluster (SC-SC) model has a product form solution (PFS) which is essential for the accurate (compared to simulation) CBP computation. The SC-SC model has been extended in [22; 23] to include the case of overlapping cells and in [24] to include the case of grouping the RRHs in many clusters, according to their RRUs capacity. Due to this particular feature, we name the model proposed in [24], single-class-multi-cluster (SC-MC) model. The SC-SC has been extended in [27] to include the case of RRHs serving quasi-random traffic, i.e., traffic generated by a finite number of MUs. We name the model of [27] finite SC-SC (f-SC-SC). Later, in [25], the SC-SC model was further extended to include the case of RRHs serving a mixture of quasi-random, random, and batched Poisson traffic, where calls arrive in the network as batches which follow a Poisson process [29; 30]. The SC-MC model has been extended in [28] to accommodate quasi-random traffic and the model was named f-SC-MC. It was also further extended in [26] to include the case of RRHs serving a mixture of quasi-random, random, and batched Poisson traffic.