## 1 Introduction
### Related Works  
The BS assignment problem in mobile communication systems has been widely studied in the literature. Different approaches that range from greedy-based to heuristic-based algorithms have been proposed in the literature [12; 13; 14]. Two significant categories for the design and deployment of the BS assignment algorithms are identified in [15], namely the centralized and distributed approaches. On the one hand, in the centralized approach, as illustrated in Figure 1a, a single entity (e.g., radio network controller in 3 GPP networks) is responsible for collecting the complete network state information and the resource demands from all devices in the system to solve the BS assignment problem. On the other hand, in the distributed approach that is illustrated in Figure 1b, each BS interacts with mobile devices and autonomously takes assignment decisions. Clearly, this latter approach implies lower implementation complexity and reduced signaling cost than the centralized solution and, hence, it is more suitable to large networks and ultra-dense network deployments [16]. In Table 1, we present a summary of the most relevant centralized and distributed BS assignment algorithms proposed in the literature so far. The related works are analyzed in terms of the modeling framework used to tackle the problem and the underlying mechanism that steers each related work's assignment process. It is also highlighted the considered resource constraints at BSs, the device types (HTC, MTC), and the simulation setup from a system and device perspective. As surveyed in [15], the vast majority of existing BS assignment algorithms in the literature assume a centralized control. For instance, the works in [17; 18; 19; 20; 21; 22; 23] propose centralized heuristic algorithms in order to iteratively solve the BS assignment approach for the support of HTC devices in a single-cell network scenario with overlaid small-cells and radio/backhaul resource constraints. However, such solutions are not appropriate for distributed RAN deployments where decision making mechanisms, such as the BS assignment process, are located at the BS. We refer interested readers to [15] for a detailed analysis of centralized approaches. The rest of this section describes the distributed solutions, which is the main focus of this paper. In [23], the joint optimization of the BS assignment and backhaul resource allocation is studied in a HetNet scenario. A heuristic algorithm is proposed, which iteratively performs the assignment process. The work presented in [24] proposes a distributed pricing-based algorithm to solve the BS assignment problem, where a coordinate descent scheme is employed to update prices per resource unit. The authors in [25] also follow a pricing scheme, but the gradient descent method is used in order to update prices in the network. The authors in [26; 27] study the BS assignment problem following pricing deployments, where the price per resource unit is updated according to interference and load conditions at BS. A common drawback of the previously described approaches is that they neglect potential backhaul constraints in the RAN, which implies that the user association is mainly driven by radio conditions and might result in unfeasible assignments from the backhaul viewpoint in scenarios where the backhaul capacity is the primary resource bottleneck (i.e., BSs with insufficient backhaul capacity to handle the aggregated data at the air interface). Besides, the described works do not consider machine type communication devices from the IoT ecosystem.