# Game Theory-Based Load-Balancing Algorithms for Small Cells Wireless Backhaul Connections +
## 2 Materials and Methods
### Problem Formulation and System Model
#### 2.1.2 User Clustering in Multi-AP Scenarios  
In some circumstances, there could be available several small cells to which the users can connect. For example, several small cells could be deployed in a building, or several APs could be installed in a train to which the users can connect. In this case, the users' access also should be controlled, i.e., should be identified the user groups/clusters that will connect to each AP. This problem involves several theoretical and practical issues:  
* the user-AP link should fulfill some QoS requirements, and the simplest solution is to connect the user terminal to the closest AP or to the AP with the largest transmission power;the users should connect with higher priority to the AP having more available transmission resources on the communications tunnels established over the cellular wireless links. This is necessary to avoid the overloading of some APs, with effect over the global QoS, and for efficient usage of the resources available on the tunnels;
* the selection process of the users who connect to one of the APs should avoid the need to install supplementary software modules on the user terminals, which would complicate the control of the users' access process.  
The transmission scenario envisioned is depicted in Figure 4a. All the users are in the coverage area of AP-A and if no other AP is installed all users will connect to this AP. A second AP, AP-B, is installed, the users also being in the coverage area of this AP. The access protocol should select the users which connect to each AP, the selection being a dynamic one based on the transmission power of the APs and the available transmission resources on the communication tunnels used as backhaul connections. The available resources depend on the virtual tunnels' instantaneous capacities and the instantaneous packet and bit rates of the users' data flows. This scenario could be extended to more complex ones with more APs. For example, the train deployment scenario could include a third AP, AP-C (see Figure 4b), with only some of the users being located in the overlapping coverage areas, i.e., the AP-A: AP-B respectively the AP-A: AP-C coverage area, while all the users are located in the coverage area of AP-A. The building deployment scenario could include more APs, installed on the same or different floors of the building, and the users located in the overlapping coverage areas of several APs.  
The users' clustering algorithm could be a decentralized one, when no central control unit is employed, or could be a centralized one when an AP Controller module is used. The presence of this module does not raise significant technical issues, the APs being part of an infrastructure network, of a building, or of a vehicle, that could integrate such a control module. The AP Controller module also could be one of the APs acting as a master.  
It should be noted that, if several APs are used the available communication tunnels will be divided between the APs, each AP selecting several users that can be served with the resources available on the allocated virtual tunnels. The number of communication tunnels is fixed, the tunnels being leased from the macro cell operators by the train or building operator, and this fixed number of tunnels should be divided between the installed APs, the users being also split between the installed APs.