# Game Theory-Based Load-Balancing Algorithms for Small Cells Wireless Backhaul Connections +
## 3 Results
### Simulation Results and Discussions
#### 3.3.3 Evaluation of the Proposed User Clustering Algorithms  
The evaluation of the user clustering algorithms was performed in the same conditions as the evaluation of the LB algorithms, meaning that the number of users and the traffic mix considered is the same. The scenarios considered are those presented in Figure 4, i.e., the scenario with the deployment of 2 APs and the scenario with the deployment of 3 APs. The APs are located at fixed distances \(D\), \(D\) = 100 m in the simulations performed, and the users are spread uniformly between the 2 or the 3 APs. The traffic types are randomly distributed among the users, but the imposed traffic mix is maintained (see Table 2). To simplify the simulations, it is considered that to each AP it is attached a single virtual tunnel, which could be the aggregation of several separate virtual tunnels. The transfer rate of these aggregated tunnels originating in the APs was simulated as in the case of the evaluation of the LB algorithms, the same traffic models being used. The parameters of the channel models were selected to obtain approximately the same average transfer rate on each aggregated tunnel (approximately 20 Mbps). The step used to adjust the power of the APs was set to 1 dB in some experiments and 2 dB in other experiments, but no significant difference can be identified between the results obtained in these two cases. In all scenarios, the statistics of the delays suffered by the transmitted packets are evaluated. Figure 14 presents the pdf of the packet delays in the system (the sojourn time) in the scenario with two APs and the following cases:  
* the two APs work separately, and no user clustering algorithm is used. The clustering of the users is performed only at the beginning of the simulation by attaching each user to the AP from which it receives the largest power-see Figure 14a. * a non-cooperative type of user clustering is used, each AP adjusting its transmission power only based on its local QSI and CSI-see Figure 14b. * a cooperative user clustering algorithm is used, each AP having access to the QSI and CSI of other APs or being controlled by an AP Controller who has access to all APs' QSI and CSI. If the controller is used this module implements the AP cooperation process and sets the transmission power of each APs-see Figure 14c. Figure 14 presents separately the pdf of the delay suffered by the transmitted packets on the two tunnels and the pdf of the delays suffered by all the packets transmitted by the system, meaning the pdf on the combined tunnel used by the system. The results presented in Figure 14 show the effects of the LB performed by the clustering algorithms among the APs. If no clustering is used most of the users might be attached to one of the APs, one of the outgoing aggregated tunnels being heavily loaded (red curve  
Figure 14: Statistical characterization of the packet delays on the aggregated virtual tunnels when 2 APs and different user clustering algorithms are used: (**a**) The pdfs of the packet delays when no user clustering algorithm is used; (**b**) The pdfs of the packet delays when the non-cooperative user clustering algorithm is used; (**c**) The pdfs of the packet delays when the cooperative user clustering algorithm is used. in Figure 14a) while the other tunnel (the blue curve in Figure 14a) is underused. If any of the clustering algorithms are used the difference in the traffic loads on the two aggregated tunnels becomes significantly smaller. To better assess the statistics of the delays suffered by the data packets on the two aggregated tunnels in the considered situations the cdf of the packet's delays is presented in Figure 15.  
The results presented in Figure 15 show clearly the huge difference in performance, in what concerns the packet delays, of the systems with no users clustering (Figure 15a) and with user clustering (Figure 15b,c). Comparing Figure 15b,c we can see the difference between the non-cooperative and the cooperative clustering algorithms.