# Game Theory-Based Load-Balancing Algorithms for Small Cells Wireless Backhaul Connections +
## 3 Results
### The Architecture of the Simulation Platform Used for the Evaluation of the LB Algorithms
#### 3.1.2 The Wireless Channel Simulator Module
AP selection or handover based on the received power level is one of the most common and simplest ways of selecting an attachment point to a wireless network and this solution is used on large scale also in cellular networks. The users are randomly distributed between the deployed APs and the distances between the users and each AP are computed. Based on the distances the attenuation on the user-AP links and the power received by the users are computed according to Equation (29). \[ \begin{gathered} a_{user-AP}(d)[dB]=a_{s}(d_{0})[dB]+10\cdot n \cdot\lg\frac{d}{d_{0}}\\ a_{s}(d_{0})=\left(\frac{4\pi\cdot d_{0}}{\lambda}\right)^{2}\\ P_{user}=P_{AP}-a_{user-AP}\end{gathered}  \tag{29}\]  
where \(d_{0}\) is the reference distance and is considered 1 m (it depends on the size of the cell), \(n\) gives the slope of the attenuation characteristic and is considered 2.5, but it depends on the simulated wireless propagation scenario and \(\lambda\) is the wavelength-the carrier frequency was considered 2.4 GHz. \begin{table}
\begin{tabular}{c c c c c} \hline
**Tunnel** & **Max/Min** & **Mean** & **Median** & **Std.** \\ \hline
1–red & 24/14.5 Mbps & 20.15 Mbps & 21.25 Mbps & 2.85 Mbps \\
2–blue & 18.5/14.25 Mbps & 16.5 Mbps & 16.5 Mbps & 1.15 Mbps \\
3–cyan & 14.75/1.5 Mbps & 6.5 Mbps & 5.75 Mbps & 4 Mbps \\
4–green & 8.5/5.25 Mbps & 6.75 Mbps & 6.75 Mbps & 0.925 Mbps \\ \hline \end{tabular}
\end{table} 
Table 1: Statistical parameters of the considered 4 virtual tunnels. \begin{table}
\begin{tabular}{c c c} \hline
**Traffic Type** & **Traffic Mixture** & **LB Parameter** \\ \hline VoIP & 20\% & \\ Video streaming & 20\% & \(c_{i}=5\) ms \\ Online gaming & 10\% & \\ Web browsing-HTTP & 30\% & \\ File transfer-FTP & 20\% & \(R_{i}^{av}=10\) Mbps \\ \hline \end{tabular}
\end{table} 
Table 2: Simulated traffic flows parameters. The estimation of the transmission resources available on the virtual tunnels can be made based on the sojourn time \(S\), i.e., the delays suffered by the source data packets in the transmission system. To take into account the variation of the sojourn time on a larger time scale, a moving average is computed on each tunnel considering a large number of packets \(N\), i.e., several thousands of packets:  
\[S_{av\_i}=\frac{S_{i}+N\cdot S_{av\_j-1}}{N+1} \tag{30}\]  
where \(S_{av\_i}\) is the average delay at moment \(i\). Other indicators related to the available resources in the system are the number of packets stored in each buffer and the number of bytes (or bits) stored in the same buffers. These parameters combined with the sojourn time could give a more detailed picture of the available resources and allow a better clustering of the users. The clustering process of the users should be performed with a relatively low frequency to avoid frequent disconnection and reconnection of the users (the so-called 'ping-pong' effect) which could generate interruption in the transmission process and increase the signaling overhead. However, at the same time the clustering process should be performed  
Figure 9: The block diagram of the simulation platform used for the evaluation of the user clustering algorithms. frequently enough to take into account the variability of the capacities of the tunnels and the users' data flows rates. In the simulations performed the clustering process was performed at a time interval of tens of seconds, but less than 1 min. The signaling overhead on the user-AP link was not considered.