# Game Theory-Based Load-Balancing Algorithms for Small Cells Wireless Backhaul Connections +
## 3 Results
### Simulation Results and Discussions  
#### 3.3.1 Evaluation of the Proposed LB Algorithm over Parallel Virtual Tunnels  
Four tunnels are set up in four different cellular networks in the evaluation scenario considered (see Figure 1), and 50 data flows are generated by the users connected to the small cell AP. We consider that the cellular networks belong to different operators, and they are independent and assign uncorrelated transfer rates to the tunnels. The considered channel and shadowing model is the urban environment model defined in [46]. The considered traffic mixture [44] of the data flows is defined in Table 2. The performance indicator which is monitored is the evolution in time of the delays suffered by the packets of the transmitted flows when different LB algorithms are used, i.e., the proposed LB algorithms and the considered reference LB algorithms. The used traffic mixture is a relevant and balanced one with 50% percent real-time traffic and 50% best effort traffic. A high percentage of real-time traffic will not be relevant for the assessment of the developed LB algorithm due to the relatively low bit rates of these traffic types, which will generate an underuse of the tunnels' transfer capacities and the delay requirements will be fulfilled without any problems. A high percentage of best effort traffic, with a relatively large expected average rate \(R_{i}^{\alpha\
u}\), will generate an overload of the tunnels and an increase in the delays inserted by the transmission system, no matter which LB algorithm is used. Figure 10 presents the Probability Density Functions (pdf) (Figure 10a) and the Cumulative Density Functions (cdf) (Figure 10b) of the delays suffered by the transmitted packets in the simulated transmission system when the proposed, GT-based LB algorithms, respectively when the reference LB algorithms are used. As expected, the delays experienced by the transmitted packets are the largest in the case of the Round Robin LB algorithm. This algorithm does not consider the statistics of the data flows and the quality of the transmission links over which the tunnels are instantiated. Due to this, the requested transfer rate on a given tunnel could become larger than the instantaneous capacity with a high probability, and this will lead to large delays of the packets waiting in the queues. Figure 10: Statistical characterization of the packet delays inserted by the considered LB algorithms: (**a**) The pdfs of the packet delays; (**b**) The cdfs of the packet delays. Using the Selfish Routing LB algorithm each packet should choose a tunnel where the expected delay is minimal but the frequent tunnel changes generate a high amount of signaling traffic. In this case, the number of the generated signaling packets was comparable with the number of payload packets, and this high overhead overloads the tunnels leading to significant delays. In the scenario when the signaling overhead is neglected (or at least significantly reduced) the experienced packet delays are much lower than in the previous case when the signaling overhead is considered. Even in this case, the social cost of the Nash equilibrium is higher than that of the optimal solution due to the lack of coordination (the price of anarchy). This loss in performance relative to the optimal solution is because in each time instance more packets could choose a given tunnel where apparently the delay conditions are the best, overloading the tunnel, thus generating temporary congestion on it, while other tunnels have free capacity. Reducing the signaling overhead can be achieved by routing several consecutive packets on the same tunnel, i.e., dealing with flows instead of individual packets. The Auction-based LB algorithms ensure the best performance because they dynamically adapt the traffic on the tunnels according to the changes in the transmission links parameters.