# 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
The Combinatorial Auction based LB algorithm over-performs the other considered algorithms because it permanently monitors the QoS performance and the system's changes, and it maximizes both the user's and the system's revenue (measured by the level of satisfaction or the cost function). The Auction-based LB algorithm also has good performance, the difference between the two GT-based algorithms not being significant, at least at low packet delays. The reference Multiple Knapsack algorithm has lower performance than the auction-based algorithms and ensures comparable performance with the ideal Selfish Routing LB algorithm with no or low overhead. Figure 11 presents separately the pdfs and the cdfs of the delays suffered by the transmitted packets in the simulated transmission system when the Auction-based LB algorithm, the Combinatorial Auction-based LB algorithm and the Selfish Routing LB algorithm with no penalty are used, respectively when the reference Multiple Knapsack LB algorithm is used (these are the best algorithms identified in Figure 10). The presented results show clearly that the Combinatorial Auction algorithm has the best performance, i.e., it inserts the smallest delays with the highest probabilities, and the Auction-based LB algorithm also has good performance. Both algorithms have significantly better performance, i.e., smaller delays with higher probabilities and larger delays with lower probabilities, compared to the Multiple Knapsack algorithm and the Selfish Routing LB algorithm with no signaling penalty. Even if all algorithms have polynomial complexity, the highest processing resources are requested by the Combinatorial Auction-based algorithm followed by the Multiple Knapsack and the Auction-based LB algorithms. The Combinatorial Auction-based algorithm has the highest computational complexity due to the continuous monitoring of the potential functions and the instantaneous call throughput, while the other two algorithms (mentioned above) must evaluate only the instantaneous call throughput. Another important issue that must be considered is how well can handle the proposed and tested LB algorithms the real-time flows. The distributions of the packet delays presented in Figures 10 and 11 do not make any difference between the different traffic types, being characterized the entire traffic mix. In the case of the real-time type data flows (see Appendix A) the interpacket delays are typically situated between 0 and 40-60 ms. In the case of VoIP flows the interpacket delay is 20 ms, the maximum allowed value of interpacket delays for video traffic is 12.5 ms and for gaming the interpacket delays are requested to be smaller than 40 ms, a 60 ms delay being considered an outage. The values of the packet delay cdfs of the algorithms considered in Figure 11 are presented in Table 3, for a better comparison of these values. The results presented in Table 3 show clearly that only the Combinatorial Auction-based LB algorithm can ensure with high probability (in the considered scenario) the delays requested by the considered real-time applications. The Combinatorial Auction-based LB algorithm computes the potential functions for each traffic flow and checks continuously if the QoS parameters can be ensured on each tunnel and if not, the data flows are redistributed. The Selfish Routing and the Auction-based LB algorithms do not consider separately the different types of flows and do not check the fulfillment of the QoS requirements after the routing decision is taken. The Multiple Knapsack LB algorithm assigns different priorities for different types of flows and routes first the flows with higher priority, but it takes the routing decisions only based on average flow rates and average tunnel capacities. The results presented in Figure 8 and Table 1 show that the wireless tunnels' capacities could change significantly in time having as consequence the possible (significant) increase of the sojourn time.