# Game Theory-Based Load-Balancing Algorithms for Small Cells Wireless Backhaul Connections +
## 4 Conclusions  
The paper considers the issue of LB over several wireless links set up in a heterogeneous cellular system, wireless links which are used as backhaul connections for the AP of a small cell. The paper proposes game theory-based algorithms for distributing the data flows generated by the users connected to the AP of the small cell over the wireless links of several macro cells, possibly owned by different operators, which cover the small cell. More precisely the Selfish Routing LB algorithm, the Auction-based LB, and the Combinatorial Auction-based LB algorithms are proposed. As references, the classical Round Robin algorithm and an algorithm based on the Multiple Knapsack problem were considered. Computer simulations performed in a complex scenario involving four macro cells and a mobile AP, i.e., installed in a vehicle, and in the condition of a congested network show that the Auction-based LB and the Combinatorial Auction-based LB algorithms have the best performance, while the performance of the Selfish Routing LB algorithm is weaker than that of the reference Multiple Knapsack LB algorithm, or is similar with the performance of this reference algorithm if the signaling penalty is not considered.  
The simulations show that in the condition of congested networks the Combinatorial Auction-based LB algorithm and the Auction-based LB algorithm are capable to manage efficiently the available resources, i.e., to distribute efficiently the flows on the available tunnels, and the packets' delays can be kept below some limits. The Multiple Knapsack LB algorithm can manage well the LB operations for some reduced traffic values, and reduced packet delays are ensured with probabilities close to that obtained with the Auction-based LB algorithm. In the situation of larger (instantaneous) traffic values the performance of the Multiple Knapsack LB algorithm decreases, and larger delays appear with large probabilities, meaning that the LB operations are performed less efficiently compared to the GT-based LB algorithms. The Round Robin LB algorithm has, as expected, poor performance, large (even very large) packet delays appearing with high probabilities.  
The proposed GT-based LB algorithms are not constrained only to the data communication scenario considered by this paper. The algorithms are general enough to be adapted to other communication scenarios, involving both wireless and wired connection, when LB operations are necessary to distribute data flows over parallel communication channels/tunnels.  
The paper also proposes two game theory-based algorithms for user clustering when several small cell APs are deployed. These algorithms select the users who connect to each AP, the goal being to avoid the overloading of some APs while other neighbor APs have available resources. The proposed algorithms use a simple power adjustment-based user clustering to avoid more complex interaction and signaling between the users and the APs. The performed simulations show that even in the case of simple clustering mechanisms the load could be distributed relatively well between the deployed APs and therefore a noticeable decrease in the packets' delays on the virtual tunnels attached to the APs is visible.  
Conceptualization, Z.A.P. and M.V.; methodology, Z.A.P.; software, M.V.; validation, Z.A.P. and M.V.; formal analysis, Z.A.P.; investigation, M.V.; resources, Z.A.P.; writing--original draft preparation, Z.A.P.; writing--review and editing, Z.A.P. and M.V.; visualization, M.V.; supervision, Z.A.P. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
Data Availability Statement: Data sharing not applicable.  
The authors declare no conflict of interest.