# An Efficient Dynamic Load Balancing Scheme Based on Nash Bargaining in SDN
## 1 Introduction
[16] proposed a switch migration-based decision-making scheme, which considered the load balancing degree and migration cost and achieved a compromise between the two performance indicators. Since the dimensions of the two performance indicators are not consistent, it is impossible to obtain the same degree of optimization. The authors in [17] proposed a heuristic approach considering the benefits of the immigration and outmigration controllers. [PERSON] et al. [18] proposed a load balancing scheme based on multi-objective optimization for a software-defined network. Using a multi-objective genetic algorithm based on NSGA-II, two conflicting objectives (i.e., the load balancing degree of the control plane and the communication overhead caused by switch migration) were optimized simultaneously to obtain a high-quality and wide Pareto frontier. However, the genetic algorithm has weak convergence and can only obtain a set of non-inferior solutions. This previous article does not suggest how to choose the optimal solution. According to the current research, switch migration as an elastic control scheme can effectively solve the problem of the unbalanced load distribution of controllers in a network. By moving the switch managed by the overload controller to the light-load controller, the dynamic load adjustment of the controllers can be realized. However, in the research on switch migration, most of the schemes still have the following problems:  
* Although the existing switch migration schemes can dynamically adjust the controller load, in the process of switch migration, network performance and migration cost are not fully considered, resulting in low migration efficiency and easily leading to the rigidity of the selection of the target controller. At the same time, the high complexity migration algorithm and multi-switch migration conflict also reduce the resource utilization of the controller. * The migration strategy is too idealized to consider the connectivity between the network's topological nodes, and the influence of isolated nodes on network performance is neglected. * Based on the above multi-objective optimization problem, it is impossible to weigh the contradictory goals fairly, and the multi-objective intelligent optimization algorithm cannot obtain the optimal solution. This paper proposes an efficient load balancing scheme based on Nash bargaining (LBSNB). Firstly, the switch migration problem is equivalent to the network remapping problem. Based on the Nash bargaining game model, two contradictory indicators, load balance degree and migration cost, are modeled and the connectivity between network devices is considered to build the policy set, which prevents an idealized reconstruction state. Then, an improved firefly algorithm is proposed to solve the model. Finally, experiments are carried out based on simulated scenarios and compared with other optimization algorithms. The experimental results show that the proposed algorithm can fairly balance the load balancing degree and migration costs and can quickly obtain a Pareto optimal solution, which verifies the effectiveness of the proposed strategy. The rest of the paper is organized as follows: Section 2 presents the model and the problem formulation of switch migration. The LBSNB schemes proposed in this paper are explained in Section 3. In Section 4, the optimization algorithm for solving the model is proposed. In Section 5, multiple scenarios, experiments, and analyses are carried out. Finally, we conclude the paper and suggest future work in Section 6.