# An Efficient Dynamic Load Balancing Scheme Based on Nash Bargaining in SDN
## 1 Introduction  
The Software-Definition Network (SDN) [1] is an innovative network architecture. Its core technology, OpenFlow, separates the network control plane from the data plane, enabling flexible centralized control of distributed forwarding devices and providing an excellent platform for the creation of core networks and applications. With the increasing demand of the network, a large amount of data traffic is sent from a forwarding device, such as a switch, to the control plane. Traditional single-controller architecture is constrained by its own performance and capacity. It faces significant challenges in network security, reliability, and robustness [2; 3]. Therefore, industry proposes to establish a multi-controller architecture with logically centralized physical distribution based on the original single-controller architecture [4]. This architecture requires multiple controllers to be deployed on the control plane and divide the appropriate subdomain for each controller. Each controller is responsible for centrally managing switches in its domain. Multiple controllers cooperate with each other to achieve efficient network management [5; 6; 7; 8; 9]. However, multi-controller deployment is a static network architecture. Switches and controller nodes form a fixed network topology, which cannot adapt to the dynamic changes of network traffic. If the switching traffic in the domain increases or decreases sharply in a specific period of time, the load difference between controllers will be huge, which will cause a load imbalance of the multi-controller network architecture, resulting in a high packet loss rate, high latency, low throughput, and other network performance degradation problems. Load imbalance issues severely impact the performance of an entire network. Therefore, in recent years, the load balancing problem of the SDN multi-controller has become a research hotspot. [PERSON] et al. [7] proposed a multi-controller sleep model for software-defined networks, allowing some controllers to enter a sleep state under light load conditions to save system costs. Following the introduction of OpenFlow 1.3 [10], [PERSON] et al. [11] proposed an elastic distributed network architecture for the first time, changing the mapping relationship between the controllers and switches through switch migration to implement controller load transfer of the OpenFlow standard. As an elastic flow control solution, switch migration can effectively balance the load imbalance network. Based on this idea, [PERSON] et al. [12] proposed to migrate the switch to the controller with the lowest resource utilization to achieve load balancing. [PERSON] et al. [13] proposed an online load balancing method, which describes the load balancing problem as an optimization problem that minimizes the control plane's response time. Because the migration process depends on the actual response time, the scheme can be implemented online. The above studies are all based on choosing a suitable switch from the overload controller to migrate to the light-load controller to achieve load balancing. Although this method reduces the number of migrations, it easily causes load oscillations. [PERSON] et al. [14] proposed a switch group-based SDN multi-controller load balancing mechanism. This mechanism chooses a group of switches to reduce the load of the overload controller to an average level and then considers the load and delay factors of the light-load controller and transfers multiple switches to the appropriate controllers. This method not only balances the load between controllers but also solves the problem of load oscillation. [PERSON] et al. [15] proposed game theoretic switch-controller mapping with traffic variations in software-defined networks, describing the problem as a Markov decision process, reducing frequent migration between controllers and obtaining a stable mapping relationship. [PERSON] et al.