# A Game Model and Fault Recovery Algorithm for SDN Multi-Domain
## 3 Reliability Game-Enhanced Model for SDN Multi-Domain Controllers  
To overcome the potential challenges in timely fault recovery and high-reliability operation of SDN controllers, this paper constructs a game enhancement model for SDN multi-domain controllers, providing a foundation for resolving issues related to fault detection and autonomous recovery of SDN controllers. The control plane is logically divided into multiple control domains, with each domain consisting of a local controller and several switches. The local controller is responsible only for managing the switches within its own domain, while different control domains interact and synchronize information through east-west interfaces between local controllers. If a local controller fails, the switches within its domain will lose control. Therefore, it is necessary to remap the switches in the failed controller's domain to other functioning controllers to ensure stable connectivity and high availability of the network system. To achieve the remapping between controllers and switches, the first step is to select a node that is either within the same control domain as the failed controller or in an adjacent control domain, ensuring that this node has sufficient remaining capacity. This node will serve as the new target controller, responsible for managing the control and data flows of the switches that were previously managed by the failed controller. To facilitate effective remapping, it is necessary to establish a controller game model [22]. The game domain refers to the analytical unit comprising participants and the combinations of actions they select over a specified timeframe. In the game domain, players can be either individuals or organizations, and they make decisions based on their own interests and goals. The collective actions chosen by all players during a concurrent period are defined as an action combination that reflects the decision-making outcomes of the players. The controller game domain is a temporary network decision domain that is autonomously formed as needed. When a controller failure occurs in the network, the switches within this domain will autonomously select a new controller to manage their data and control flows. The SDN-oriented controller game domain consists of a collection of out-of-control switches and controllers participating in the decision-making process. When a controller fails, the functioning controllers within the domain or adjacent domain will take over the control and management of the switches belonging to the failed controller. They will collaborate with other neighboring controllers to negotiate and determine the optimal controller mapping scheme. Definition 1: The SDN multi-domain controller network is represented as an undirected graph \(G\), as shown in Equation (1). \[G=(V,E,C,Q) \tag{1}\]  
where \(V\) represents the set of switches in the network. \(V=\{v_{1},v_{2},\ldots,v_{n}\}\), \(n=|\,V|\) is the number of switches; \(E\) denotes the set of data links in the network; and \(C\) shows the set of controllers. \(C=\{c_{1},c_{2},\ldots,c_{m}\}\), \(m=|\,C|\) is the number of controllers; \(Q\) indicates the set of control domains. \(Q=\left\{\langle c_{1}^{i},v_{c_{1}^{j}}^{j}\,\rangle_{1}\,\langle c_{2}^{i},v _{c_{2}^{j}}^{j}\,\rangle_{2},\ldots,\langle c_{q}^{i},v_{c_{q}^{i}}^{j}\, \rangle_{q}\right\}\), \(q\) signifies the number of control domains. \(\langle c_{k}^{i},v_{c_{k}^{i}}^{j}\,\rangle_{k}\) denotes that the \(k\)-th control domain consists of the mapping from the controller set \(c_{k}^{i}\) to the switch set \(v_{c_{k}^{i}}^{j}\), where \(k\) represents the current domain number and \(j\) indicates the number of switches managed by the controller indexed by \(i\) within the current control domain. To fully leverage the characteristics and performance of switches and controllers in SDN, while also considering the requirements for load balancing and fault tolerance within the network, a hybrid mapping approach is adopted between switches and controllers.