Software-defined Networking (SDN) is a new network architecture that decouples the control plane from the data plane. Scalability of the control plane with respect to network size and update frequency is an important problem that has been addressed by previous studies from a variety of viewpoints. However, the solutions found in these studies may be only locally optimized solutions. To find a globally optimized solution, a broader viewpoint is required: one in which various SDN architectures can be evaluated and compared. In this paper, we propose an abstract model of SDN architectures, which enables multiple SDN architectures to be compared under a unified evaluation condition, and discuss the modeling of SDN architecture and its variations to find the optimal design from a global viewpoint. We first propose a generic model of SDN architectures and derive variations in terms of composition unit (single or multiple), processing principle (sequential or parallel), or location (intra- or inter-node). We then show that existing SDN architectures can be represented as one of the variations of our abstract model with fitted parameters. Finally we discuss how variation of components affects performance and show, using message-driven simulations, that our model enables comprehensive performance comparisons of different SDN designs represented as parameterized models.