Volume of the Internet traffic has increased significantly in recent years. Service providers (SPs) are now striving to make resource management and considering dynamically changing large volume of network traffic. In this context, software defined networking (SDN) has been alluring the attention of SPs, as it provides virtualization, programmability, ease of management, and so on. Yet severe scalability issues are one of the key challenges of the SDN due to its centralized architecture. First of all, SDN controller may become the bottleneck as the number of flows and switches increase. It is because routing and admission control decisions are made per flow basis by the controller. Second, there is a signaling overhead between the controller and switches since the controller makes decisions on behalf of them. In line with the aforementioned explanations, this paper proposes an SDN-based scalable routing and resource management model (SRRM) for SPs. The proposed model is twofold. SRRM performs routing, admission control, and signaling operations (RASOs) in a scalable manner. Additionally, resource management has also been accomplished to increase link use. To achieve high degree of scalability and resource use, pre-established paths (PEPs) between each edge node in the domain are provided. The proposed controller performs RASOs based on PEPs. The controller also balances the load of PEPs and adjusts their path capacities dynamically to increase resource use. Experimental results show that SRRM can successfully perform RASOs in a scalable way and also increase link use even under heavy traffic loads.