Although many solutions have been proposed from both industry and academia, pricing the Internet services is still an ongoing research problem for researchers. In this paper, we propose an optimal pricing scheme for inter-AS traffic requests with QoS made by customers in Software Defined Networks (SDNs). This pricing scheme exploits the Nash bargaining problem which aims to maximize benefits of both service providers and customers. We integrate a new cost function and network connectivity degree factor into the proposed pricing scheme. Also, we give a general scheme of revenue and profit that a service provider makes. This scheme employs the idea of penalty for each request that a service provider cannot provide for its customers. Furthermore, we apply these schemes in our scalable hierarchic architecture with extensive experiments.