Mobile Edge Computing (MEC) has been recognized as one of the key emerging technologies in the evolution towards 5G cellular wireless networks. In this paper, we present an application-specific MEC architecture that applies the concept of software-defined data plane to Mobile Virtual Network Operators (MVNOs) network. We first characterize the flow properties of popular mobile applications with data trace collected from the MVNO network connecting customized smartphones that enable us to identify applications and devices with 100% accuracy. We then develop an application-specific MEC processing to optimize MVNO network through applying different MEC services to different mobile applications. As a case study of application-specific MEC optimization, we present a theoretical analysis of the optimal number of TCP connections per mobile user and develop a mobile-friendly optimization mechanism to achieve fairness between tethering and smartphone users by regulating the concurrent TCP connections.