Nowadays, a paradigm shift in mobile computing has been introduced by the ever-increasing heterogenous terminal devices, from the centralized mobile cloud towards the mobile edge. Multi-access edge computing (MEC) emerges as a promising ecosystem to support multi-service and multi-tenancy. It takes advantage of both mobile computing and wireless communication technologies for cloud-network integration. However, the physical hardware constraints of the terminal devices, along with the limited connection capacity of the wireless channel pose numerous challenges for cloud-network integration. The incapability of control over all the possible resources (e.g., computation, communication, cache) becomes the main hurdle of realizing delay-sensitive and real time services. To break this stalemate, this article investigates a software-defined fine-grained multi-access architecture, which takes full control of the computation and communication resources. We further investigate a Q-Learning based two-stage resource allocation strategy to better cater the heterogenous radio environments and various user requirements. We discuss the feasibility of the proposed architecture and demonstrate its effectiveness through extensive simulations.