Fifth-generation (5G) and beyond networks are envisioned to serve multiple emerging applications having diverse and strict quality of service (QoS) requirements. To meet ultra-reliable and low latency communication, real-time data processing and massive device connectivity demands of the new services, network slicing and edge computing, are envisioned as key enabling technologies. Network slicing will prioritize virtualized and dedicated logical networks over common physical infrastructure and encourage flexible and scalable networks. On the other hand, edge computing offers storage and computational resources at the edge of networks, hence providing real-time, high-bandwidth, low-latency access to radio network resources. As the integration of two technologies delivers network capabilities more efficiently and effectively, this paper provides a comprehensive study on edge-enabled network slicing frameworks and potential solutions with example use cases. In addition, this article further elaborated on the application of machine learning in edge-sliced networks and discussed some recent works as well as example deployment scenarios. Furthermore, to reveal the benefits of these systems further, a novel framework based on reinforcement learning for controller synchronization in distributed edge sliced networks is proposed.

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