The application of network slicing to mobile edge computing (MEC) systems has aroused great interests from both academia and industry. However, the optimization of network slicing and MEC in most existing research works only focuses on resource slicing, energy scheduling, and power allocation from the perspective of mobile devices, without considering the operator's revenue. In this paper, we propose a novel framework for network slicing in MEC systems, including slice request admission and a revenue model, to investigate the operator's revenue escalation problem while considering traffic variations. The revenue model is mainly composed of the longer-term revenue and short-term revenue. Particularly, we jointly optimize slice request admission in the long-term and resource allocation in the short-term to maximize the operator's average revenue. By employing the Lyapunov optimization technique, we develop an algorithm without requiring any prior-knowledge of traffic distributions, referred to as the DNSRA, to solve the problem. To reduce the computational complexity of directly solving the DNSRA, we decouple the optimization variables for efficient algorithm design. By this, the strategies for user association and CPU-cycle frequency are obtained in closed forms, respectively. Power allocation and subcarriers assignment are obtained by employing the successive convex approximation approach. Meanwhile, we develop a heuristic algorithm to obtain the dynamic slice request admission decision. Simulation results show that the proposed DNSRA can strike a flexible balance between the average revenue and the average delay, and can significantly increase the operator's revenue against existing schemes.