To meet the real-time requirement of the edge computing applications, technologies of software defined network and network function virtualization are introduced to reconstruct the edge computing network. On this basis, we consider the design of online computing and communication resource allocation method, aiming at maximizing the longterm average probability of successfully processing the real-time tasks. By establishing a Markov decision process framework, an online resource allocation method based on Q-learning is proposed. Nevertheless, Q-learning occupies a lot of memory when the state action space is large, and it is prone to dimensional disasters. Therefore, a DQN-based online resource allocation method is proposed. Simulation results show that both proposed algorithms converge quickly and the average probability of successfully processing the real-time tasks achieved by the DQN algorithm is the highest among all the baseline algorithms.