Multi-access edge computing provides computation and network resources in proximity to user applications in mobile environments. Deploying edge servers in network boundary can not only offload the heavy task loading on the cloud, but also alleviate resource-limited capabilities of mobile devices. Rather than many stand-alone edge servers, the concept of multi-server edge computing is recently advocated to contend with the issues of system scalability and service quality against dynamic task workload. This study exploits collaborative computing resources and designs a task migration strategy for multiple edge servers in mobile networks. This study formulates a queueing optimization problem of minimizing the overall service time in a multi-server system. An intelligent task migration scheme is then developed using the deep reinforcement learning and Q-learning techniques. With a variety of numerical attributes derived from the queueing model, this intelligent scheme can arrange the task distribution among edge servers to enhance the task processing capability. Simulation-based results show that the proposed task migration scheme can sustain service efficiency and resource utilization, which is promising as compared with conventional designs without collaborative intelligence in mobile environments.