With the goal of meeting the stringent throughput and delay requirements of classified network flows, we propose a Deep Q-learning Network (DQN) for optimal weight selection in an active queue management system based on Weighted Fair Queuing (WFQ). Our system schedules flows belonging to different priority classes (Gold, Silver, and Bronze) into separate queues, and learns how and when to dequeue from each queue. The neural network implements deep reinforcement learning tools such as target networks and replay buffers to help learn the best weights depending on the network state. We show, via simulations, that our algorithm converges to an efficient model capable of adapting to the flow demands, producing thus lower delays with respect to traditional WFQ.