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In this paper, we explore the use of multi-agent deep learning as well as learning to cooperate principles to meet stringent service level agreements, in terms of throughput and end-to-end delay, for a set of classified network flows. We consider agents built on top of a weighted fair queuing algorithm that continuously set weights for three flow groups: gold, silver, and bronze. We rely on a novel graph-convolution based, multi-agent reinforcement learning approach known as DGN. As benchmarks, we propose centralized and distributed deep Q-network approaches and evaluate their performances in different network, traffic, and routing scenarios, highlighting the effectiveness of our proposals and the importance of agent cooperation. We show that our DGN-based approach meets stringent throughput and delay requirements across all scenarios.