This study explores a model of a multilinear queueing system (QS) with channel switching under uncertainty, where the statistical characteristics of the homogeneous Markov chain, which governs the transition probabilities of the environment from state to state, remain unknown. The application of neural networks and the Q-learning algorithm, specifically Deep Q-Networks (DQN), is proposed to effectively control such a system. This approach leverages the capability of neural networks to approximate the optimal policy in complex environments, thereby enhancing the decision-making process in the face of uncertainty. The performance of several reinforcement learning algorithms is compared, highlighting the advantages of using DQN in this context. The results demonstrate that DQN can significantly improve the system’s adaptability and efficiency, providing a robust solution for control multilinear queueing systems under uncertain conditions.