Quality of Service (QoS) monitoring is an essential component in cloud computing scenarios, and its feedback results are a quantitative expression of user experience, which also determines the reusability of computing resources. Although existing deep learning-based QoS models offer high detection accuracy, their large model sizes and high deployment costs pose challenges for effective deployment in resource-constrained environments. This study proposes an Asymmetric Knowledge Distillation algorithm (AKD) tailored for QoS monitoring models, which deeply integrates domain knowledge into the entire process of model compression and distillation training, aiming to optimize both model performance and efficiency. AKD incorporates an asymmetric compression strategy, task-weighted distillation objectives, and a refined loss function design. Experimental results show that AKD can reduce model parameters by up to 94% while maintaining prediction performance, with only a 0.0008 increase in the average Mean Absolute Error (MAE). In addition, the student model reduces memory consumption by 35% and improves inference speed by an order of magnitude.