Abstract Workload measurements in enterprise systems often lead to observe a dependence between the number of requests running at a resource and their mean service requirements. However, multiclass performance models that feature these dependences are challenging to analyze, a fact that discourages practitioners from characterizing workload dependences. We here focus on closed multiclass queueing networks and introduce QD-AMVA, the first approximate mean-value analysis (AMVA) algorithm that can efficiently and robustly analyze queue-dependent service times in a multiclass setting. A key feature of QD-AMVA is that it operates on mean values, avoiding the computation of state probabilities. This property is an innovative result for state-dependent models, which increases the computational efficiency and numerical robustness of their evaluation. Extensive validation on random examples, a cloud load-balancing case study and comparison with a fluid method and an existing AMVA approximation prove that QD-AMVA is efficient, robust and easy to apply, thus enhancing the tractability of queue-dependent models.