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In this paper we address the problem of dynamic power management in a distributed multimedia system with a required quality of service (QoS). Using a generalized stochastic Petri net model where the non-exponential inter-arrival time distribution of the incoming requests is captured by the "stage method", we provide a detailed model of the power-managed multimedia system under general QoS constraints. Based on this mathematical model, the power-optimal policy is obtained by solving a linear programming problem. We compare the new problem formulation and solution technique to previous dynamic power management techniques that can only optimize power under delay constraints. We then demonstrate that these other techniques yield policies with higher power dissipation by over-constraining the delay target in an attempt to indirectly satisfy the QoS constraints. In contrast, our new method correctly formulates the power management problem under QoS constraints and obtains the optimal solution.