In this paper, we introduce a new technique for modeling and solving the dynamic power management (DPM) problem for systems with complex behavioral characteristics such as concurrency, synchronization, mutual exclusion and conflict. We model a power-managed distributed computing system as a controllable Generalized Stochastic Petri Net (GSPN) with cost. The obtained GSPN model is automatically converted to an isomorphic continuous-time Markov decision process. Given the delay constraints, the optimal power management policy for system components as well as the optimal dispatch policy for requests are calculated by solving a linear programming problem on the Markov decision process. Experimental results show that the proposed technique can achieve more than 20% power saving compared to other existing DPM techniques.