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We consider the problem of energy-efficient on-line scheduling for slice-parallel video decoders on multicore systems with Dynamic Voltage Frequency Scaling (DVFS) enabled processors. In the past, scheduling and DVFS policies in multi-core systems have been formulated heuristically due to the inherent complexity of the on-line multicore scheduling problem. The key contribution of this paper is that we rigorously formulate the problem as a Markov decision process (MDP), which simultaneously takes into account the on-line scheduling and per-core DVFS capabilities; the power consumption of the processor cores and caches; and the loss tolerant and dynamic nature of the video decoder. The objective of the MDP is to minimize long-term power consumption subject to a minimum Quality of Service (QoS) constraint related to the decoder's throughput. We evaluate the proposed on-line scheduling algorithm in Matlab using realistic video decoding traces generated from a cycle-accurate multiprocessor ARM simulator.