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Multimedia streaming applications running on next-generation parallel multiprocessor arrays in sub-45 nm technology face new challenges related to device and process variability, leading to performance and power variations across the cores. In this context, Quality of Service (QoS), as well as energy efficiency, could be severely impacted by variability. In this work, we propose a runtime variability-aware workload distribution technique for enhancing real-time predictability and energy efficiency based on an innovative Linear-Programming + Bin-Packing formulation which can be solved in linear time. We demonstrate our approach on the virtual prototype of a next-generation industrial multicore platform running representative multimedia applications. Experimental results confirm that our technique compensates variability, while improving energy-efficiency and minimizing deadline violations in presence of performance and power variations across the cores. The proposed policy can save up to 33 percent of energy with respect to the state-of-the-art policies and 65 percent of energy with respect to one variability-unaware task allocation policy while providing better QoS.