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We present an energy-efficient real-time scheduling algorithm called EUA*, for the unimodal arbitrary arrival model (or UAM). UAM embodies a "stronger" adversary than most arrival models. The algorithm considers application activities that are subject to time/utility function time constraints, UAM, and the multi-criteria scheduling objective of probabilistically satisfying utility lower bounds, and maximizing system-level energy efficiency. Since the scheduling problem is intractable, EUA* allocates CPU cycles, scales clock frequency, and heuristically computes schedules using statistical estimates of cycle demands, in polynomial-time. We establish that EUA* achieves optimal timeliness during under-loads, and identify the conditions under which timeliness assurances hold. Our simulation experiments illustrate EUA*'s superiority.