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We present strategies for "online" dynamic power management (DPM) based on the notion of the competitive ratiothat allows us to compare the effectiveness of algorithmsagainst an optimal strategy. This paper makes two contributions:it provides a theoretical basis for the analysis of DPMstrategies for systems with multiple power down states; andprovides a competitive algorithm based on probabilisticallygenerated inputs that improves the competitive ratio overdeterministic strategies. Experimental results show that ourprobability-based DPM strategy improves the efficiency ofpower management over the deterministic DPM strategy by25%, bringing the strategy to within 23% of the optimal offlineDPM.