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These reservations are pessimistic as they accommodate the worst case execution time of each real-time task. We model real-time tasks using probabilistic execution times instead of worst case execution times which are difficult to calculate and are not representative of the actual execution times. In this thesis, we present a probabilistic hierarchical framework to schedule real-time virtual machines. Our framework reduces the number CPUs reserved for each guest by up to 45%, while only decreasing the deadline satisfaction by 2.7%. In addition, we introduce an introspection mechanism capable of gathering real-time characteristics from the guest systems and present them to the host scheduler. 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