In industry there has been a large focus on system integration and server consolidation, even for real-time systems, leading to an interest in virtualization. However, many modern hypervisors do not inherently support the strict timing guarantees of real-time applications. There are several challenges that arise when trying to virtualize a real-time application. One key challenge is to maintain the guest's real-time guarantees. In a typical virtualized environment there is a hierarchy of schedulers. Past solutions solve this issue by strict resource reservation models. 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. Evaluations show that our mechanism incurs up to 21x less overhead than that of bleeding edge introspection techniques when tracing real-time events.