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A mixed-criticality real-time system is a real-time system having multiple tasks classified according to their criticality. Research on mixed-criticality systems started to provide an effective and cost efficient a priori verification process for safety critical systems. The higher the criticality of a task within a system and the more the system should guarantee the required level of service for it. However, such model poses new challenges with respect to scheduling and fault tolerance within real-time systems. Currently, mixed-criticality scheduling protocols severely degrade lower criticality tasks in case of resource shortage to provide the required level of service for the most critical ones. The actual research challenge in this field is to devise robust scheduling protocols to minimise the impact on less critical tasks. This dissertation introduces two approaches, one short-term and the other medium-term, to appropriately allocate computing resources to tasks within mixed-criticality systems both on uniprocessor and multiprocessor systems. The short-term strategy consists of a protocol named Lazy Bailout Protocol (LBP) to schedule mixed-criticality task sets on single core architectures. Scheduling decisions are made about tasks that are active in the ready queue and that have to be dispatched to the CPU. LBP minimises the service degradation for lower criticality tasks by providing to them a background execution during the system idle time. After, I refined LBP with variants that aim to further increase the service level provided for lower criticality tasks. However, this is achieved at an increased cost of either system offline analysis or complexity at runtime. The second approach, named Adaptive Tolerance-based Mixed-criticality Protocol (ATMP), decides at runtime which task has to be allocated to the active cores according to the available resources. ATMP permits to optimise the overall system utility by tuning the system workload in case of shortage of computing capacity at runtime. Unlike the majority of current mixed-criticality approaches, ATMP allows to smoothly degrade also higher criticality tasks to keep allocated lower criticality ones.