Real-time systems are increasingly running a mix of tasks with different criticality levels: for instance, unmanned aerial vehicle has multiple software functions with different safety criticality levels, but runs them on a single, shared computational platform. In addition, these systems are increasingly deployed on multiprocessor platforms because this can help to reduce their cost, space, weight, and power consumption. To assure the safety of such systems, several mixed-criticality scheduling algorithms have been developed that can provide mixed-criticality timing guarantees. However, most existing algorithms have two important limitations: they do not guarantee strong isolation among the high-criticality tasks, and they offer poor real-time performance for the low-criticality tasks.