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An increasing trend in embedded system design is to integrate components with different levels of criticality into a shared hardware platform for better cost and power efficiency. Such mixed-criticality systems are subject to certifications at different levels of rigorousness, for validating the correctness of different subsystems on various confidence levels. The realtime scheduling of certifiable mixed-criticality systems has been recognized to be a challenging problem, where using traditional scheduling techniques may result in unacceptable resource waste. In this paper we present an algorithm called PLRS to schedule certifiable mixed-criticality sporadic tasks systems. PLRS uses fixed-job-priority scheduling, and assigns job priorities by exploring and balancing the asymmetric effects between the workload on different criticality levels. Comparing with the state-of-the-art algorithm by Li and Baruah for such systems, which we refer to as LB, PLRS is both more effective and more efficient:(i) The schedulability test of PLRS not only theoretically dominates, but also on average significantly outperforms LB’s.(ii) The run-time complexity of PLRS is polynomial (quadratic in the number of tasks), which is much more efficient than the pseudo-polynomial run-time complexity of LB.