In this paper, we are concerned with scheduling a mix of high-criticality (HI) and low-criticality (LO) tasks under Earliest Deadline First (EDF) on one processor. To this end, the system implements two operation modes, LO and HI mode. In LO mode, HI tasks execute for no longer than their optimistic execution budgets and are scheduled together with the LO tasks. The system switches to HI mode, where all LO tasks are prevented from running, when one or more HI tasks run for longer than expected. Since these mode changes may happen at arbitrary points in time, it is difficult to find an accurate bound on carry-over jobs, i.e., those HI jobs that were released before, but did not finish executing at the point of the transition. To overcome this problem, we propose a technique that works around the computation of carry-over execution demand. Basically, the proposed technique separates the schedulability analysis of the transition between LO and HI mode from that of stable HI mode. We prove that a transition from LO to HI mode is feasible, if an equivalent task set derived from the original is schedulable under plain EDF. On this basis, we can apply approximation techniques such as, e.g., the well-known Devi's test to derive further tests that trade off accuracy versus complexity/runtime. Finally, we perform a detailed comparison with respect to weighted schedulability on synthetic data illustrating benefits by the proposed technique.
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