Systems in many safety-critical application domains are subject to certification requirements. For any given system, however, it may be the case that only a subset of its functionality is safety-critical and hence subject to certification, the rest of the functionality is non safety critical and does not need to be certified, or is certified to a lower level of assurance. An algorithm called EDF-VD (for Earliest Deadline First with Virtual Deadlines) is described for the scheduling of such mixed-criticality task systems. Analyses of EDF-VD significantly superior to previously-known ones are presented, based on metrics such as processor speedup factor (EDF-VD is proved to be optimal with respect to this metric) and utilization bounds. © 2012...