Safety-critical real-time standards define several criticality levels for the tasks. In this paper we consider the real-time systems designed under the DO-178B safety assessment process (i.e., Software Considerations in Airborne Systems and Equipment Certification). Vestal introduced a new multiple criticality task model to efficiently take into account criticality levels in the schedulability analysis of such systems. Such a task model represents a potentially very significant advance in the modeling of safety-critical real-time softwares. Baruah and Vestal continue this investigation, with a new scheduling algorithm combining fixed and dynamic priority policies. Another major design issue is to allow a system developer to determine how sensitive is the schedulability analysis to changes in execution time of various software components.In this paper, we first prove that the well-known Audsley's algorithm is optimal for assigning priorities to tasks with multiple criticality levels. We then provide a proof on the optimality of Vestal's algorithm for optimizing the resource requirements to schedule tasks with multiple criticality levels. We then present a sensitivity analysis for multiple criticality tasks that is based on Bini et al. results on sporadic tasks.
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