Considerations on the Least Upper Bound for Mixed-Criticality Real-Time Systems

Real-time mixed-criticality systems (MCS) are designed so that tasks with different criticality levels share the same computing platform. Scheduling mechanisms must ensure that high criticality tasks are safe independently of lower criticality tasks´ behaviour. In this paper we provide theoretical schedulability properties for MCS by showing that: (a) the least upper bound on processor utilisation of MCS is in general null for both uniprocessor and multiprocessor platforms, (b) this bound lies in interval [ln 2, 2 (v2-1)] if higher criticality tasks do not have periods larger than lower criticality ones, and (c) if the task of these uniprocessor systems have harmonic periods, the least upper bound reaches 1.