Schedulability of probabilistic mixed-criticality systems

Mixed-criticality systems often need to fulfill safety standards that dictate different requirements for each criticality level, for example given in the ‘probability of failure per hour’ format. A recent trend suggests designing this kind of systems by jointly scheduling tasks of different criticality levels on a shared platform. When this is done, the usual assumption is that tasks of lower criticality are degraded when a higher criticality task needs more resources, for example when it overruns a bound on its execution time. However, a way to quantify the impact this degradation has on the overall system is not well understood. Meanwhile, to improve schedulability and to avoid over-provisioning of resources due to overly pessimistic worst-case execution time estimates of higher criticality tasks, a new paradigm emerged where task’s execution times are modeled with random variables. In this paper, we analyze a system with probabilistic execution times, and propose metrics that are inspired by safety standards. Among these metrics are the probability of deadline miss per hour, the expected time before degradation happens, and the duration of the degradation. We argue that these quantities provide a holistic view of the system’s operation and schedulability.