Probabilistic Analysis of Low-Criticality Execution

The mixed-criticality toolbox promises system architects a powerful framework for consolidating real-time tasks with different safety properties on a single computing platform. Thanks to the research efforts in the mixed-criticality field, guarantees provided to the highest criticality level are well understood. However, lower-criticality job execution depends on the condition that all high-criticality jobs complete within their more optimistic low-criticality execution time bounds. Otherwise, no guarantees are made. In this paper, we add to the mixed-criticality toolbox by providing a probabilistic analysis method for low-criticality tasks. While deterministic models reduce task behavior to constant numbers, probabilistic analysis captures varying runtime behavior. We introduce a novel algorithmic approach for probabilistic timing analysis, which we call symbolic scheduling. For restricted task sets, we also present an analytical solution. We use this method to calculate per-job success probabilities for low-criticality tasks, in order to quantify, how low-criticality tasks behave in case of high-criticality jobs overrunning their optimistic low-criticality reservation.