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.