Necessary feasibility analysis for mixed-criticality task systems on uniprocessor

While feasibility of timing guarantees has been extensively studied for single-criticality (SC) task systems, the same cannot be said true for mixed-criticality (MC) task systems. In particular, there exist only a few studies that address necessary feasibility conditions for MC task systems, and all of them have derived trivial results from existing SC studies that rely on simple demand-supply comparison. In this paper, we develop necessary feasibility tests for MC task systems on a uniprocessor platform, which is the first study that yields non-trivial results for MC necessary feasibility. To this end, we investigate characteristics of MC necessary feasibility conditions. Due to the existence of the mode change and consequences thereof, the characteristics pose new challenges that cannot be resolved by existing techniques for SC task systems, including how to calculate demand when the mode change occurs, how to determine the target sub-intervals for demand-supply comparison, how to derive an infeasibility condition from demand-supply comparisons with different possible mode change instants, how to select a scenario to specify the mode change instant without the target scheduling algorithm, and how to find infeasible task sets with reasonable time-complexity. By addressing those challenges, we develop a new necessary feasibility test and its simplified version. The simulation results demonstrate that the proposed tests find a number of additional infeasible task sets which have been proven neither feasible nor infeasible by any existing studies.