Mixed Criticality Scheduling of Probabilistic Real-Time Systems

In this paper we approach the problem of Mixed Criticality (MC) for probabilistic real-time systems where tasks execution times are described with probabilistic distributions. In our analysis, the task enters high criticality mode if its response time exceeds a certain threshold, which is a slight deviation from a more classical approach in MC. We do this to obtain an application oriented MC system in which criticality mode changes depend on actual scheduled execution. This is in contrast to classical approaches which use task execution time to make criticality mode decisions, because execution time is not affected by scheduling while the response time is. We use a graph-based approach to seek for an optimal MC schedule by exploring every possible MC schedule the task set can have. The schedule we obtain minimizes the probability of the system entering high criticality mode. In turn, this aims at maximizing the resource efficiency by the means of scheduling without compromising the execution of the high criticality tasks and minimizing the loss of lower criticality functionality. The proposed approach is applied to test cases for validation purposes.