Schedulability analysis of dependent probabilistic real-time tasks

The complexity of modern architectures has increased the timing variability of programs (or tasks). In this context, new approaches based on probabilistic methods are proposed to decrease the pessimism by associating probabilities to the worst case values of the programs (tasks) time execution. In this paper, we extend the original work of Chetto et al. [7] on precedence constrained tasks to the case of tasks with worst case execution times described by probability distributions. The precedence constraints between tasks are defined by acyclic directed graphs and these constraints are transformed in appropriate release times and deadlines. The new release times and deadlines are built using new maximum and minimum relations between pairs of probability distributions. We provide a probabilistic schedulability condition based on these new relations.