Probabilistic optimisation of checkpoint intervals for real-time multi-tasks

This article considers the checkpoint placement problem for real-time systems. In our environment, multiple real-time tasks with arbitrary periods are scheduled in the system by the rate monotonic algorithm, and checkpoints are inserted at a constant interval in each task while the width of the interval is different with respect to the task. We derive an explicit formula of the probability that all the tasks are successfully completed with a given set of checkpoint intervals. Then we determine the optimal checkpoint intervals that maximise the probability of task completion. The probability computation includes the schedulability analysis with respect to the numbers of re-executed checkpoint intervals. Our method does not necessitate any algebraic condition on the periods of the scheduled tasks.