An Analytical Bound for Probabilistic Deadlines

The application of a resource reservation scheduler to soft real -- time systems requires effective means to compute the probability of a deadline miss given a particular choice for the scheduling parameters. This is a challenging research problem, for which only numeric solutions, complex and difficult to manage, are currently available. In this paper, we adopt an analytical approach. By using an approximate and conservative model for the evolution of a periodic task scheduled through a reservation, we construct a closed form lower bound for the probability of a deadline miss. Our experiments reveal that the bound remains reasonably close to the experimental probability for many real -- time applications of interest.