Abstract : In this paper, we consider a probabilistic model for real-time task systems with probabilistic worst-case execution times, probabilistic minimum inter-arrival times and probabilistic deadlines. We propose an analysis computing response time distributions of the tasks scheduled on one processor under a task-level fixed-priority preemptive scheduling policy. The complexity of our method is analyzed and it is improved by re-sampling techniques on worst-case execution time distributions and/or minimal inter-arrival time distributions. The improvements are shown through experimental results. Also, experiments are conducted in order to investigate the improvement obtained by using a probabilistic model in terms of precision and schedulability gained as opposed to a deterministic worst-case reasoning.