Optimal Priority Assignment Algorithms for Probabilistic Real-Time Systems

In this paper we investigate the problem of optimal priority assignment in fixed priority pre-emptive single processor systems where tasks have probabilistic execution times. We identify three sub-problems which optimise different metrics related to the probability of deadline failures. For each sub-problem we propose an algorithm that is proved optimal. The first two algorithms are inspired by Audsley’s algorithm which is a greedy (lowest priority first) approach that is optimal in the case of tasks with deterministic execution times. Since we prove that such a greedy approach is not optimal for the third sub-problem, we propose a tree search algorithm in this case.