Reliability Analysis of Replicated And -

{ A computation task running in distributed systems can be represented as a directed graph H(V; E) whose vertices and edges may fail with known probabilities. In this paper, we introduce a reliability measure, called distributed task reliability, to model the reliability of such computation tasks. The distributed task reliability is deened to be the probability that the task can be successfully executed. Due to the And-Fork/And-Join constraint, the traditional network reliability problem is a special case of the distributed task reliability problem, where the former is known to be NP-hard in general graphs. For two-terminal And-Or Series-Parallel (AOSP) graphs, the distributed task reliability can be computed in polynomial time.