Revisiting the bicriteria (length,reliability) multiprocessor static scheduling problem

Our starting point is a dependency task graph and an heterogeneous distributed memory target architecture. We revisit the well studied problem of bicriteria (length,reliability) multiprocessor static scheduling of this task graph onto this architecture. Our first criteria remains the static schedule's length: this is crucial to assess the system's real-time property. For our second criteria, we consider the global system failure rate, seen as if the whole system were a single task scheduled onto a single processor, instead of the usual reliability, because it does not depend on the schedule length like the reliability does (due to its computation in the classical reliability model of Shatz and Wang). Therefore, we control better the replication factor of each individual task of the dependency task graph given as a specification, with respect to the desired failure rate. To solve this bicriteria optimization problem, we take the failure rate as a constraint, and we minimize the schedule length. We are thus able to produce, for a given application task graph and multiprocessor architecture, a Pareto curve of non-dominated solutions, among which the user can choose the compromise that fits his requirements best.