Static Fault-Tolerant Real-Time Scheduling with "Pseudo-topological" Orders

We give a graph-theoretical model for off-line fault-tolerant scheduling of dataflow algorithms onto multiprocessor architectures with distributed memory. Our framework allows the modeling of both processor and communication channel failures of the “fail silent” type (either transient or permanent), and failure masking is achieved by replicating operations and data communications. We show that, in general, the graph representing a fault-tolerant scheduling may have circuits; hence, the classical computation of starting and ending times of the operations and communications, based upon a topological order, is inapplicable. We thus provide a notion of “pseudo-topological order” that permits the computation of the starting and ending times even in the case of cyclic graphs. We also derive algorithms for computing the timeouts that are used for failure detection.