Computing First-to-First Propagation Delays through Sequences of Fixed-Priority Periodic Tasks

We examine the problem of computing the worst-case first-to-first information propagation delay through a sequence of fixed-priority periodic tasks with different periods. This propagation delay is the span of time from the moment information becomes available until the first time the final task in the sequence produces an output that uses this (or more recent) input. We consider task systems in which all tasks are initially ready for execution, and the periods are harmonically related. We give efficient algorithms for computing this delay for the special cases in which the task priorities in the sequence are either monotonically decreasing or monotonically increasing. We then show how to combine these algorithms to compute an upper bound for the case in which priorities are ordered arbitrarily.