Quasi-Static Scheduling of Communicating Tasks

Good scheduling policies for distributed embedded applications are required for meeting hard real time constraints and for optimizing the use of computational resources. We study the

quasi-static scheduling

problem in which (uncontrollable) control flow branchings can influence scheduling decisions at run time. Our abstracted task model consists of a network of sequential processes that communicate via point-to-point buffers. In each round, the task gets activated by a request from the environment. When the task has finished computing the required responses, it reaches a pre-determined configuration and is ready to receive a new request from the environment. For such systems, we prove that determining existence of quasi-static scheduling policies is undecidable. However, we show that the problem is decidable for the important sub-class of “data branching” systems in which control flow branchings are due exclusively to data-dependent internal choices made by the sequential components. This decidability result—which is non-trivial to establish—exploits ideas derived from the Karp and Miller coverability tree [8] as well as the existential boundedness notion of languages of message sequence charts [6].