Scheduling periodic task graphs with communication delays

We consider the problem of finding an optimal assignment of tasks, which constitute a parallel application, to an unlimited number of identical processors. The precedence constraints among the tasks are given in the form of a directed acyclic graph (DAG). We are given processing times for each task and the communication delays between precedence-constrained tasks, which are incurred if the corresponding tasks are executed on different processors. Furthermore, the system must be able to process real-time periodic input with a fixed period. This problem occurs, for example, in multiprocessor scheduling of video processing applications, where each frame has to be processed by a number of software filters, and some filters use data pre-processed by other filters, thus forming a DAG of data dependencies. We formulate several variants of this problem, and briefly discuss some of our results for special precedence graphs.