Analyzing Asynchronous Pipeline Schedules

Asynchronous pipelining is a form of parallelism which may be used in distributed memory systems. An asynchronous pipeline schedule is a generalization of a noniterative DAG schedule. Accurate estimation of the execution time of a pipeline schedule is needed to determine if pipelining is appropriate for a loop, and to compare alternative schedules. Pipeline execution of n iterations of a loop requires time at most a + bn, for some constants a and b. The coefficient b is the iteration interval of the pipeline schedule, and is the primary measure of the performance of a schedule. The startup time a is a secondary performance measure. We generalize previous work on determining if a pipeline schedule will deadlock, and generalize Reiter's well-known formula (1) for determining the iteration interval b of a deadlock-free schedule, to account for nonzero communication times (easy) and the assignment of multiple tasks to processors (nontrivial). Two key components of our generalization are ..