Analyzing Asynchronous Pipeline

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 coeecient 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 the use of pipeline scheduling edges, and the notion of negative data dependence distances (in a single unnested loop). We also discuss implementation of an asynchronous pipeline schedule at runtime; show how to eeciently simulate pipeline execution on a sequential processor; derive bounds on the startup time a; and discuss evaluation of the iteration interval formula, including development of a new algorithm.