One benefit of partitionable parallel processing systems is their ability to execute multiple, independent tasks simultaneously. Previous work has identified conditions such that, when there are k tasks to be processed, partitioning the system so that all k tasks are processed simultaneously results in a mininium overall execution time. An alternate condition is developed that provides additional insight into the effects of parallelism on execution time. This result, and previous results, however, assume that execution times are data independent. It is shown that data-dependent tasks do not necessarily execute faster when processed simultaneously even if the condition is met. A model is developed that provides for the possible variability of a task′s execution time and is used in a new framework to study the problem of finding an optimal mapping for identical, independent data-dependent execution time tasks onto partitionable systems. Executing one, some, or all of the k tasks simultaneously is considered. Because this new framework is general, it can also serve as a new method for the study of data-independent tasks. Extension of this framework to situations where the k tasks are nonidentical is discussed. © 1993 Academic Press, Inc.