Performance modelling for task-parallel programs

Many applications from scientific computing and physical simulations can benefit from a mixed task and data parallel implementation on parallel machines with a distributed memory organization, but it may also be the case that a pure data parallel implementation leads to faster execution times. Since the effort for writing a mixed task and data parallel implementation is large, it would be useful to have an a priori estimation of the possible benefits of such an implementation on a given parallel machine. In this article, we propose an estimation method for the execution time that is based on the modelling of computation and communication times by runtime formulas. The effect of concurrent message transmissions is captured by a contention factor for the specific target machine. To demonstrate the usefulness of the approach, we consider a complex method for the solution of ordinary differential equations with a potential for a mixed task and data parallel execution. As distributed memory machine we consider the Cray T3E and a Linux cluster.