Isoefficiency Maps for Divisible Computations

In this paper, we propose a new technique of presenting performance relationships in parallel processing. Performance of parallel processing is a hard matter with many counterintuitive phenomena. It is relatively easy to obtain some numerical indicators of the performance using various performance models. However, it is far more difficult to comprehend the nature of the analyzed problem. To facilitate understanding the performance relationships, we propose a new visualization technique based on the concept of isoefficiency. In this paper, isoefficiency is represented as a relation on points in the space of system parameters for which efficiency of parallel processing is equal. We visualize this relation on two-dimensional maps analogously to isobars and isotherms on weather maps. This concept is applied to depict the performance relationships in two standard performance laws: Amdahl's speedup law and Gustafson's speedup law. Then, we use isoefficiency maps to analyze the performance relationships in divisible load processing. Divisible load model conforms with data-parallel computations in an environment with communication delays. The results we obtain give interesting insights into relationships existing in parallel processing.