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In high performance computing environments, we observe an ongoing increase inthe available numbers of cores. This development calls for re-emphasizingperformance (scalability) analysis and speedup laws as suggested in theliterature (e.g., Amdahl's law and Gustafson's law), with a focus on asymptoticperformance. Understanding speedup and efficiency issues of algorithmicparallelism is useful for several purposes, including the optimization ofsystem operations, temporal predictions on the execution of a program, and theanalysis of asymptotic properties and the determination of speedup bounds.However, the literature is fragmented and shows a large diversity andheterogeneity of speedup models and laws. These phenomena make it challengingto obtain an overview of the models and their relationships, to identify thedeterminants of performance in a given algorithmic and computational context,and, finally, to determine the applicability of performance models and laws toa particular parallel computing setting. In this work, we provide a genericspeedup (and thus also efficiency) model for homogeneous computingenvironments. Our approach generalizes many prominent models suggested in theliterature and allows showing that they can be considered special cases of aunifying approach. The genericity of the unifying speedup model is achievedthrough parameterization. Considering combinations of parameter ranges, weidentify six different asymptotic speedup cases and eight different asymptoticefficiency cases. Jointly applying these speedup and efficiency cases, wederive eleven scalability cases, from which we build a scalability typology.Researchers can draw upon our typology to classify their speedup model and todetermine the asymptotic behavior when the number of parallel processing unitsincreases. In addition, our results may be used to address various extensionsof our setting.

Speedup and efficiency of computational parallelization: A unifying approach and asymptotic analysis