Program Scalability Analysis for HPC Cloud: Applying Amdahl's Law to NAS Benchmarks

The availability of high performance computing (HPC) clouds requires scalability analysis of parallel programs for multiple different environments in order to maximize the promised economic benefits. Unlike traditional HPC application performance studies that aim to predict performances of like-kind processors, this paper reports an instrumentation assisted complexity analysis method based on Amdahl's Law framework for program scalability analysis for different HPC environments. We show that program instrumentation helps Gustafson's scaled speedup formulation to quantify the elusive quality in Amdahl's Law. We report that without separating communication time from computing, prediction results are not trustworthy. We demonstrate a methodology that can transform asymptotic complexity models to timing models in order to separate communication time and to identify the optimal degree of parallelism. A traditional HPC cluster and a private HPC cloud are used to validate the proposed methodology by showing the feasibility of optimal parallel processing and by scalability analysis of five NAS benchmarks. Our results show that either cloud or cluster can be effectively exploited if the application can adapt to changing processing conditions dynamically. As we dig deeper into the performance analysis myths, “scalability limit” seems to mean less than its common interpretation but more on the inadequacy our programming habits and architecture support.