Speedup and scalability analysis of Master–Slave applications on large heterogeneous clusters

Although cluster environments have an enormous potential processing power, real applications that take advantage of this power remain an elusive goal. This is due, in part, to the lack of understanding about the characteristics of the applications best suited for these environments. This paper focuses on Master/Slave applications for large heterogeneous clusters. It defines application, cluster and execution models to derive an analytic expression for the execution time. It defines speedup and derives speedup bounds based on the inherent parallelism of the application and the aggregated computing power of the cluster. The paper derives an analytical expression for efficiency and uses it to define scalability of the algorithm–cluster combination based on the isoefficiency metric. Furthermore, the paper establishes necessary and sufficient conditions for an algorithm–cluster combination to be scalable which are easy to verify and use in practice. Finally, it covers the impact of network contention as the number of processors grow.