Statistical predictors of computing power in heterogeneous clusters

If cluster C₁ consists of computers with a faster mean speed than the computers in cluster C₂, does this imply that cluster C₁ is more productive than cluster C₂? What if the computers in cluster C₁ have the same mean speed as the computers in cluster C₂: is the one with computers that have a higher variance in speed more productive? Simulation experiments are performed to explore the above questions within a formal framework for measuring the performance of a cluster. Simulation results show that both mean speed and variance in speed (when mean speeds are equal) are typically correlated with the performance of a cluster, but not always; these statements are quantified statistically for our simulation environments. In addition, simulation results also show that: (1) If the mean speed of computers in cluster C₁ is faster by at least a threshold amount than the mean speed of computers in cluster C₂, then C₁ is more productive than C₂. (2) If the computers in clusters C₁ and C₂ have the same mean speed, then C₁ is more productive than C₂ when the variance in speed of computers in cluster C₁ is higher by at least a threshold amount than the variance in speed of computers in cluster C₂.