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.