Statistical predictors of computing power in heterogeneous clusters

Abstract

Abstract-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.

Characterizing heterogeneous computing environments using singular value decomposition

“…For example, to calculate MPH of the canonical ECS matrix in Figure 3, we calculate the sums of the columns. The sums are (6,8,32). The ratios are (0.75, 0.25).…”

“…An important research problem in the field of heterogeneous computing is how one can characterize and quantify the heterogeneity of a system [8]. We treat heterogeneous computing (HC) systems as those that consist of a collection of machines able to perform task types at different speeds.…”

Characterizing Task-Machine Affinity in Heterogeneous Computing Environments

“…Examples of such applications include, predicting the performance of HC environments [9], selecting appropriate heuristics to use in an HC environment based on its heterogeneity [3], "what-if studies" to identify the effect of adding/removing task types or machines from an HC system on its heterogeneity, and generating ETC matrices for simulation studies that span the entire range of heterogeneities [2]. The purpose of this paper is to provide heterogeneity measures that can be used as a standard way to compare different heterogeneous computing environments.…”

Statistical measures for quantifying task and machine heterogeneities

“…Hence, many heuristics have been developed for allocating tasks to machines in HC systems. The performance of allocation heuristics and the HC system is affected by several factors, one of which is the level of machine heterogeneity [9,13]. Therefore, quantifying the heterogeneity of a given environment will allow the selection of a heuristic that is the most appropriate.…”