Task and Machine Heterogeneities: Higher Momenets Matter

One type of heterogeneous computing (HC) systems consists of machines with diverse capabilities harnessed together to execute a set of tasks that vary in their computational complexity. An HC system can be characterized using an Estimated Time to Compute (ETC) matrix. Each value in this matrix represents the ETC of a specific task on a specific machine when executed exclusively. Heuristics use the values in the ETC matrix to allocate tasks to machines in the HC system. The performance of resource allocation heuristics can be affected significantly by factors such as task and machine heterogeneities. Therefore, quantifying heterogeneity will allow a system to select a heuristic appropriate for the given heterogeneous environment. In this paper, we identify different central moments used to quantify the heterogeneity of ETC matrices obtained from real world systems and benchmark data, and show the effect of these moments on the performance of heuristics both through simple examples and simulations.