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In this paper we analyze the impact of memory hierarchies on time-energy trade-off in parallel computations. Contemporary computing systems have deep memory hierarchies with significantly different speeds and power consumptions. This results in nonlinear phenomena in the processing time and energy usage emerging when the size of the computation is growing. In this paper the nonlinear dependence of the time and energy on the size of the solved problem is formalized and verified using measurements in practical computer systems. Then it is applied to formulate a problem of minimum time and minimum energy scheduling parallel processing of divisible loads. Divisible load theory is a scheduling and performance model of data-parallel applications. Mathematical programming is exploited to solve the scheduling problem. A trade-off between energy and schedule length is analyzed and again nonlinear relationships between these two criteria are observed. Further performance analysis reveals that energy consumption and schedule length are ruled by a complex interplay between the costs and speeds of on-core and out-of-core computations, communication delays, and activating new machines.

Time and Energy Performance of Parallel Systems with Hierarchical Memory