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Workload Frequency Scaling Law: Derivation and Verification


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Many processors expose performance-monitoring counters that help measure 'productive performance' associated with workloads. Productive performance is typically represented by scale factor, a term that refers to the extent of stalls compared with stall-free cycles within a time window. The scale factor of workload is also influenced by clock frequency as selected by frequency-selection governors. Hence, in a dynamic voltage/frequency scaling or DVFS system (such as Intel Speed Shift1), the utilization, power, and performance outputs are also functions of the scale factor and its variations. Some governance algorithms do treat the scale factor in ways that are native to their governance philosophy.

This article presents equations that relate to workload utilization scaling at a per-DVFS subsystem level. A relation between frequency, utilization, and scale factor (which itself varies with frequency) is established. The verification of these equations turns out to be tricky, since inherent to workload, the utilization also varies seemingly in an unspecified manner at the granularity of governance samples. Thus, a novel approach called histogram ridge trace is applied. Quantifying the scaling impact is critical when treating DVFS as a building block. Typical application includes DVFS governors and/or other layers that influence utilization, power, and performance of the system. The scope here though, is limited to demonstrating well-quantified and verified scaling equations.


 

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