Power consumption is one of the major concerns for high performance VLSI design. Under the well-known trade-off between power and speed performance driven by the selection supply voltage level, Voltage-Frequency Scaling (VFS) is one of the promising techniques for saving energy while keeping performance requirement. In this paper, we consider multiple tasks to be processed on a single processor with a single overall deadline, and ask how supply voltage levels are determined in the VFS environment. Our solution is derived from Karush-Kuhn-Tucker (KKT) conditions of the formulated nonlinear optimization problem, and later on, it is shown that KKT conditions correspond to a kind of energy balance between tasks, where Energy-vs-Time efficiency is shown to play an important role for voltage-frequency schedule. While the discussions done in this paper are limited for the case of single processor, they might be important bases for various DVFS models including DVFS for multiple-processor system, DVFS with limited number of voltage levels, etc.
