On a certain class of power- and energy-related scheduling problems

We consider problems of power and energy allocation to computational jobs performed on identical processors, where jobs may be performed with different speeds. Each job requires for its execution a processor as well as an amount (unknown in advance) of electrical power. Power is a continuous, doubly-constrained resource whose consumption over time is represented by energy. The amount of power allocated to a job is nonlinearly related to a particular speed of the job. Jobs are preemptable and independent, and all are available at the start of the process. Two general types of scheduling problems are considered: laptop problems, where the objective is to minimize the schedule length subject to power and/or energy constraints, and server problems, where power usage or energy consumption is to be minimized subject to a given schedule deadline. We present formulations of the analyzed problems, as well as methodologies for solving them for the cases of parallel processors and a single processor.