Stochastic analysis of energy consumption in pool depletion systems

The evolutions of digital technologies and software applications have introduced a new computational paradigm that involves initially the creation of a large pool of jobs followed by a phase in which all the jobs are executed in systems with limited capacity. For example, a number of libraries have started digitizing their old books, or video content providers, such as YouTube or Netflix, need to transcode their contents to improve playback performances. Such applications are characterized by a huge number of jobs with different requests of computational resources, like CPU and GPU. Due to the very long computation time required by the execution of all the jobs, strategies to reduce the total energy consumption are very important. In this work we present an analytical study of such systems, referred to as pool depletion systems, aimed at showing that very simple configuration parameters may have a non-trivial impact on the performance and especially on the energy consumption. We apply results from queueing theory coupled with the absorption time analysis for the depletion phase. We show that different optimal settings can be found depending on the considered metric.