Optimal speed profile of a DVFS processor under soft deadlines

We consider a Dynamic Voltage and Frequency Scaling (DVFS) processor executing jobs with obsolescence deadlines: A job becomes obsolete is removed from the system if it not completed before its deadline. The objective to design dynamic speed policy for that minimizes average energy consumption plus an cost per deadline miss. Under Poisson arrivals exponentially distributed deadlines sizes, we show this problem can be modeled as continuous time Markov decision process (MDP) unbounded state space rates. While MDP admits optimality equation cost, standard uniformization approach applicable. Inspired by scaling method introduced Blok Spieksma, first define family of truncated MDPs then optimal profiles are increasing in number uniformly bounded constant. Finally, these properties inherited original (infinite) system. proposed upper bound on profile tight used develop extremely simple accurately approximates heavy traffic conditions.