Slow Down & Sleep for Profit in Online Deadline Scheduling
Abstract
We present and study a new model for energyaware and profitoriented scheduling on a single processor. The processor features dynamic speed scaling as well as suspension to a sleep mode. Jobs arrive over time, are preemptable, and have different sizes, values, and deadlines. On the arrival of a new job, the scheduler may either accept or reject the job. Accepted jobs need a certain energy investment to be finished in time, while rejected jobs cause costs equal to their values. Here, power consumption at speed $s$ is given by $P(s)=s^{\alpha}+\beta$ and the energy investment is power integrated over time. Additionally, the scheduler may decide to suspend the processor to a sleep mode in which no energy is consumed, though awaking entails fixed transition costs $\gamma$. The objective is to minimize the total value of rejected jobs plus the total energy. Our model combines aspects from advanced energy conservation techniques (namely speed scaling and sleep states) and profitoriented scheduling models. We show that \emph{rejectionoblivious} schedulers (whose rejection decisions are not based on former decisions) have  in contrast to the model without sleep states  an unbounded competitive ratio w.r.t\text{.} the processor parameters $\alpha$ and $\beta$. It turns out that the worstcase performance of such schedulers depends linearly on the jobs' value densities (the ratio between a job's value and its work). We give an algorithm whose competitiveness nearly matches this lower bound. If the maximum value density is not too large, the competitiveness becomes $\alpha^{\alpha}+2e\alpha$. Also, we show that it suffices to restrict the value density of lowvalue jobs only. Using a technique from \cite{Chan:2010} we transfer our results to processors with a fixed maximum speed.
 Publication:

arXiv eprints
 Pub Date:
 September 2012
 arXiv:
 arXiv:1209.2848
 Bibcode:
 2012arXiv1209.2848K
 Keywords:

 Computer Science  Data Structures and Algorithms
 EPrint:
 An extended abstract of this paper has been accepted for publication in the proceedings of the 1st Mediterranean Conference on Algorithms