2012/09/13 by Peter Kling, Kling, Peter, Andreas Cord-Landwehr +3
Computer Science · #Cloud Computing and Resource Management #Data Structures and Algorithms (cs.DS) #FOS: Computer and information sciences #Parallel Computing and Optimization Techniques #Stochastic Gradient Optimization Techniques #cs.DS
paper · pdf · doi:10.48550/arxiv.1209.2848
An extended abstract of this paper has been accepted for publication in the proceedings of the 1st Mediterranean Conference on Algorithms
arxiv created 2012/09/13 · openalex publication_date 2012/09/13 · arxiv updated 2012/09/14 · openalex created_date 2022/09/02 · openalex updated_date 2026/07/28
We present and study a new model for energy-aware and profit-oriented 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)=sα+β 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 γ. 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 profit-oriented scheduling models. We show that rejection-oblivious 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. the processor parameters α and β. It turns out that the worst-case 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 αα+2eα. Also, we show that it suffices to restrict the value density of low-value jobs only. Using a technique from \citeChan:2010 we transfer our results to processors with a fixed maximum speed.