Slow Down and Sleep for Profit in Online Deadline Scheduling

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) = s α  + 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.