  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
$P(s)=s^{\alpha}+\beta$ 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 profit-oriented scheduling models.
We show that \emph{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\text{.} the processor
parameters $\alpha$ and $\beta$. 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 $\alpha^{\alpha}+2e\alpha$. Also, we show that it
suffices to restrict the value density of low-value jobs only. Using a
technique from \cite{Chan:2010} we transfer our results to processors with a
fixed maximum speed.
