  We consider the problem of online dynamic power management that provides hard
real-time guarantees. In this problem, each of the given jobs is associated
with an arrival time, a deadline, and an execution time, and the objective is
to decide a schedule of the jobs as well as a sequence of state transitions on
the processors so as to minimize the total energy consumption.
  In this paper, we examine the problem complexity and provide online
strategies to achieve energy-efficiency. First, we show that the competitive
factor of any online algorithm for this problem is at least 2.06. Then we
present an online algorithm which gives a 4-competitive schedule. When the
execution times of the jobs are unit, we show that the competitive factor
improves to 3.59. At the end, the algorithm is generalized to allow a trade-off
between the number of processors we use and the energy-efficiency of the
resulting schedule.
