  We present several competitive ratios for the online busy time scheduling
problem with flexible jobs. The busy time scheduling problem is a fundamental
scheduling problem motivated by energy efficiency with the goal of minimizing
the total time that machines with multiple processors are enabled. In the busy
time scheduling problem, an unbounded number of machines is given, where each
machine has $g$ processors. No more than $g$ jobs can be scheduled
simultaneously on each machine. A machine consumes energy whenever at least one
job is scheduled at any time on the machine. Scheduling a single job at some
time $t$ consumes the same amount of energy as scheduling $g$ jobs at time $t$.
In the online setting, jobs are revealed when they are released.
  We consider the cases where $g$ is unbounded and bounded. In this paper, we
revisit the bounds of the unbounded general setting from the literature and
tighten it significantly. We also consider agreeable jobs. For the bounded
setting, we show a tightened upper bound. Furthermore, we show the first
constant competitive ratio in the bounded setting that does not require
lookahead.
