  This paper studies an optimal ON-OFF control problem for a class of discrete
event systems with real-time constraints. Our goal is to minimize the overall
costs, including the operating cost and the wake-up cost, while still
guaranteeing the deadline of each individual task. In particular, we consider
the homogeneous case in which it takes the same amount of time to serve each
task and each task needs to be served by d seconds upon arrival. The problem
involves two subproblems: (i) finding the best time to wake up the system and
(ii) finding the best time to let the system go to sleep. We study the two
subproblems in both off-line and on-line settings. In the off-line case that
all task information is known a priori, we combine sample path analysis and
dynamic programming to come up with the optimal solution. In the on-line
scenario where future task information is completely unknown, we show that the
optimal time to wake up the system can be obtained without relying on future
task arrivals. We also perform competitive analysis for on-line control and
derive the competitive ratios for both deterministic and random controllers.
