Applied Mathematics & Information Sciences

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On-off scheduling of systems that have the ability to sleep can be used to extend system idle periods and enable greater opportunities for energy savings from sleeping. In this paper, we achieve a theoretical understanding of the delay behavior of on-off scheduling as it may apply to communications links and other systems capable of sleeping. We consider a single-server coalescing queue with a scheduler that schedules on-off periods for the server in order to extend idle periods of the downstream link. At the start of an off period (duration To f f ) the server stops serving jobs immediately if idle, or after processing a job already in service. Service of any queued and arriving jobs begins at the start of the next on period (duration Ton). On and off periods are fixed. We solve for the scheduling queue behavior as a function of To f f , Ton, interarrival time t, service time x, and time of first arrival g for periodic job arrivals. Our results are closed form and have both theoretical and practical significance.

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