Delayed (de-)activation in servers with a sleep mode

Many electrical devices have a sleep mode to reduce their power consumption. However, changing into and out of the sleep mode delays processing and consumes power without performing useful work. Different strategies to activate the sleep mode allow different trade-offs between power consumption and latency. In this paper, we calculate which effects delayed activation and deactivation of a queueing system have on power consumption and latency. To this end, we created a Markov model as an abstraction of queuing systems with sleep modes and added delayed activation and deactivation. We analytically determined the steady state distribution of model states and give closed formulas for both power consumption and latency depending on the rate of arrival, processing, activation, deactivation, activation delay, and deactivation delay. We use this result to show that, surprisingly, cases exist in which adding both an activation delay and a deactivation delay reduces both mean power consumption and mean latency. Our simulation results demonstrate that this also holds for other random distributions. This shows that the opposing effects of activation delay and deactivation delay do not necessarily cancel each other out but can be used to reduce both power consumption and latency at the same time. (C) 2016 Elsevier Inc. All rights reserved.