Evaluation of Continuous Power-Down Schemes

We consider a power-down system with two states-"on" and "off"-and a continuous set of power states. The system has to respond to requests for service in the "on" state and, after service, the system can power off or switch to any of the intermediate power-saving states. The choice of states determines the cost to power on for subsequent requests. The protocol for requests is "online", which means that the decision as to which intermediate state (or the off-state) the system will switch has to be made without knowledge of future requests. We model a linear and a non-linear system, and we consider different online strategies, namely piece-wise linear, logarithmic and exponential. We provide results under online competitive analysis, which have relevance for the integration of renewable energy sources into the smart grid. Our analysis shows that while piece-wise linear systems are not specific for any type of system, logarithmic strategies work well for slack systems, whereas exponential systems are better suited for busy systems.