We investigate how a power-save mode effects the battery life of a device subject to stochastically determined charging and discharging periods. We use a multi-regime fluid queue, imposing a threshold at some value. When the power level falls below the threshold, a power-save mode is entered and the rate of discharge decreased. An expression for the Laplace transform of the battery life's probability density function is found and inverted numerically in particular instances. We show the life of battery can be significantly improved by the introduction of the power saving threshold.
Information from pubs.doc.ic.ac.uk/fluid-battery-model.