Computing battery lifetime distributions

The usage of mobile devices like cell phones, navigation systems, or laptop computers, is limited by the lifetime of the included batteries. This lifetime depends naturally on the rate at which energy is consumed, however it also depends on the usage pattern of the battery. Continuous drawing of a high current results in an excessive drop of residual capacity. However during intervals with no or very small currents, batteries do recover to a certain extend. We model this complex behaviour with an inhomogeneous Markov reward model, following the approach of the so-called Kinetic battery Model (KiBaM). The state-dependent reward rates thereby correspond to the power consumption of the attached device and to the available charge, respectively. We develop a tailored numerical algorithm for the computation of the distribution of the consumed energy and show how different workload patterns influence the overall lifetime of a battery.