Evaluation of Battery Lifetimes using Inhomogeneous Markov Reward Models

The usage of mobile devices like cell phones, navigation systems, or laptop computers, is limited by the lifetime of the included batteries. This lifetimes 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. The state-dependent reward rates thereby correspond to the power consumption of the attached device and to the available charge, respectively. We develop new numerical algorithms for the computation of the distribution of the consumed energy and show how different workload patterns influence the overall lifetime of a battery.