The use 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 extent. The usage pattern of a device can be well modeled with stochastic workload models. However, one still needs a battery model to describe the effects of the power consumption on the state of the battery. Over the years many different types of battery models have been developed for different application areas. In this paper we give a detailed analysis of two well-known analytical models, the kinetic battery model and the so-called diffusion model. We show that the kinetic battery model is actually an approximation of the more complex diffusion model; this was not known previously. Furthermore, we tested the suitability of these models for performance evaluation purposes, and found that both models are well suited for doing battery lifetime predictions. However, one should not draw conclusions on what is the best usage pattern based on only a few workload traces. 2 Battery models In this section we give a short introduction to the essential battery properties which need to be modeled to obtain an accurate battery model. Furthermore, short descriptions of the electrochemical, electrical circuit and stochastic battery models are given. Although these models give a good description of the battery, they are not that well suited to be used for performance modelling. The two analytical models described in Section 3 are better suited for this purpose. These models are described in more detail.

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.

The use of mobile devices is limited by the battery lifetime. Some devices have the option to connect an extra battery, or to use smart battery-packs with multiple cells to extend the lifetime. In these cases, scheduling the batteries over the load to exploit recovery properties usually extends the system lifetime. Straightforward scheduling schemes, like round robin or choosing the best battery available, already provide a big improvement compared to a sequential discharge of the batteries. In this paper we compare these scheduling schemes with the optimal scheduling scheme produced with a priced-timed automaton battery model (implemented and evaluated in Uppaal Cora). We see that in some cases the results of the simple scheduling schemes are close to optimal. However, the optimal schedules also clearly show that there is still room for improving the battery lifetimes.

The use of mobile devices is often limited by the battery lifetime. Some devices have the option to connect an extra battery, or to use smart battery-packs with multiple cells to extend the lifetime. In these cases, scheduling the batteries or battery cells over the load to exploit the recovery properties of the batteries helps to extend the overall systems lifetime. Straightforward scheduling schemes, like round robin or choosing the best battery available, already provide a big improvement compared to a sequential discharge of the batteries. In this paper we compare these scheduling schemes with the optimal scheduling scheme produced with two different modeling approaches: an approach based on a priced-timed automaton model (implemented and evaluated in Uppaal Cora), as well as an analytical approach (partly formulated as non-linear optimization problem) for a slightly adapted scheduling problem. We show that in some cases the results of the simple scheduling schemes (round robin, and best-first) are close to optimal. However, the optimal schedules, computed according to both methods, also clearly show that in a variety of scenarios, the simple schedules are far from optimal.

The use of mobile devices is often limited by the lifetime of the included batteries. This lifetime naturally depends on the battery's capacity and on the rate at which the battery is discharged. However, it also depends on the usage pattern, i.e., the workload, of the battery. When a battery is continuously discharged, a high current will cause it to provide less energy until the end of its lifetime than a lower current. This effect is termed the rate-capacity effect. On the other hand, during periods of low or no discharge current, the battery can recover to a certain extent. This effect is termed the recovery effect. In order to investigate the influence of the device workload on the battery lifetime a battery model is needed that includes the above described effects.Many different battery models have been developed for different application areas. We make a comparison of the main approaches that have been taken. Analytical models appear to be the best suited to use in combination with a device workload model, in particular, the so-called kinetic battery model. This model is combined with a continuous-time Markov chain, which models the workload of a battery powered device in a stochastic manner. For this model, we have developed algorithms to compute both the distribution and expected value of the battery lifetime and the charge delivered by the battery. These algorithms are used to make comparisons between different workloads, and can be used to analyse their impact on the system lifetime.In a system where multiple batteries can be connected, battery scheduling can be used to "spread" the workload over the individual batteries. Two approaches have been taken to find the optimal schedule for a given load. In the first approach scheduling decisions are only taken when a change in the workload occurs. The kinetic battery model is incorporated into a priced-timed automata model, and we use the model checking tool Uppaal Cora to find schedules that lead to the longest system lifetime.The second approach is an analytical one, in which scheduling decisions can be made at any point in time, that is, independently of workload changes. The analysis of the equations of the kinetic battery model provides an upper bound for the battery lifetime. This upper bound can be approached with any type v Abstract of scheduler, as long as one can switch fast enough. Both the approaches show that battery scheduling can potentially provide a considerable improvement of the system lifetime. The actual improvement mainly depends on the ratio between the battery capacity and the average discharge current.vi