Applications of Fluid Queues in Rechargeable Batteries

In this paper, the transient solution of the amount of charge in a rechargeable battery of finite capacity is obtained. The level of charge in the battery is governed by different input and output processes and are dependent on the level of charge in the battery. This model has been already discussed in Jones et al. (Fluid queue models of battery life. In: IEEE 19th international symposium on modeling, analysis and simulation of computer and telecommunication systems (MASCOTS), pp. 278–285, 2011), and the distribution of the hitting time was found numerically. In this paper, the method chosen is based on probabilistic approach which allows us to achieve a closed form solution for the distribution of the level of charge in the battery at any time t. Numerical illustrations are presented to verify the analytical results.