Markov-modulated fluid flow model with server maintenance period

Abstract

We consider a Markov-modulated fluid flow model with server maintenance period. As soon as the fluid level reaches zero, the server begins a maintenance period of a random length. During the maintenance period, fluid arrives from outside depending on the state of the background Markov process and the level increases either vertically or linearly. This model can be applied to various real-world systems such as inventory systems and production systems. We first derive the distribution of the fluid level and the mean performance measures. Then, we present some numerical examples to show the effect of the maintenance time.