Exhaustive fluid vacation model with Markov modulated load

In this paper we analyze stable fluid vacation models with exhaustive discipline, in which the fluid source is modulated by a background continuous-time Markov chain and the fluid is removed at constant rate during the service period. Due to the continuous nature of the fluid the state space of the model becomes continuous, which is the major novelty and challenge of the analysis. We adapt the descendant set approach used in polling models to the fluid vacation model. We provide steady-state vector Laplace Transform and mean of the fluid level at arbitrary epoch. First we consider the case when the fluid input rate is less than the fluid service rate during service and later we study the case when the fluid input rate is larger than the fluid service rate in some states of the model.