Exact results for a fluid model with state-dependent flow rates

Abstract

We consider a modulated fluid system with a finite state-space Markov chain J(t) as modulating process and general state-dependent net input rates. We derive differential equations for the transient and the stationary distribution of (W-t, J(t)), where W-t is the content process, and the corresponding Laplace transforms with respect to time. Moreover, we study the level hitting times of W-t. Our results lead to explicit formulas in the case of two modulating states.