Fluid Models with Jumps

In this paper we study a general stochastic fluid model with a single infinite capacity buffer, where the buffer content can change continuously as well as by instantaneous upward jumps. The continuous as well as the instantaneous change is modulated by an external environment process modelled as a finite state continuous time Markov chain. The Laplace-Stieltjes transform of the steady-state joint distribution of the buffer content and the state of the environment is determined explicitly in terms of the solutions of a generalized eigenvalue problem. The methodology is illustrated by several well-known queueing problems.