We consider a single-server two-class fluid model with a static priority service discipline under which type 1 fluid receives full service priority over type 2 fluid. The two types of fluid are stored in two separate infinite capacity buffers that are emptied at the constant rate of the server. The inputs to the buffers are governed by an external environment process which is taken to be an irreducible finite state continuous time Markov chain. We derive the Laplace-Stieltjes transform of the steady-state joint distribution of the two buffer con-tent processes. The analytic results are illustrated by two simple examples and we display computational results for three larger scale examples.
