Fluid Models in Queueing Theory and Wiener-Hopf Factorization of Markov Chains

This paper applies the earlier work of Barlow, Rogers and Williams on the Wiener-Hopf factorization of finite Markov chains to a number of questions in the theory of fluid models of queues. Specifically, the invariant distribution for an infinite-buffer model and for a finite-buffer model are derived. The laws of other functionals of the fluid models can be easily derived and compactly expressed in terms of the fundamental Wiener-Hopf factorization.