Fluid models in queueing theory and Wiener-Hopf factorization of Markov chains (Q1333380)

A two-dimensional continuous time process is considered. The first component is a Markov chain and the second component is a continuous nonnegative function whose derivative depends on the first component. This implies that the second component can be given in term of a fluctuating additive functional. To investigate stationary distribution of this process a theorem about Wiener-Hopf factorization of Markov chains is proved. Some applications to fluid flow models with infinite and finite buffer are considered.