Matrix-analytic methods for fluid queues with finite buffers

The application of matrix-analytic methods to the resolution of fluid queues has shown a close connection to discrete-state quasi-birth-and-death (QBD) processes. We further explore this similarity and analyze a fluid queue with finite buffer. We show, using a renewal approach, that the stationary distribution is expressed as a linear combination of two matrix-exponential terms. We briefly indicate how these terms may be computed in an efficient and numerically stable manner.