Fluid Buffers - Changing the Behaviour at the Borders

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 fluid queues with finite and infinite capacities, for which the evolution of the buffer content changes when it is either empty or full. We briefly indicate how the stationary density of the fluid buffer may be computed in an efficient manner.