A semi-Markov approach to the analysis of fluid queues

Fluid queues in a random environment are used to modeltelecommunication networks and are amenable to a variety of approachesfor solution. Recently, it has been shown that they may be solved byfollowing the same renewal-type arguments as for quasi-birth-and-deathprocesses. The advantages are that one may concentrate on thestructural behaviour of the process and rely on fast, numericallystable algorithmic procedures. We shall briefly describe theconceptual approach and discuss the infinite and finite buffer cases.