Analysis of feedback fluid queues

We consider the stationary behaviour of a class of feedback fluid queues. A feedback fluid queue is a natural generalisation of the well-known Markov modulated fluid queue. The essential difference is that the current state of the fluid buffer influences the behaviour of the regulating process. Therefore these models are relevant for the performance evaluation of certain regulation mechanisms in telecommunications access networks. Typically, the enable the analysis of mechanisms in which the content of a buffer is driven by some source process, while the source process itself is influences by feedback signals coming from the buffer. We write down the differential equations governing the stationary distribution for a large class of these models, and subsequently solve them using the spectral method. The unknown parameters in the solution are determined by an equal number of boundary conditions.