Multiclass Markovian fluid queues

This paper considers a multiclass Markovian fluid queue with a buffer of infinite capacity. Input rates of fluid flows in respective classes and the drain rate from the buffer are modulated by a continuous-time Markov chain with finite states. We derive the joint Laplace-Stieltjes transform for the stationary buffer contents in respective classes, assuming the FIFO service discipline. Further we develop a numerically feasible procedure to compute the joint and marginal moments of the stationary buffer contents in respective classes. Some numerical examples are then provided.