Fluid Queues Driven by Denumerable Markov Chains

Abstract. We analyze the stationary behavior of a fluid queue when the instantaneous rate of the input process is governed by a continuous time Markov chain with nite or in nite state space. These fluid flows models are widely used in the performance analysis of telecommunication systems. In the case of innite state spaces and for particular classes of denumerable Markov chains, such as quasi birth and death processes or Markov chains of the G/M/1 type, we develop algorithms to compute the stationary distribution of the buer level in the fluid queue using simple recurrence relations.