Waiting time and queue length analysis of Markov-modulated fluid priority queues

Abstract

This paper considers a multi-type fluid queue with priority service. The input fluid rates are modulated by a Markov chain, which is common for all fluid types. The service rate of the queue is constant. Various performance measures are derived, including the Laplace–Stieltjes transform and the moments of the stationary waiting time of the fluid drops and the queue length distributions. An Erlangization-based numerical method is also provided to approximate the waiting time and the queue length distributions up to arbitrary precision. All performance measures are formulated as reward accumulation problems during busy periods of simple Markovian fluid flow models, for which efficient matrix-analytic solutions are provided, enabling us to solve large models with several hundred states.