Asmussen, Søren et Bladt, Mogens, A sample path approach to mean busy periods for Markov-modulated queues and fluids, Advances in applied probability , 26(4), 1994, pp. 1117-1121
The mean busy period of a Markov-modulated queue or fluid model is computed by an extension of the time-reversal argument connecting the steady-state distribution and the maximum of a related Markov additive process.