S. Asmussen et M. Bladt, 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 com
puted by an extension of the time-reversal argument connecting the ste
ady-state distribution and the maximum of a related Markov additive pr
ocess.