Fluid queues and mountain processes

This paper is devoted to the analysis of a fluid queue with a buffer conten t that varies linearly during periods that are governed by a three-state se mi-Markov process. Two cases are being distinguished: (i) two upward slopes and one downward slope, and (ii) one upward slope and two downward slopes. In both cases, at least one of the period distributions is allowed to be c ompletely general. We obtain exact results for the buffer content distribut ion, the busy period distribution, and the distribution of the maximal buff er content during a busy period. The results are obtained by establishing r elations between the fluid queues and ordinary queues with instantaneous in put and by using level crossing theory.