Occupation times for the finite buffer fluid queue with phase-type ON-times

In this short communication we study a fluid queue with a finite buffer. The performance measure we are interested in is the occupation time over a finite time period, i.e., the fraction of time the workload process is below some fixed target level. We construct an alternating sequence of sojourn times $D_1,U_1,\mathrm{.}\mathrm{.}\mathrm{.}$ where the pairs $(D_i,U_i{)}_{i\in \mathbb{N}}$ are i.i.d. random vectors. We use this sequence to determine the distribution function of the occupation time in terms of its double transform.