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. Using an alternating renewal sequence, we determine the double transform of the occupation time; the occupation time for the finite buffer M/G/1 queue with phase-type jumps follows as a limiting case.

Doubly reflected process, Finite buffer queue, Fluid model, Occupation time, Phase-type distribution
dx.doi.org/10.1016/j.orl.2017.10.012
Operations Research Letters
Centrum Wiskunde & Informatica, Amsterdam, The Netherlands

Starreveld, N.J, Bekker, R, & Mandjes, M.R.H. (2018). Occupation times for the finite buffer fluid queue with phase-type ON-times. Operations Research Letters, 46(1), 27–32. doi:10.1016/j.orl.2017.10.012