FLUID QUEUES AND MOUNTAIN PROCESSES
Boxma a1, D.
Perry a2 and F. A.
van der Duyn Schouten a3|
a1 Department of Mathematics and Computing
Science, Eindhoven University of Technology,
P.O. Box 513, 5600 MB Eindhoven, The Netherlands, and,
CWI, P.O. Box 94079, 1090 GB Amsterdam, The Netherlands
a2 Department of Statistics, University
of Haifa, 31999 Haifa, Israel
a3 CentER for Economic Research, Tilburg
University, P.O. Box 90153, 5000 LE Tilburg, The
Netherlands, and CWI, P.O. Box 94079, 1090 GB
Amsterdam, The Netherlands
This paper is devoted to the analysis of a fluid
queue with a buffer content that varies linearly during
periods that are governed by a three-state semi-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 completely general.
We obtain exact results for the buffer content distribution,
the busy period distribution, and the distribution of the
maximal buffer content during a busy period. The results
are obtained by establishing relations between the fluid
queues and ordinary queues with instantaneous input and
by using level crossing theory.