Author:
Boxma O. J.,Perry D.,van der Duyn Schouten F. A.
Abstract
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.
Publisher
Cambridge University Press (CUP)
Subject
Industrial and Manufacturing Engineering,Management Science and Operations Research,Statistics, Probability and Uncertainty,Statistics and Probability
Cited by
16 articles.
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