Fluid queues and mountain processes

Fluid queues and mountain processes

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Article ID: iaor20002479
Country: United States
Volume: 13
Issue: 4
Start Page Number: 407
End Page Number: 427
Publication Date: Oct 1999
Journal: Probability in the Engineering and Informational Sciences
Authors: , ,
Keywords: markov processes
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 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.

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