Fluid queues and mountain processes

O. J. Boxma, D. Perry, F. A. Van Der Duyn Schouten

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Pages (from-to)407-427
Number of pages21
JournalProbability in the Engineering and Informational Sciences
Issue number4
StatePublished - 1999

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty
  • Management Science and Operations Research
  • Industrial and Manufacturing Engineering


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