Fluid level dependent Markov fluid models with continuous zero transition

Márton Balázs, Gábor Horváth, Sándor Kolumbán, Péter Kovács, Miklós Telek*

*Corresponding author for this work

Research output: Contribution to journalArticle (Academic Journal)peer-review

3 Citations (Scopus)


Markov fluid models with fluid level dependent behaviour are considered in this paper. One of the main difficulties of the analysis of these models is to handle the case when in a given state the fluid rate changes sign from positive to negative at a given fluid level. We refer to this case as zero transition. The case when this sign change is due to a discontinuity of the fluid rate function results in probability mass at the given fluid level. We show that the case when the sign change is due to a continuous finite polynomial function of the fluid rate results in a qualitatively different behaviour: no probability mass develops and different stationary equations apply. We consider this latter case of sign change, present its stationary description and propose a numerical procedure for its evaluation.

Original languageEnglish
Pages (from-to)1149-1161
Number of pages13
JournalPerformance Evaluation
Issue number11
Publication statusPublished - Nov 2011


  • Differential equation
  • Fluid level dependence
  • Markov fluid model
  • Stationary behaviour


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