Fluid level dependent Markov fluid models with continuous zero transition

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

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

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
Volume68
Issue number11
DOIs
Publication statusPublished - Nov 1 2011

Keywords

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

ASJC Scopus subject areas

  • Software
  • Modelling and Simulation
  • Hardware and Architecture
  • Computer Networks and Communications

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