Exhaustive fluid vacation model with positive fluid rate during service

Gábor Horváth, Miklós Telek

Research output: Contribution to journalArticle

2 Citations (Scopus)


Abstract Using an elegant transform domain iterative operator approach exhaustive fluid vacation models with strictly negative fluid rate during service have been analyzed, recently. Unfortunately, the potential presence of positive fluid rate during service (when the fluid input rate is larger than the fluid service rate) inhibits the use of all previously applied methodologies and makes the extension of the analysis approaches of discrete vacation and polling models towards fluid vacation and polling models rather difficult. Based on the level crossing analysis of Markov fluid models the paper introduces an analysis approach which is applicable for the stationary analysis of the fluid level distribution and its moments. In the course of the analysis compact new matrix exponential expressions are obtained for the distribution of fluid level during a busy period starting from a given positive fluid level and by exploiting the relations of upward and downward measures of fluid processes several matrix transformations are applied to avoid Kronecker expansion matrix multiplications. Finally, the obtained fluid level distribution is related with previous results of fluid vacation models.

Original languageEnglish
Article number1832
Pages (from-to)286-302
Number of pages17
JournalPerformance Evaluation
Publication statusPublished - Sep 1 2015


  • Busy period
  • Exhaustive discipline
  • Fluid vacation model
  • Level crossing
  • Markov fluid queue

ASJC Scopus subject areas

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

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