Busy period, congestion analysis and loss probability in fluid queues

Fabrice Guillemin, Marie-Ange Remiche, Bruno Sericola

Research output: Contribution in Book/Catalog/Report/Conference proceedingChapter (peer-reviewed)peer-review

Abstract

Stochastic fluid flow models and in particular those driven by Markov chains have been intensively studied in the last two decades. This chapter analyzes congestion when the buffer content is described by means of a Markov modulated fluid flow model in the stationary regime. It describes a methodology to compute exactly the loss probability of a finite-capacity system. The approach is based on the computation of hitting probabilities jointly with the peak level reached during a busy period, both in the infinite and finite buffer case. The chapter considers a classical fluid queue with infinite buffering capacity. This allows us to describe the buffer fluctuations and introduce the notation and the variables necessary to study the fluid queue when the buffer is finite.

Original languageEnglish
Title of host publicationAdvanced Trends in Queuing Theory 1
EditorsVladimir Anisimov, Nikolaos Limnios
PublisherISTE Editions
Chapter2
Pages21-61
Number of pages41
ISBN (Electronic)9781119755432
ISBN (Print)9781789450019
DOIs
Publication statusPublished - 2021

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