Transient analysis of Markov-fluid-driven queues
type: Item
instance of: scholarly article
title: Transient analysis of Markov-fluid-driven queues
zbMATH Open document ID: 1227.60106
author: Abdelghafour Es-Saghouani
author: M. R. H. Mandjes
published in: Top
publication date: 2011-08-25T00:00:00Z
full work available at URL: https://ir.cwi.nl/pub/13636
review text: The paper focuses on some transient characteristics of Markov-fluid-driven queues. It adopts a new approach for computing the Laplace transform of the busy period expressing it in terms of a number of auxiliary transforms (as many as there are states with net buffer increase). A sufficient number of additional constraints to uniquely determine them are given; this analysis carries over to the correlation function. One shows the tail distribution of the busy period can be written in terms of the asymptotic log-moment generating function of the input process invoking sample-path large deviations. Denoting by \(Q(t)\) the buffer content at time \(t\), the covariance function Cov\((Q(0),Q(t))\) is a measure of dependence between the workload at time 0 and at time \(t\). Using the methodology for analyzing the busy period, one characterizes it by its Laplace transform. In some cases, the correlation function can be determined explicitly. An example illustrates the results obtained in the paper.
Mathematics Subject Classification ID: 60K20
Mathematics Subject Classification ID: 62J10
Mathematics Subject Classification ID: 60J25
zbMATH DE Number: 5942595
zbMATH Keywords: Markov-fluid-driven queue
zbMATH Keywords: transient analysis
reviewed by: László Lakatos
MaRDI profile type: Publication
OpenAlex ID: W2101557478
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DOI: 10.1007/S11750-009-0078-3
description: scientific article; zbMATH DE number 5942595