Large deviations for a simple closed queueing model
type: Item
instance of: scholarly article
title: Large deviations for a simple closed queueing model
zbMATH Open document ID: 0787.60114
DOI: 10.1007/BF01153524
author: R. Liptser
published in: Queueing Systems
publication date: 1994-05-19T00:00:00Z
review text: The author considers a simple queueing model with one service station. The arrival and service processes have intensities \(a(N-Q_ t)\) and \(Nf(N^{-1}Q_ t)\), respectively, where \(Q_ t\) is the queue length, \(N\) is a large integer, \(a>0\) and \(f(x)\) is a positive continuous function. He establishes the large deviation principle for the sequence of the normalized queue length process \(q^ N_ t=N^{-1}Q_ t\), \(N\geq 1\), for both light \((a<f(0))\) and heavy \((a\geq f(0))\) traffic and uses this result for an investigation of ergodic properties of \(q^ N_ t\), \(N\geq 1\).
Mathematics Subject Classification ID: 60K25
Mathematics Subject Classification ID: 60F10
Mathematics Subject Classification ID: 60G42
zbMATH DE Number: 438290
zbMATH Keywords: heavy traffic
zbMATH Keywords: Fenchel-Legendre transform
zbMATH Keywords: queueing model
zbMATH Keywords: large deviation principle
zbMATH Keywords: ergodic properties
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 438290