Conditions for the light-traffic insensitivity to loss probability in a \(\text{GI}/ \text{G}/m/0\) queueing system
type: Item
instance of: scholarly article
title: Conditions for the light-traffic insensitivity to loss probability in a \(\text{GI}/ \text{G}/m/0\) queueing system
zbMATH Open document ID: 1036.60084
published in: Cybernetics and Systems Analysis
publication date: 2003-09-09T00:00:00Z
review text: The authors consider the loss system \(\text{GI}/ \text{G}/m/0\) with service time distribution function \(B(x)\) having mean \(1/\mu\) and an interarrival time density \(a(x)\) that behaves like \(c\lambda^\alpha x^{\alpha -1}\) for small \(x\). They study the limiting behavior of the probability that the \(n\)th customer will be lost as \(\lambda/\mu \) tends to zero. Under certain conditions this loss probability turns out to be sensitive with respect to the form of \(a(x)\) and \(B(x)\) for \(\alpha \neq 1\) and insensitive for \(\alpha = 1\).
reviewed by: Wolfgang Stadje
Mathematics Subject Classification ID: 60K25
Mathematics Subject Classification ID: 90B22
zbMATH DE Number: 1978237
zbMATH Keywords: Loss system
zbMATH Keywords: light traffic, insensitivity
author: I. M. Kovalenko
author: J. Ben Atkinson
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1978237