A degenerate central limit theorem for single resource loss systems
type: Item
instance of: scholarly article
title: A degenerate central limit theorem for single resource loss systems
zbMATH Open document ID: 1031.60079
author: Christine Fricker
author: Philippe Robert
author: Danielle Tibi
published in: The Annals of Applied Probability
publication date: 2003-11-17T00:00:00Z
review text: This paper deals with a loss network at which \(R\) types of calls arrive and require only one link. The sojourn times in the network are exponentially distributed. Due to the intrinsic complexity of this type of networks, the authors assume a scaling parameter (introduced by Kelly) to get the asymptotic loss probabilities and limiting results. It is known that the scaled number of customers of type \(r\) in the network converges to a fluid limit. The aim of the paper is to investigate the case when the fluid limit is on the boundary of the domain. In this case, the perturbation around the fluid limit is shown to be a degenerate \((R-1)\)-dimensional diffusion.
Mathematics Subject Classification ID: 60K25
Mathematics Subject Classification ID: 60F05
Mathematics Subject Classification ID: 90B22
zbMATH DE Number: 2005168
zbMATH Keywords: loss networks
zbMATH Keywords: diffusion approximation
reviewed by: Jesus R. Artalejo
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aoap/1050689594
OpenAlex ID: W2028432351
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DOI: 10.1214/AOAP/1050689594
description: scientific article; zbMATH DE number 2005168