Asymptotic analysis for closed multichain queueing networks with bottlenecks
type: Item
instance of: scholarly article
title: Asymptotic analysis for closed multichain queueing networks with bottlenecks
zbMATH Open document ID: 0879.60086
DOI: 10.1007/BF01206559
author: O. Diekmann
published in: Queueing Systems
publication date: 1997-11-20T00:00:00Z
review text: The authors obtain explicit asymptotic expressions for the partition function for a large two-chain network consisting of one infinite server and two processor-sharing on FMFS single server stations. The key step in asymptotic evaluation of the multidimensional contour integral is its transformation to the saddle-point contour integral, which has an explicit asymptotic expression. This approach requires one to find the saddle-point contour, move the initial integration contour to the saddle-point contour, pick-up the residues between these two contours and find the term providing the main contribution to the asymptotic expansion of the partition function. This paper generalizes the results of the one-dimensional case discussed by \textit{A. Birman} and \textit{Y. Kogan} [Commun. Stat., Stochastic Models 8, No. 3, 543-563 (1992; Zbl 0756.60087)].
Mathematics Subject Classification ID: 60K20
Mathematics Subject Classification ID: 60K25
zbMATH DE Number: 1042833
zbMATH Keywords: explicit asymptotic expressions for the partition function
zbMATH Keywords: single server stations
zbMATH Keywords: saddle-point contour
reviewed by: P. R. Parthasarathy
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1042833