Bounds and asymptotics for the rate of convergence of birth-death processes

Erik A. van Doorn; A.I. Zeifman; T.L. Panfilova

doi:10.1137/S0040585X97984097

Bounds and asymptotics for the rate of convergence of birth-death processes

Erik A. van Doorn, A.I. Zeifman, T.L. Panfilova

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Abstract

We survey a method initiated by one of us in the 1990's for finding bounds and representations for the rate of convergence of a birth-death process. We also present new results obtained by this method for some specific birth-death processes related to mean-field models and to the $M/M/N/N+R$ service system. The new findings pertain to the asymptotic behaviour of the rate of convergence as the number of states tends to infinity.

Original language	Undefined
Article number	10.1137/S0040585X97984097
Pages (from-to)	97-113
Number of pages	22
Journal	Theory of probability and its applications
Volume	54
Issue number	1
DOIs	https://doi.org/10.1137/S0040585X97984097
Publication status	Published - 2010

Keywords

EWI-17628
IR-70170
MSC-60J80
MSC-60J27

Access to Document

10.1137/S0040585X97984097

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Cite this

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KW - IR-70170

KW - MSC-60J80

KW - MSC-60J27

U2 - 10.1137/S0040585X97984097

DO - 10.1137/S0040585X97984097

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