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A note on the rate of convergence to equilibrium for Erlang's model in the subcritical case

Part of: Limit theorems Markov processes Special processes

Published online by Cambridge University Press:  14 July 2016

Michael Voit
Michael Voit*
Affiliation:
Universität Tübingen
*
∗Postal address: Mathematisches Institut, Universität Tübingen, Auf der Morgenstelle 10, 72076 Tübingen, Germany. Email address: voit@uni-tuebingen.de
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Abstract

We derive some asymptotic results for the rate of convergence to equilibrium for the number of busy servers in an M/M/N/N queue with input rate λN and service rate 1 for N → ∞ in the ‘subcritical’ case λ ∈]0, 1[. These results improve recent contributions of Fricker, Robert and Tibi.

Keywords

QueueM/M/N/N queueM/M/∞ queuetime to reach stationaritycutoff phenomenon

MSC classification

Primary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)
Secondary: 60K25: Queueing theory 60F05: Central limit and other weak theorems
Type
Short Communications
Information
Journal of Applied Probability , Volume 37 , Issue 3 , September 2000 , pp. 918 - 923
Copyright
Copyright © Applied Probability Trust 2000 

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