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On the rates of convergence of Erlang's model

Part of: Special processes Operations research and management science

Published online by Cambridge University Press:  14 July 2016

Christine Fricker ,
Philippe Robert  and
Danielle Tibi
Christine Fricker*
Affiliation:
INRIA
Philippe Robert*
Affiliation:
INRIA
Danielle Tibi*
Affiliation:
Université de Paris 7
*
∗Postal address: INRIA, Domaine de Voluceau, BP 105, 78153 Le Chesnay Cedex, France.
∗Postal address: INRIA, Domaine de Voluceau, BP 105, 78153 Le Chesnay Cedex, France.
∗∗∗Postal address: Université de Paris 7, URA 1321, 2 Place Jussieu, 75251 Paris Cedex 05, France.
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Abstract

The convergence to equilibrium of the renormalized M/M/N/N queue is analysed. Upper bounds on the distance to equilibrium are obtained and the cut-off property for two regimes of this queue is proved. Simple probabilistic methods, such as coupling techniques and martingales, are used to obtain these results.

Keywords

The M/M/N/N queueconvergence to equilibriumcut-off propertyhitting times of the M/M/∞ queueOrnstein–Ühlenbeck processesGamma functions

MSC classification

Primary: 60K25: Queueing theory
Secondary: 90B22: Queues and service
Type
Research Papers
Information
Journal of Applied Probability , Volume 36 , Issue 4 , December 1999 , pp. 1167 - 1184
Copyright
Copyright © Applied Probability Trust 1999 

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