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On the cut-off phenomenon in some queueing systems

Published online by Cambridge University Press:  14 July 2016

P. Konstantopoulos  and
F. Baccelli
P. Konstantopoulos
Affiliation:
INRIA
F. Baccelli*
Affiliation:
INRIA
*
∗ Postal address for both authors: INRIA, Sophia Antipolis, 2004 Route des Lucioles, 06565 Valbonne Cedex, France.
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Abstract

A number of stochastic queueing systems exhibit an interesting phenomenon known as the cut-off phenomenon. A properly scaled version of the distance between the transient process and the stationary one converges to a step function as the initial load converges to infinity. The purpose of this paper is to promote the idea that this phenomenon is a direct consequence of the coupling between the two processes, being thus generalizable to systems lacking any kind of Markovian structure.

Keywords

STATIONARY AND ERGODIC QUEUEING SYSTEMSTOTAL VARIATION DISTANCESETTLING TIME
Type
Research Papers
Information
Journal of Applied Probability , Volume 28 , Issue 3 , September 1991 , pp. 683 - 694
Copyright
Copyright © Applied Probability Trust 1991 

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Footnotes

The work of P. Konstantopoulos was supported in part by the National Science Foundation under grant ASC 88–8802764.

References

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