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Discrete Event Dynamic Systems

, Volume 18, Issue 4, pp 563–584 | Cite as

Tail Asymptotics for Discrete Event Systems

  • Marc Lelarge
Article

Abstract

In the context of communication networks, the framework of stochastic event graphs allows a modeling of control mechanisms induced by the communication protocol and an analysis of its performances. We concentrate on the logarithmic tail asymptotics of the stationary response time for a class of networks that admit a representation as (max,plus)-linear systems in a random medium. We are able to derive analytic results when the distribution of the holding times are light-tailed. We show that the lack of independence may lead in dimension bigger than one to non-trivial effects in the asymptotics of the sojourn time. We also study in detail a simple queueing network with multipath routing.

Keywords

Queueing theory Large deviations 

Notes

Acknowledgements

The author would like to thank Peter Friz for pointing out a mistake in an earlier version of this work and the participants of Valuetools 2006 (where this work was presented) and especially Bruno Gaujal for a comment related to Remark 1.

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Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  1. 1.ENS-INRIAParisFrance

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