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.
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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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This work was partially done while the author was with Boole Centre for Research in Informatics, Science Foundation Ireland Research Grant No. SFI 04/RP1/I512.
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Lelarge, M. Tail Asymptotics for Discrete Event Systems. Discrete Event Dyn Syst 18, 563–584 (2008). https://doi.org/10.1007/s10626-008-0037-4
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DOI: https://doi.org/10.1007/s10626-008-0037-4