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Tail Asymptotics for Discrete Event Systems

Marc Lelarge
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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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Marc Lelarge. 2007-03-16. Tail Asymptotics for Discrete Event Systems. https://arxiv.org/abs/math/0701420

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