Tail asymptotics for discrete event systems

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 lighttailed. We show that the lack of independence may lead in dimension bigger than one to non-trivial efects in the asymptotics of the sojourn time. We also study in detail a simple queueing network with multipath routing.