  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.
