Rare events in networks

The goal of this thesis is the study of rare events in stochastic networks, i.e. events with very small probability. The one dimensional example of such an event is the tail of the stationary workload W of a stable single server queue, P(W> x) as x!1: The main tool to extend this kind of results to a network setting is the monotone separable framework. The rst merit of the algebraic framework advocated here is to allow for a mathematical representation of networks re-gardless of their dimension. This formalism also allows one to dene classes of networks (e.g. event graphs, free choice nets etc.) for which similar meth-ods of analysis work. Based on this mathematical representation, one can then design controls or evaluate analytically performances in new ways, quite dierent from the more classical Markovian approach. An important issue in this setting is that of the computation and analytical characterization of the stationary distributions in networks. In an introductive part, we presen