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 light-tailed. We show that the lack of independence may lead in dimension bigger than one to nontrivial effects in the asymptotics of the sojourn time. We also study in detail a simple queueing network with multipath routing. Keywords Queueing theory · Large deviations

• Type: Conference
• Year: 2006
• Where: VALUETOOLS
• Authors: Marc Lelarge
• Keywords: Hardware, Logarithmic Tail Asymptotics, Stationary Response Time, Stochastic Event Graphs, VALUETOOLS 2006