Sample path large deviations and intree networks

Using the contraction principle. This paper derives a set of closure properties for sample path large deviations. These properties include sum, reduction, composition and reflection mapping. Using these properties, the paper shows that the exponential decay rates of the steady state queue length distributions in an intree network with routing can be derived by a set of recursive equations. The solution of this set of equations is related to the recently developed theory of effective bandwidth for high speed digital networks, especially ATM networks. The paper also proves a conditional limit theorem that illustrates how a queue builds up in an intree network.