Large multiservice loss models and applications to ATM networks

Abstract

The problem of estimating call blocking probabilities in ATM networks is addressed in this thesis. We develop a new, two-step iterated framework for call acceptance control (CAC). In the first step, we define a new variable bit rate (VBR) traffic descriptor called effective rate and we use a known effective bandwidth technique in the second step to estimate cell loss. This approach yields decoupled estimators at the call level so that loss systems models can be used to perform network analysis. Our work on loss systems is divided in three parts: single-link problems, reservation and network problems. In the single-link context, we generalize existing asymptotic approximation formulae for blocking probabilities and propose a uniform estimate under light up to critical loading conditions. We present the salient features of commonly used reservation schemes while proposing and reviewing ways to estimate blocking probabilities in each case. In the case of networks, we provide an overview of classical techniques to evaluate blocking probabilities such as fixed-point methods. We propose a novel fixed-point technique for large capacity systems which yields dramatic reduction in computational complexity. We also analyze loss networks from an analytic point of view using the Laplace method and a change of probability law technique. We obtain asymptotic formulae for every loading conditions and a number of asymptotic results regarding network behavior. Many numerical examples are provided as well as a model example where we illustrate how our asymptotic formulae can be used to perform network optimization