Improved Fixed Point Methods for Loss Networks with Linear Structure

: This paper is concerned with the performance evaluation of loss networks. For the simplest networks there are explicit analytical formulae for the important measures of performance, but for networks which involve some level of dynamic control, exact analytical methods have had only limited success. Under several regimes the Erlang Fixed Point (EFP) method provides a good approximation for the blocking probabilities, but when these regimes are not operative the method can perform badly. In many cases this is because the key assumption of independent blocking does not hold. We derive methods for estimating the blocking probabilities which specifically account for the dependencies between neighbouring links. For the network considered here, namely a ring network with two types of traffic, our method produced relative errors typically 10 \Gamma5 of that found using the EFP approximation. 1. INTRODUCTION We shall be concerned with circuit-switched networks of the kind depicted in Figu..