# Journal of theKorean Mathematical SocietyJKMS

ISSN(Print) 0304-9914 ISSN(Online) 2234-3008

## Article

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J. Korean Math. Soc. 1998; 35(3): 539-557

Published online September 1, 1998

## Two-link approximation schemes for linear loss networks without controls

M. S. Bebbington, P. K. Pollett, and I. Ziedins

Massey University, The University of Queensland and University of Auckland

### Abstract

This paper is concerned with the performance evaluation of loss networks. We shall review the {\it Erlang Fixed Point\/} (EFP) method for estimating the blocking probabilities, which is based on an assumption that links are blocked independently. For networks with linear structure, the behaviour of adjacent links can be highly correlated. We shall give particular attention to recently-developed fixed-point methods which specifically account for the dependencies between neighbouring links. For the network considered here, namely a ring network with two types of traffic, these methods produce relative errors typically $10^{-5}$ of that found using the basic EFP approximation.

Keywords: blocking probabilities, Erlang's formula

MSC numbers: primary 60K30, secondary 60K35; 90B12