Two-link approximation schemes for linear loss networks without controls

Mark Bebbington, Phil Pollett and Ilze Ziedins

Abstract: This paper is concerned with the performance evaluation of loss networks. We shall review the 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: Approximation, Blocking probabilities, Erlang Fixed Point, Ring network

Acknowledgement: This worked was funded by the Australian Research Council.

The authors:

• Mark Bebbington, Department of Statistics, Massey University. M.Bebbington@massey.ac.nz
• Phil Pollett, Discipline of Mathematics, The University of Queensland. pkp@maths.uq.edu.au
• Ilze Ziedins, Department of Mathematics and Statistics, The University of Auckland ziedins@stat.auckland.ac.nz

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Last modified: 11th February 1998