Improved fixed point methods for loss networks with linear structure

Mark Bebbington, Phil Pollett and Ilze Ziedins

Abstract: 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^-5 of that found using the EFP approximation.

Keywords: Circuit-switching; networks; fixed-point methods

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

The authors:

• Phil Pollett, Discipline of Mathematics, The University of Queensland. pkp@maths.uq.edu.au
• Mark Bebbington, Department of Statistics, Massey University. M.Bebbington@massey.ac.nz
• 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