Product form approximations for highly linear loss networks with trunk reservation

Mark Bebbington, Phil Pollett and Ilze Ziedins

[Full Text]

Abstract: Admission controls, such as trunk reservation, are often used in loss networks to optimize their performance. Since the numerical evaluation of performance measures is complex, much attention has been given to finding approximation methods. The Erlang Fixed Point Approximation, which is based on an independent blocking assumption, has been used for networks both with and without controls. Certain methods of accounting for dependencies in blocking behaviour have been developed for the uncontrolled setting. We explore extensions to the controlled case, in order to gain insight into the essential elements of an effective approximation. We are able to isolate the dependency factor by restricting our attention to a highly linear network.

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: 15th May 1999