Estimating Blocking Probabilities in Telecommunications Networks with Linear Structure

Mark Bebbington, Phil Pollett and Ilze Ziedins

Abstract: Telecommunications networks can be modelled as collections of links, on which are defined routes, each route being offered traffic at a given rate. The traditional performance measure in these situations is the blocking probability, for which a widely used approximation is the Erlang Fixed Point (EFP). This assumes that links block independently of one another, and performs well in situations where both the link capacities and offered traffics are large, or where the number of routes is much larger than the number of links. Since there are many situations far from either of these ideals, it is important to have a more accurate method for calculating blocking, and some idea of the error in the EFP. We shall consider these issues by taking a simple situation in which the EFP is expected to perform poorly, a ring network with one and two-link traffic, where the link capacities are small. By allowing for dependencies between neighbouring links, we can construct an approximation for the blocking probabilities with error typically 10^{-5} of that found using the EFP. This can be extended to cases where admission controls, such as trunk reservation, are used.

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

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Last modified: 1st March 1996