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Approximation in Large-Scale Circuit-Switched Networks

Published online by Cambridge University Press:  27 July 2009

P. Whittle
P. Whittle
Affiliation:
Statistical LaboratoryUniversity of Cambridge, Cambridge, CB2 1SB England
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Abstract

The most probable equilibrium configuration in a circuit-switched network is determined, in the limit of very large scale, by a primal optimization problem whose dual determines the blocking probabilities. This approximation can be inadequate for moderate scale, and so the blocking probabilities are usually determined by the Erlang fixed-point principle. In this paper, it is shown that there is a “softened” form of the dual natural to the problem. This gives determinations of the blocking probabilities agreeing with those derived from the Erlang principle as far as terms of order (scale)-1. It is more attractive than the Erlang principle, however, in that it has a mathematical basis, provides an extremal principle by its nature, yields immediately the geometric distribution of the numbers of free circuits, and clearly agrees with the “hard” dual in the limit of large scale.

Type
Articles
Information
Probability in the Engineering and Informational Sciences , Volume 2 , Issue 3 , July 1988 , pp. 279 - 291
Copyright
Copyright © Cambridge University Press 1988

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