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Blocking probabilities in large circuit-switched networks

Published online by Cambridge University Press:  01 July 2016

F. P. Kelly
F. P. Kelly*
Affiliation:
University of Cambridge
*
∗Postal address: Statistical Laboratory, Department of Pure Mathematics and Mathematical Statistics, University of Cambridge, 16 Mill Lane, Cambridge, CB2 1SB, UK.
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Abstract

This paper is concerned with blocking and loss probabilities in circuit-switched networks. We show that when the capacity of links and the offered traffic are increased together, a limiting regime emerges in which loss probabilities are as if links block independently, with blocking probabilities given by the solution of a simple convex programming problem. We then show that an approximate procedure, based on solving Erlang&s formula under the assumption of independent blocking, produces a unique solution when routes are fixed, and that under the limiting regime the estimates of loss probabilities obtained from the procedure converge to the correct values.

Keywords

LOSS PROBABILITIESNETWORK FLOWLOCAL LIMIT THEOREMSERLANGS FORMULAFIXED ROUTINGDYNAMIC ROUTINGCELLULAR RADIO
Type
Research Article
Information
Advances in Applied Probability , Volume 18 , Issue 2 , June 1986 , pp. 473 - 505
Copyright
Copyright © Applied Probability Trust 1986 

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