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Loss networks under diverse routing: the symmetric star network

Part of: Special processes

Published online by Cambridge University Press:  01 July 2016

P. J. Hunt
P. J. Hunt*
Affiliation:
University of Cambridge
*
*Present address: NatWest Capital Markets, 135 Bishopsgate, London EC2M 3UR, UK.
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Abstract

A highly symmetric loss network is considered, the symmetric star network previously considered by Whitt and Ziedins and Kelly. As the number of links, K, becomes large, the state space for this process also grows, so we consider a functional of the network, one which contains all information relevant to blocking probabilities within the network but which is easier to analyse. We show that this reduced process obeys a functional law of large numbers and a functional central limit theorem, the limit in this latter case being an Ornstein-Uhlenbeck diffusion process. Finally, by considering the network in equilibrium, we are able to prove that the well-known Erlang fixed point approximation for blocking probabilities is correct to within o(K-1/2) as K → ∞.

Keywords

FUNCTIONAL LAW OF LARGE NUMBERSORNSTEIN-UHLENBECK PROCESSSYMMETRIC STAR NETWORK

MSC classification

Primary: 60K25: Queueing theory
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 27 , Issue 1 , March 1995 , pp. 255 - 272
Copyright
Copyright © Applied Probability Trust 1995 

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Footnotes

Supported by Christ's College, Cambridge.

References

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