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Loss networks under diverse routing: the symmetric star network
Published online by Cambridge University Press: 01 July 2016
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 → ∞.
MSC classification
- Type
- General Applied Probability
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- Copyright
- Copyright © Applied Probability Trust 1995
Footnotes
Supported by Christ's College, Cambridge.
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