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Implied costs in loss networks

Published online by Cambridge University Press:  01 July 2016

P. J. Hunt
P. J. Hunt*
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

Implied costs in loss networks are measures of the rate of change of an objective function with respect to the parameters of the network. This paper considers these costs and the costs predicted by the Erlang fixed-point approximation. We derive exact expressions for the implied costs and consider the asymptotic accuracy of the approximation. We show that the approximation is asymptotically valid in some cases but is not valid in one important limiting regime. We also show that a linearity approximation for the implied costs is asymptotically correct when taken over suitable subsets of links.

Keywords

OPTIMISATIONERLANG'S FORMULA
Type
Research Article
Information
Advances in Applied Probability , Volume 21 , Issue 3 , September 1989 , pp. 661 - 680
Copyright
Copyright © Applied Probability Trust 1989 

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Footnotes

Supported by SERC grant No. 87001346.

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