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On critically loaded loss networks

Published online by Cambridge University Press:  01 July 2016

P. J. Hunt  and
F. P. Kelly
P. J. Hunt*
Affiliation:
University of Cambridge
F. P. Kelly*
Affiliation:
University of Cambridge
*
Postal address for both authors: Statistical Laboratory, Department of Pure Mathematics and Mathematical Statistics, University of Cambridge, 16 Mill Lane, Cambridge CB2 1SB, UK.
Postal address for both authors: 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 studies the behaviour of large loss networks, paying particular attention to links at a certain critical loading where the load offered very nearly matches capacity. We correct and extend an earlier central limit theorem for the stationary distribution of a loss network with critically loaded links. We then use this result to show that acceptance probabilities have a limiting product-form decomposition, despite marked dependencies between the occupancies of critically loaded links.

Keywords

BLOCKING PROBABILITIESERLANG'S FORMULA
Type
Research Article
Information
Advances in Applied Probability , Volume 21 , Issue 4 , December 1989 , pp. 831 - 841
Copyright
Copyright © Applied Probability Trust 1989 

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Footnotes

∗

Supported by SERC grant No. 8700 1346.

References

[1] Brockmeyer, E., Halstrom, H. L. and Jensen, A. (1948) The Life and Works of A. K. Erlang. Academy of Technical Sciences, Copenhagen.Google Scholar
[2] Burman, D. Y., Lehoczky, J. P. and Lim, Y. (1984) Insensitivity of blocking probabilities in a circuit-switched network. J. Appl. Prob. 21, 850–859.CrossRefGoogle Scholar
[3] Cooper, R. B. and Katz, S. S. (1964) Analysis of alternate routing networks with account taken of the nonrandomness of overflow traffic. Bell Laboratories.Google Scholar
[4] Dziong, Z. and Roberts, J. W. (1987) Congestion probabilities in a circuit-switched integrated services network. Performance Evaluation 7, 267–284.CrossRefGoogle Scholar
[5] Hunt, P. J. (1989) Implied costs in loss networks. Adv. Appl. Prob. 21, 661–680.Google Scholar
[6] Jagerman, D. L. (1974) Some properties of the Erlang loss function. Bell Syst. Tech. J. 53, 525–557.Google Scholar
[7] Kelly, F. P. (1979) Reversibility and Stochastic Networks. Wiley, Chichester.Google Scholar
[8] Kelly, F. P. (1986) Blocking probabilities in large circuit-switched networks. Adv. Appl. Prob. 18, 473–505.Google Scholar
[9] Kelly, F. P. (1988) Routing in circuit-switched networks: optimization, shadow prices and decentralization. Adv. Appl. Prob. 20, 112–144.Google Scholar
[10] Rao, C. R. (1965) Linear Statistical Inference and Its Applications. Wiley, New York.Google Scholar
[11] Ross, S. M. (1970) Applied Probability Models with Optimization Applications. Holden-Day, San Francisco.Google Scholar
[12] Whitt, W. (1985) Blocking when service is required from several facilities simultaneously. A.T. & T. Tech. J. 64, 1807–1856.Google Scholar