Hostname: page-component-78c5997874-dh8gc Total loading time: 0 Render date: 2024-11-05T09:37:46.786Z Has data issue: false hasContentIssue false
  • English
  • Français

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.
Get access Rights & Permissions [Opens in a new window]

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 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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