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Approximation in Large-Scale Circuit-Switched Networks

Published online by Cambridge University Press:  27 July 2009

P. Whittle
P. Whittle
Affiliation:
Statistical LaboratoryUniversity of Cambridge, Cambridge, CB2 1SB England
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Abstract

The most probable equilibrium configuration in a circuit-switched network is determined, in the limit of very large scale, by a primal optimization problem whose dual determines the blocking probabilities. This approximation can be inadequate for moderate scale, and so the blocking probabilities are usually determined by the Erlang fixed-point principle. In this paper, it is shown that there is a “softened” form of the dual natural to the problem. This gives determinations of the blocking probabilities agreeing with those derived from the Erlang principle as far as terms of order (scale)-1. It is more attractive than the Erlang principle, however, in that it has a mathematical basis, provides an extremal principle by its nature, yields immediately the geometric distribution of the numbers of free circuits, and clearly agrees with the “hard” dual in the limit of large scale.

Type
Articles
Information
Probability in the Engineering and Informational Sciences , Volume 2 , Issue 3 , July 1988 , pp. 279 - 291
Copyright
Copyright © Cambridge University Press 1988

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References

Brockmeyer, E., Haistrom, H.L., & Jensen, A. (1948). The life and works of A.K. Erlang. Copenhagen: Academy of Technical Sciences.Google Scholar
Burman, D.Y., Lehoczky, J.P., & Lim, Y. (1984). Insensitivity of blocking probabilities in a circuit-switching network. Journal of Applied Probability 21: 850–859.CrossRefGoogle Scholar
Gallager, R.G. (1977). A minimum delay routing algorithm using distributed computation. IEEE Transactions on Communication 25: 73–85.CrossRefGoogle Scholar
Girard, A. & Ouimet, Y. (1983). End-to-end blocking for circuit-switched networks: polynomial algorithms for some special cases. IEEE Transactions on Communication 31: 1269–1273.CrossRefGoogle Scholar
Kelly, F.P. (1986). Blocking probabilities in large circuit-switched networks. Advances in Applied Probability 18: 473–505.CrossRefGoogle Scholar
Kelly, F.P. (1986). Blocking and routing in circuit-switched networks. In Boxma, O.J., Cohen, J.W. & Tijms, H.C. (eds.), Teletraffic analysis and computer performance evaluation. Amsterdam: Elsevier, pp. 37–45.Google Scholar
Kelly, F.P. (1988). Routing in circuit-switched networks: optimization, shadow prices, and decentralization. Advances in Applied Probability 20: 112–144.Google Scholar
Kelly, F.P. (1988). The optimization of queueing and loss networks. In Boxma, O.J. and Syski, R. (eds.), Queueing Theory and its Applications. Amsterdam: Elsevier.Google Scholar
Mitra, D. (1985). Asymptotic analysis and computational methods for a class of simple circuit-switched networks with blocking. A.T.&T. Bell Laboratories.Google Scholar
Whitt, W. (1985). Blocking when service is required from several facilities simultaneously. A.T&.Technical Journal 1807–1856.Google Scholar
Whittle, P. (1985). Scheduling and characterization problems for stochastic networks. Journal of the Royal Statistical Society Series B 47: 407–428.Google Scholar
Whittle, P. (1986). Systems in stochastic equilibrium. Chichester: Wiley.Google Scholar
Ziedins, I. (1987). Quasi-stationary distributions and one-dimensional circuit-switched networks. Journal of Applied Probability 24: 965–977.Google Scholar
Ziedins, I. (1986). Stochastic models of traffic in star and line networks. Ph.D. Thesis, University of Cambridge, Cambridge, England.Google Scholar