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Asymptotic Estimates for Blocking Probabilities in a Large Multi-Rate Loss Network

Part of: Operations research and management science Special processes

Published online by Cambridge University Press:  01 July 2016

A. Simonian ,
J. W. Roberts ,
F. Théberge  and
R. Mazumdar
A. Simonian*
Affiliation:
France Télécom—CNET
J. W. Roberts*
Affiliation:
France Télécom—CNET
F. Théberge*
Affiliation:
McGill University
R. Mazumdar*
Affiliation:
University of Essex
*
∗ Postal address: France Télécom—CNET, 38-40r. Général Leclerc, 92131 Issy-les-Moulineaux, France.
∗ Postal address: France Télécom—CNET, 38-40r. Général Leclerc, 92131 Issy-les-Moulineaux, France.
∗∗ Postal address: McGill University, Department of Electrical Engineering, Montreal, P.Q., H3A 2A7, Canada.
∗∗∗ Postal address: Department of Mathematics, University of Essex, Colchester CO4 3SQ, UK.
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Abstract

In this paper, asymptotic estimates for the blocking probability of a call pertaining to a given route in a large multi-rate circuit-switched network are given. Concentrating on low load and critical load conditions, these estimates are essentially derived by using probability change techniques applied to the distribution of the number of occupied links. Such estimates for blocking probabilities are also given a uniform expression applicable to both load regimes. This uniform expression is numerically validated via simple examples.

Keywords

MULTI-RATE LOSS NETWORKSBLOCKING PROBABILITYLARGE DEVIATIONSASYMPTOTIC ESTIMATE

MSC classification

Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory
Secondary: 60K25: Queueing theory 60K30: Applications (congestion, allocation, storage, traffic, etc.) 90B15: Network models, stochastic
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 29 , Issue 3 , September 1997 , pp. 806 - 829
Copyright
Copyright © Applied Probability Trust 1997 

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References

[1] Bertsekas, D. P. (1982) Constrained Optimization and Lagrange Multiplier Methods. Academic Press, New York.Google Scholar
[2] Bhattacharya, R. N. and Rao, R. R. (1976) Normal Approximation and Asymptotic Expansions Wiley, New York.Google Scholar
[3] Boros, E. and Prekopa, A. (1989) Closed form two-sided bounds for probabilities that at least r and exactly r out of n events occur. Math. Operat. Res. 14, 317–342.CrossRefGoogle Scholar
[4] Bucklew, J. A. (1990) Large Deviations Techniques in Decision, Simulation and Estimate. Wiley, New York.Google Scholar
[5] Choudhury, G. L., Leung, K. and Whitt, W. (1994) An algorithm to compute blocking probabilities in multi-rate multi-class multi-resource loss models. Adv. Appl. Prob. 27, 1104–1143.CrossRefGoogle Scholar
[6] Chung, S. and Ross, K. W. (1993) Reduced load approximations for multirate loss networks, IEEE Trans. Commun. 41, 1222–1231.CrossRefGoogle Scholar
[7] Dziong, Z. and Roberts, J. W. (1987) Congestion probabilities in a circuit switched integrated services network. Perf. Eval. 7.CrossRefGoogle Scholar
[8] Gazdzicki, P., Lambadaris, I. and Mazumdar, R. R. (1993) Blocking probabilities for large multirate Erlang loss systems. Adv. Appl. Prob. 25, 997–1009.CrossRefGoogle Scholar
[9] Hunt, P. J. and Kelly, F. P. (1989) On critically loaded loss networks. Adv. Appl. Prob. 21, 831–841.CrossRefGoogle Scholar
[10] Kelly, F. P. (1986) Blocking probabilities in large circuit-switched networks. Adv. Appl. Prob. 18, 473–505.CrossRefGoogle Scholar
[11] Kelly, F. P. (1991) Loss networks. Ann. Appl. Prob. 1, 319–378.CrossRefGoogle Scholar
[12] Mitra, D. and Morrison, J. (1994) Erlang capacity and uniform approximations for shared unbuffered resources. IEEE/ACM Trans. Network. 2, 558–570.CrossRefGoogle Scholar
[13] Murray, J. D. (1984) Asymptotic Analysis. Springer, New York.CrossRefGoogle Scholar
[14] Reiman, M. I. (1991) A critically loaded multi-class Erlang loss system. Queueing Systems 9, 65–82.CrossRefGoogle Scholar
[15] Simonian, A. (1992) Analyse asymptotique des taux de blocage pour un trafic multidébit. Ann Télécommunications 47, 56–63.CrossRefGoogle Scholar
[16] Theberge, F. and Mazumdar, R. R. (1996) A new reduced load heuristic for computing blocking in large multirate loss networks. Proc. IEE Commun. 134, 206–211.CrossRefGoogle Scholar
[17] Tong, Y. L. (1990) The Multivariate Normal Distribution (Springer Series in Statistics). Springer, Berlin.CrossRefGoogle Scholar