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

Part of: Special processes Operations research and management science

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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