Hostname: page-component-848d4c4894-8kt4b Total loading time: 0 Render date: 2024-06-21T14:34:10.976Z Has data issue: false hasContentIssue false
  • English
  • Français

The transient blocking probabilities in M/M/N loss systems via large deviations

Part of: Special processes

Published online by Cambridge University Press:  01 July 2016

T. Choukri
T. Choukri*
Affiliation:
Telecom Paris
*
∗Postal address: E.N.S.T. Département Réseaux, 46 Rue Barrault, 75634 Paris Cedex, France.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

By using large devaitions theory, we give asymptotic formulas for the transient blocking probabilities of M/M/N/N and M (with finite Poissonian sources) M/N/N queues.

Keywords

LARGE DEVIATIONSLOSS SYSTEM

MSC classification

Primary: 60K25: Queueing theory
Type
Letters to the Editor
Information
Advances in Applied Probability , Volume 25 , Issue 2 , June 1993 , pp. 483 - 486
Copyright
Copyright © Applied Probability Trust 1993 

References

[1] Dreyfus, S. E. (1965) Dynamic Programming and the Calculus of Variations. Academic Press, New York.Google Scholar
[2] Freidlin, M. I. (1972) The action functional for a class of stochastic processes. Theory Prob. Appl. 17, 511–515.CrossRefGoogle Scholar
[3] Jagerman, D. L. (1975) Nonstationary blocking in telephone traffic. Bell System Tech. J. 54, 625–661.CrossRefGoogle Scholar
[4] Varadham, S. R. S. (1984) Large Deviations and Applications. CBMS-NSF Regional Conference Series in Applied Mathematics 46, SIAM, Philadelphia.CrossRefGoogle Scholar
[5] Ventsel, A. D. (1976) Rough limit theorems on large deviations for Markov stochastic processes 1. Theory Prob. Appl. 11, 225–242.Google Scholar
[6] Weiss, A. (1986) A new technique for analyzing large traffic systems. Adv. Appl. Prob. 18, 506–532.CrossRefGoogle Scholar
[7] Yunus, M. N. (1986) A simple derivation of an approximation to the transient blocking probability in a loss system. Adv. Appl. Prob. 18, 862–863.CrossRefGoogle Scholar