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Insensitivity of blocking probabilities in a circuit-switching network

Published online by Cambridge University Press:  14 July 2016

D. Y. Burman ,
J. P. Lehoczky  and
Y. Lim
D. Y. Burman*
Affiliation:
AT&T Bell Laboratories
J. P. Lehoczky*
Affiliation:
Carnegie–Mellon University
Y. Lim
Affiliation:
GTE Laboratories
*
∗Postal address: AT&T Bell Laboratories, Room 3B341, 600 Mountain Avenue, Murray Hill, NJ 07974, USA.
∗∗Postal address: Department of Statistics, Carnegie-Mellon University, Schenley Park, Pittsburgh, PA 15213, USA.
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Abstract

Consider a network of nodes (switches) and connecting links. Each link consists of a group of channels (trunks). A call instantaneously seizes channels along a route between the originating and terminating node, holds them for a randomly distributed length of time and frees them instantaneously at the end of the call. If no channels are available, the call is blocked. For special networks with exponential call holding times, Erlang has shown that the steady-state probabilities are in product form. In this paper, we extend this work to general networks and show that if for each pair of nodes there is a unique route, then the blocking probabilities are in product form and are insensitive to the call holding-time distribution, which means that they depend on the call duration only through its mean.

Type
Research Papers
Information
Journal of Applied Probability , Volume 21 , Issue 4 , December 1984 , pp. 850 - 859
Copyright
Copyright © Applied Probability Trust 1984 

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Footnotes

Research supported in part by NSF Grant ECS 81 01576.

References

Brockmeyer, E., Halström, H. L. and Jensen, A. (1948) The Life and Works of A. K. Erlang. The Copenhagen Telephone Co., Copenhagen.Google Scholar
Burman, D. (1981) Insensitivity in queueing systems. Adv. Appl. Prob. 13, 846–859.CrossRefGoogle Scholar
Kelly, F. P. (1979) Reversibility and Stochastic Networks. Wiley, New York.Google Scholar
Lam, S. S. (1977) Queueing networks with population size constraints. IBM J. Res. Devel. 21, 370–378.CrossRefGoogle Scholar
Lehoczky, J. P. and Lim, Y. (1983) Performance of a network voice/data communication system.Google Scholar
Mckenna, J., Mitra, D. and Ramakrishnan, K. G. (1981) A class of closed Markovian queueing networks: integral representations, asymptotic expansions and generalizations. Bell. System Tech. J. 60, 599–642.CrossRefGoogle Scholar
Sauer, C. H. and Chandy, K. M. (1981) Computer Systems Performance Modeling. Prentice-Hall, Englewood Cliffs, NJ.Google Scholar
Schassberger, R. (1978) Insensitivity of steady-state distributions in generalized semi-Markov processes with speeds. Adv. Appl. Prob. 10, 906–912.CrossRefGoogle Scholar