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Combinatorial properties of a queueing system by limited availability

Published online by Cambridge University Press:  01 July 2016

J. M. Pollard
J. M. Pollard*
Affiliation:
Plessey Telecommunications Research, Taplow Court, Taplow, Maidenhead, Berkshire
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Abstract

A type of service system of particular interest in teletraffic theory has the property that calls (customers) originating from different sources have access to different subsets of a single group of devices (servers). One may or may not allow the formation of queues. Thierer [11], [12] has studied such a system with queues assuming it to be reversible. We investigate the conditions under which this assumption is exact.

Keywords

QUEUEING NETWORKSREVERSIBLE PROCESSTELEPHONE TRAFFICLIMITED ACCESS
Type
Research Article
Information
Advances in Applied Probability , Volume 7 , Issue 4 , December 1975 , pp. 864 - 877
Copyright
Copyright © Applied Probability Trust 1975 

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References

[1] Anderson, I. (1974) A First Course in Combinatorial Mathematics. Clarendon Press, Oxford.Google Scholar
[2] Berge, C. (1962) The Theory of Graphs and its Applications. Methuen, London.Google Scholar
[3] Brockmeyer, E. Halstrom, H. L. and Jensen, A. (1948) The life and works of A. K. Erlang. Trans. Danish Acad. Tech. Sci. No. 2.Google Scholar
[4] Carlsson, S. G. and Elldin, A. (1958) Solving equations of state in telephone traffic theory with digital computers. Proc. Second International Teletraffic Congress, Paper 9. Reprinted in Ericsson Technics 4, 221–244.Google Scholar
[5] Kingman, J. F. C. (1961) The ergodic behaviour of random walks. Biometrika 48, 391–396.Google Scholar
[6] Kingman, J. F. C. (1961) Two similar queues in parallel. Ann. Math. Statist. 32, 314–323.CrossRefGoogle Scholar
[7] Kingman, J. F. C. (1969) Markov population processes. J. Appl. Prob. 6, 1–18.Google Scholar
[8] Kuhn, P. (1973) Waiting time distributions in multiqueue delay systems with grading. Proc. Seventh International Teletraffic Congress, Paper 242.Google Scholar
[9] Reich, E. (1957) Waiting times when queues are in tandem. Ann. Math. Statist. 28, 768–773.CrossRefGoogle Scholar
[10] Syski, R. (1960) Introduction to Congestion Theory in Telephone Systems. Oliver and Boyd, Edinburgh and London.Google Scholar
[11] Thierer, M. H. (1967) Delay systems with limited accessibility. Proc. Fifth International Teletraffic Congress, 203–213.Google Scholar
[12] Thierer, M. H. (1968) Delay Tables for Limited and Full Availability according to the Interconnection Delay Formula. Seventh Report on Studies in Congestion Theory, Institute for Switching and Data Technics, Technical University of Stuttgart.Google Scholar