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Non-standard insensitivity

Published online by Cambridge University Press:  14 July 2016

W. Henderson
W. Henderson*
Affiliation:
University of Adelaide
*
∗ Postal address: Department of Applied Mathematics, The University of Adelaide, Box 498, G.P.O., Adelaide, SA 5001, Australia.
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Abstract

The paper takes a closer look at some insensitivity results which are not contained in the class of insensitive generalised semi-Markov schemes. Based on a study of a special insensitive queue, a conjecture is proposed which covers all known results on insensitive equilibrium distributions. When insensitive events are also included, a study of the G/G/1 queue shows that the conjecture does not always hold.

Keywords

INSENSITIVE DISTRIBUTIONSINSENSITIVE EVENTSSUPPLEMENTARY VARIABLES
Type
Research Papers
Information
Journal of Applied Probability , Volume 20 , Issue 2 , June 1983 , pp. 288 - 296
Copyright
Copyright © Applied Probability Trust 1983 

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Footnotes

This paper was researched and written at the Statistical Laboratory, Cambridge University and the Department of Statistics, University of Newcastle upon Tyne, while the author was on sabbatical leave.

References

Baskett, F., Chandy, M., Muntz, R. and Palacios, J. (1975) Open, closed and mixed networks of queues with different classes of customers. J. Assoc. Comput. Mach. 22, 248–260.CrossRefGoogle Scholar
Brumelle, S. (1978) A generalisation of Erlang's loss system to state dependent arrival and service rates. Math. Operat. Res. 3, 10–16.CrossRefGoogle Scholar
Chaiken, J. M. and Ignall, E. (1972) An extension of Erlang's formulas which distinguishes individual servers. J. Appl. Prob. 9, 192–197.CrossRefGoogle Scholar
Chandy, K. M., Howard, J. H. and Towsley, D. F. (1977) Product form and local balance in queueing networks. J. Assoc. Comput. Mach. 24, 250–263.Google Scholar
Henderson, W. (1972) Alternative approaches to the analysis of the M/G/1 and G/M/1 queues. J. Operat. Res. Soc. Japan 15, 92–101.Google Scholar
Henderson, W. (1982) Insensitivity and reversed Markov processes.Google Scholar
Kelly, F. P. (1976) Networks of queues. Adv. Appl. Prob. 8, 416–432.Google Scholar
Kelly, F. P. (1979) Reversibility and Stochastic Networks. Wiley, New York.Google Scholar
König, D. and Jansen, U. (1978) Stochastic processes and properties of invariance for queueing systems with speeds and temporary interruptions. Trans. 7th Prague Conference on Information Theory A, Reidel, Dordrecht, 335–343.Google Scholar
Matthes, K. (1964) Zür theorie der Bedienungprozesse. Trans. 3rd Prague Conference on Information Theory, Czechoslovak Academy of Sciences, 513–528.Google Scholar
Oakes, D. (1976) Random overlapping intervals: a generalisation of Erlang's loss formula. Ann. Prob. 4, 940–994.CrossRefGoogle Scholar
Schassberger, R. (1978a) Insensitivity of steady state distributions of generalised semi-Markov processes with speeds. Adv. Appl. Prob. 10, 836–851.Google Scholar
Schassberger, R. (1978b) The insensitivity of stationary probabilities in networks of queues. Adv. Appl. Prob. 10, 906–912.Google Scholar
Wolff, R. W. and Wrightson, C. W. (1976) An extension of Erlang's loss formula. J. Appl. Prob. 13, 628–632.Google Scholar