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Two remarks on insensitive stochastic models

Published online by Cambridge University Press:  01 July 2016

R. Schassberger
R. Schassberger*
Affiliation:
Technical University of Berlin
*
∗Postal address: Technische Universität Berlin, Fachbereich 3-Mathematik, Strasse des 17 Juni 135, 1000 Berlin 12, W. Germany.
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Abstract

This paper contains two contributions to the insensitivity theory for generalized semi-Markov schemes, namely

  1. (1) a detailed account of a close relationship between insensitive schemes and partially balanced discrete-state Markov chains, and

  2. (2) an extension of the notion of an insensitive scheme in order to incorporate insensitivity phenomena not previously covered.

Keywords

QUEUING NETWORKSPARTIAL BALANCEMARKOV CHAINGENERALIZED SEMI-MARKOV PROCESS
Type
Research Article
Information
Advances in Applied Probability , Volume 18 , Issue 3 , September 1986 , pp. 791 - 814
Copyright
Copyright © Applied Probability Trust 1986 

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References

1. Barbour, A. D. (1982) Generalized semi-Markov schemes and open queuing networks. J. Appl. Prob. 19, 469–474.CrossRefGoogle Scholar
2. Barbour, A. D. and Schassberger, R. (1981) Insensitive average residence times in generalized semi-Markov processes. Adv. Appl. Prob. 13, 720–735.CrossRefGoogle Scholar
3. 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.Google Scholar
4. Cohen, J. W. (1957) Basic problems of telephone traffic theory and the influence of repeated calls. Philips Telecomm. Rev. 18, 49–100.Google Scholar
5. Henderson, W. (1983) Insensitivity and reversed Markov processes. Adv. Appl. Prob. 15, 752–768.CrossRefGoogle Scholar
6. Jansen, U. (1984) Conditional expected sojourn times in insensitive queuing systems and networks. Adv. Appl. Prob. 16, 906–919.Google Scholar
7. Jansen, U., König, D. and Nawrotzki, K. (1979) A criterion of insensitivity for a class of queuing systems with random marked point processes. Math. Operationsforsch. Statist. 10, 379–403.Google Scholar
8. Kelly, F. P. (1979) Reversibility and Stochastic Networks. Wiley, London.Google Scholar
9. König, D. and Jansen, U. (1974) Stochastic processes and properties of invariance for queuing systems with speeds and temporary interruptions. Trans. 7th Prague Conf. Information Theory , 335–343.Google Scholar
10. König, D., Matthes, K. and Nawrotzki, K. (1967) Verallgemeinerungen der Erlangschen und Engsetschen Formeln (Eine Methode der Bedienungstheorie). Akademie-Verlag, Berlin.Google Scholar
11. Rényi, A. (1970) Foundations of Probability Theory. Holden-Day, San Francisco.Google Scholar
12. Schassberger, R. (1978) Insensitivity of steady-state distributions of generalized semi-Markov processes with speeds. Adv. Appl. Prob. 10, 836–851.Google Scholar
13. Schassberger, R. (1983) Decomposable stochastic networks: some observations. Proc. Internat. Sem. Modelling and Perform. Eval. methodology, INRIA, Vol. 1, 203–220.Google Scholar
14. Whitt, W. (1980) Continuity of generalized semi-Markov processes. Math. Oper. Res. 5, 494–501.Google Scholar
15. Whittle, P. (1985) Partial balance and insensitivity J. Appl. Prob. 22, 168–176.Google Scholar