Hostname: page-component-586b7cd67f-vdxz6 Total loading time: 0 Render date: 2024-11-27T03:36:29.915Z Has data issue: false hasContentIssue false
  • English
  • Français

On the relation between partial balance and insensitivity

Published online by Cambridge University Press:  14 July 2016

D. Fakinos
D. Fakinos*
Affiliation:
University of Thessaloniki
*
∗Postal address: Department of Mathematics, University of Thessaloniki, 54006 Thessaloniki, Greece.
Get access Rights & Permissions [Opens in a new window]

Abstract

Direct and simple proofs are given of the equivalence of partial balance over a set of states and the fact that the corresponding equilibrium distribution is insensitive to nominal sojourn time in that set and independent of its past and remaining duration. By a counter-example it is shown that solely insensitivity is not sufficient for partial balance.

Keywords

MARKOV PROCESSESSOJOURN TIMES
Type
Short Communications
Information
Journal of Applied Probability , Volume 27 , Issue 2 , June 1990 , pp. 445 - 451
Copyright
Copyright © Applied Probability Trust 1990 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Henderson, W. (1983) Insensitivity and reversed Markov processes. Adv. Appl. Prob. 15, 752–768.Google Scholar
Hordijk, A. (1984) Insensitivity for stochastic networks. In Mathematical Computer Performance and Reliability, ed. Iazeolla, G., Courtois, P. J. and Hordijk, A., Elsevier North-Holland, Amsterdam.Google Scholar
Hordijk, A. and Van Dijk, N. (1983a) Networks of queues. INRIA 1, 79–135.Google Scholar
Hordijk, A. and Van Dijk, N. (1983b) Adjoint process, job local balance and insensitivity for stochastic networks. Proc. 44th Session ISI, 776–788.Google Scholar
Kelly, F. P. (1979) Reversibility and Stochastic Networks. Wiley, New York.Google Scholar
König, D., Matthes, K. and Nawrotzki, K. (1967) Verallgemeinerungen der Erlangschen und Engsetschen Formeln (Eine Methode der Bedienungstheorie). Academie-Verlag, Berlin.Google Scholar
Matthes, K. (1962) Zür Theorie der Bedienungsprozesse. Trans. 3rd Prague Conf. Inf. Theory Google Scholar
Schassberger, R. (1977) Insensitivity of steady-state distributions of generalized semi-Markov processes. Part I. Ann. Prob. 5, 87–99.Google Scholar
Schassberger, R. (1978a) Insensitivity of steady-state distributions of generalized semi-Markov processes. Part II. Ann. Prob. 6, 85–93.Google Scholar
Schassberger, R. (1978b) Insensitivity of steady-state distributions of generalized semi-Markov processes with speeds. Adv. Appl. Prob. 10, 836–851.Google Scholar
Schassberger, R. (1986) Two remarks on insensitive stochastic models. Adv. Appl. Prob. 18, 791–814.CrossRefGoogle Scholar
Taylor, P. (1989) Insensitivity in processes with zero speeds. Adv. Appl. Prob. 21, 612–628.CrossRefGoogle Scholar
Whittle, P. (1985) Partial balance and insensitivity. J. Appl. Prob. 22, 168–176.Google Scholar
Whittle, P. (1986) Partial balance, insensitivity and weak coupling. Adv. Appl. Prob. 18, 706–723.Google Scholar