Hostname: page-component-78c5997874-j824f Total loading time: 0 Render date: 2024-11-11T05:56:11.372Z Has data issue: false hasContentIssue false
  • English
  • Français

Partial balance and insensitivity

Published online by Cambridge University Press:  14 July 2016

P. Whittle
P. Whittle*
Affiliation:
University of Cambridge
*
∗Postal address: Statistical Laboratory, 16 Mill Lane, Cambridge CB2 1SB, UK.
Get access Rights & Permissions [Opens in a new window]

Abstract

A direct and general proof is given of the equivalence of partial balance and insensitivity.

Keywords

LOCAL BALANCE
Type
Research Papers
Information
Journal of Applied Probability , Volume 22 , Issue 1 , March 1985 , pp. 168 - 176
Copyright
Copyright © Applied Probability Trust 1985 

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

Barbour, A. D. (1982) Generalised semi-Markov schemes and open queueing networks. J. Appl. Prob. 19, 469–474.Google Scholar
Hordijk, A. and Van Dijk, N. (1983a) Networks of queues. Prob. International Seminar on Modelling and Performance Evaluation Methodology, INRIA 1, 79–135.Google Scholar
Hordijk, A. and Van Dijk, N. (1983b) Adjoint processes, job local balance and insensitivity for stochastic networks. Bull. Internat. Statist. Inst. 50, 776–788.Google Scholar
Jansen, U. and König, D. (1980) Insensitivity and steady-state probabilities in product form for queueing networks. Elektron. Informationsverarbeit. Kybernet. 16, 385–397.Google Scholar
Kelly, F. P. (1979) Reversibility and Stochastic Networks. Wiley, New York.Google Scholar
Koenig, D., Matthes, K. and Nawrotzki, K. (1967) Verallgemeinerungen der Erlangschen und Engsetschen Formeln (Eine Methode der Bedienungstheorie). Akademie-Verlag, Berlin.Google Scholar
Matthes, K. (1962) Zur Theorie der Bedienungsprozesse. Trans. 3rd Prague Conf. Inf. Theory. Google Scholar
Schassberger, R. (1977) Insensitivity of steady-state distributions of generalised semi-Markov processes. Part I. Ann. Prob. 5, 87–99.Google Scholar
Schassberger, R. (1978a) Insensitivity of steady-state distributions of generalised semi-Markov processes. Part II. Ann. Prob. 6, 85–93.CrossRefGoogle Scholar
Schassberger, R. (1978b) Insensitivity of steady-state distributions of generalised semi-Markov processes with speeds. Adv. Appl. Prob. 10, 836–851.Google Scholar
Schassberger, R. (1978C) The insensitivity of stationary probabilities in networks of queues. Adv. Appl. Prob. 10, 906–912.Google Scholar
Schassberger, R. (1979) A definition of discrete product-form distributions. Z. Operat. Res. 23, 189–195.Google Scholar
Whittle, P. (1967) Nonlinear migration processes. Bull. Internat. Inst. Statist. 42, 642–647.Google Scholar
Whittle, P. (1968) Equilibrium distributions for an open migration process. J. Appl. Prob. 5, 567–571.CrossRefGoogle Scholar