Hostname: page-component-78c5997874-m6dg7 Total loading time: 0 Render date: 2024-11-13T06:47:42.224Z Has data issue: false hasContentIssue false
  • English
  • Français

Insensitivity with age-dependent routing

Published online by Cambridge University Press:  01 July 2016

M. Rumsewicz  and
W. Henderson
M. Rumsewicz*
Affiliation:
University of Adelaide
W. Henderson*
Affiliation:
University of Adelaide
*
Postal address for both authors: Department of Applied Mathematics, University of Adelaide, GPO Box 498, Adelaide SA 5001, Australia.
Postal address for both authors: Department of Applied Mathematics, University of Adelaide, GPO Box 498, Adelaide SA 5001, Australia.
Get access Rights & Permissions [Opens in a new window]

Abstract

The theory of insensitivity is extended to include processes where some of the routing probabilities of the process are made dependent upon the length of time the generally distributed variables have been alive. Examples of such systems are given, including networks of queues with age-dependent routing.

Keywords

PARTIAL BALANCEPRODUCT-FORM QUEUEING NETWORKSAGE-DEPENDENT ROUTING
Type
Research Article
Information
Advances in Applied Probability , Volume 21 , Issue 2 , June 1989 , pp. 398 - 408
Copyright
Copyright © Applied Probability Trust 1989 

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

Baskett, F., Chandy, K. M., Muntz, R. R. and Palacios, F. G. (1975) Open, closed and mixed networks of queues with different classes of customers. J. Assoc. Comput. Mach. 22, 248–260.Google Scholar
Bunday, B. D. and Scraton, R. E. (1980) The G/M/r machine interference model. Eur. J. Operat. Res. 4, 399–402.Google Scholar
Buzen, J. P. (1973) Computational algorithms for closed queueing networks with exponential servers. Comm. Assoc. Comput. Mach. 16, 527–531.Google Scholar
Chandy, K. M. and Martin, A. J. (1983) A characterization of product form queueing networks. J. Assoc. Comput. Mach. 30, 286–299.Google 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. (1983) Insensitivity and reversed Markov processes. Adv. Appl. Prob. 15, 752–768.Google Scholar
Henderson, W. and Lucic, D. (1988) Applications of generalised semi-Markov processes to stochastic Petri nets. Int. Sem. Performance of Distributed and Parallel Systems, Kyoto.Google Scholar
Henderson, W. and Taylor, P. (1989) Insensitivity of processes with interruptions. J. Appl. Prob. 26.CrossRefGoogle Scholar
Kelly, F. P. (1975a) Networks of queues with customers of different types. J. Appl. Prob. 12, 542–554.CrossRefGoogle Scholar
Kelly, F. P. (1975b) Markov processes and Markov random fields. Bull. Inst. Internat. Statist. 46, 397–404.Google Scholar
Kelly, F. P. (1976) Networks of queues. Adv. Appl. Prob. 8, 416–432.Google Scholar
Kelly, F. P. (1979) Reversibility and Stochastic Processes. Wiley, London.Google Scholar
König, D. and Jansen, U. (1974) Stochastic processes and properties of invariance for queueing systems with speeds and interruptions. Trans 7th Prague Conference on Information Theory, Reidel, Dordrecht, 335–343.Google Scholar
König, D. and Jansen, U. (1980) Insensitivity and steady state probabilities in product form for queueing networks. Elektron. Informationsverarbeit. Kybernetik 16, 385–397.Google Scholar
Matthes, K. (1962) Zur Theories der Bedienungprozesse. Trans 3rd Prague Conf Information Theory.Google Scholar
Rumsewicz, M. (1988) Some Contributions to the Theory of Insensitivity and Queueing Theory. , University of Adelaide.Google Scholar
Schassberger, R. (1977) Insensitivity of steady state distributions of generalised semi-Markov processes, Part I. Ann. Prob. 5, 87–99.CrossRefGoogle Scholar
Schassberger, R. (1978) Insensitivity of steady state distributions of generalized semi-Markov processes with speeds. Adv. Appl. Prob. 10, 836–851.Google Scholar
Taylor, P. (1987) Aspects of Insensitivity in Stochastic Processes. , University of Adelaide.Google Scholar
Whittle, P. (1985) Partial balance and insensitivity. J. Appl. Prob. 22, 168–176.Google Scholar