Hostname: page-component-586b7cd67f-t7czq Total loading time: 0 Render date: 2024-12-04T10:16:03.031Z Has data issue: false hasContentIssue false
  • English
  • Français

Sensitivity bounds on a GI/M/n/n queueing system

Published online by Cambridge University Press:  17 February 2009

Andrew Coyle
Andrew Coyle
Affiliation:
Department of Applied Mathematics, The University of Adelaide, South Australia 5001.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

A method for determining the upper and lower bounds for performance measures for certain types of Generalised Semi-Markov Processes has been described in Taylor and Coyle [8]. A brief description of this method and its use in finding an upper bound for the time congestion of a GI/M/n/n queueing system will be given. This bound turns out to have a simple form which is quickly calculated and easy to use in practice.

Type
Research Article
Information
The ANZIAM Journal , Volume 31 , Issue 2 , October 1989 , pp. 135 - 149
Copyright
Copyright © Australian Mathematical Society 1989

References

[1]Avriel, M., Nonlinear programming: analysis and methods (Prentice-Hall, New Jersey, 1976).Google Scholar
[2]Coyle, A. J., “An upper bound on the time congestion in a GI/M/n/n system”, to appear.Google Scholar
[3]Feller, W., An introduction to probability theory and its applications Vol. 2 (John Wiley, New York, 1966).Google Scholar
[4]König, D. and Jansen, U., “Stochastic processes and properties of invariance for queueing systems and speeds and temporary interruption” Trans. 7th Prague Conference Inf. Th., Stat. Dec. Fns. and Rand. Proc. (1974) 335–343.Google Scholar
[5]Kuczura, A., “Queues with mixed renewal and Poisson inputs” Bell System Tech. J. 51 (1972) 1305–1326.CrossRefGoogle Scholar
[6]Pearce, C. E. M., “On the peakedness of primary and secondary processes” Australian Telecommunications Research 12,2 (1978) 18–24.Google Scholar
[7]Taylor, P. G., “Aspects of insensitivity in stochastic processes”, Ph.D. Thesis, The University of Adelaide, 1987.Google Scholar
[8]Taylor, P. G. and Coyle, A. J., “Bounds on the sensitivity of generalised semi-Markov processes with a single generally distributed lifetime”, submitted.Google Scholar