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A single server queue in discrete time with customers served in random order

Published online by Cambridge University Press:  14 July 2016

D. W. Balmer
D. W. Balmer*
Affiliation:
Salford University
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Abstract

This paper aims at showing that for the discrete time analogue of the M/G/l queueing model with service in random order and with a traffic intensity ρ > 0, the condition ρ < ∞ is sufficient in order that every customer joining the queue be served eventually, with probability one (Theorem 2).

Keywords

M/G/1 QUEUEDISCRETE TIMERANDOM SERVICE DISCIPLINE
Type
Short Communications
Information
Journal of Applied Probability , Volume 9 , Issue 4 , December 1972 , pp. 862 - 867
Copyright
Copyright © Applied Probability Trust 1972 

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References

[1] Ailam, G. and Tata, M. N. (1970) One-to-one functions on the positive integers. J. Appl. Prob. 7, 505–507.Google Scholar
[2] Dafermos, S. C. and Neuts, M. F. (1971) A single server queue in discrete time. Cahiers Centre Rech. Opérat. 13, no. 1, 23–40.Google Scholar
[3] Feller, W. (1957) An Introduction to Probability Theory and its Applications. Vols. I and II. John Wiley, New York.Google Scholar
[4] Kingman, J. F. C. (1961) On queues in which customers are served in random order. Proc. Camb. Phil. Soc. 58, 79–90.Google Scholar
[5] Neuts, M. F. (1968) Are many 1–1 functions on the positive integers onto? Math. Mag. 41, 103–109.Google Scholar