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Single server queues with modified service mechanisms

Published online by Cambridge University Press:  09 April 2009

G. F. Yeo
G. F. Yeo
Affiliation:
The Australian National University, Canberra.
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Summary

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This paper considers a generalisation of the queueing system M/G/I, where customers arriving at empty and non-empty queues have different service time distributions. The characteristic function (c.f.) of the stationary waiting time distribution and the probability generating function (p.g.f.) of the queue size are obtained. The busy period distribution is found; the results are generalised to an Erlangian inter-arrival distribution; the time-dependent problem is considered, and finally a special case of server absenteeism is discussed.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 2 , Issue 4 , December 1962 , pp. 499 - 507
Copyright
Copyright © Australian Mathematical Society 1962

References

[1]Ewens, W. J. and Finch, P. D., “A generalised single server queue with Erlang inputs” (1962) 49, 242–245.Google Scholar
[2]Finch, P. D., “A probability limit theorem with application to a generalisation of queueing theory”, Acta. Math. Acad. Sci. Hung., (1959) 10, 317–325.CrossRefGoogle Scholar
[3]Gani, J. and Prabhu, N. U., “Remarks on the dam with Poisson type inputs”, Aust. J. Appl. Sci., (1959) 10, 113–122.Google Scholar
[4]Kendall, D. G., “Some problems in the theory of dams”, J. Roy. Statist. Soc., (1957) B19, 207–212.Google Scholar
[5]Lindley, D. V., “The theory of queues with a single server’, Proc. Cambridge Phil. Soc., (1952) 48, 277–289.CrossRefGoogle Scholar
[6]Takács, L., “Investigation of waiting time problems by reduction to Markov processes”, Acta. Math. Acad. Sci. Hung., (1955) 6, 101–129.CrossRefGoogle Scholar
[7]Yeo, G. F., and Weesakul, B., “Distribution of delay to traffic at an intersection, (1962) (submitted for publication).Google Scholar