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A note on the queueing systems GI/D/1 and D/G/1

Published online by Cambridge University Press:  14 July 2016

A. G. Pakes
A. G. Pakes*
Affiliation:
Monash University
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Extract

In this note we adopt the notation and terminology of Kingman (1966) without further comment. For the general single server queue one has For the queueing systems GI/D/1 and D/G/1 we shall show that it is possible to make use of the special form of the service time and inter-arrival time distributions, respectively, to evaluate the right hand side of (1). A similar evaluation applies to the limiting distribution when it exists. The results obtained could also be obtained from those of Finch (1969) and Henderson and Finch (1970) by using suitable limiting arguments.

Type
Short Communications
Information
Journal of Applied Probability , Volume 7 , Issue 2 , August 1970 , pp. 465 - 468
Copyright
Copyright © Applied Probability Trust 1970 

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References

Finch, P. D. (1969) A note on the queueing system GI/Ek/1. J. Appl. Prob. 6, 708–710.Google Scholar
Henderson, J. and Finch, P. D. (1970) A note on the queueing system Ek/G/1. J. Appl. Prob. 7, 473–475.Google Scholar
Kingman, J. F. C. (1966) On the algebra of queues. J. Appl. Prob. 3, 285–326.CrossRefGoogle Scholar