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A note on the queueing system GI/Ek/1

Published online by Cambridge University Press:  14 July 2016

P. D. Finch
P. D. Finch*
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 system GI/Ek/1 it is possible to make use of the particular nature of the service time distribution to evaluate the right-hand side of Equation (1) in terms of the k roots of a certain equation. This evaluation is carried out in detail in Prabhu (1965) to which reference should be made for the technicalities involved. A similar evaluation applies to the limiting distribution when it exists. However, the resulting expression again involves the k roots of a certain equation. In this note we draw attention to an alternative procedure which does not involve the calculation of roots. We remark that a similar, but slightly different, procedure can be used in the study of the queueing system Ek/GI/1. Details of this will be presented in a separate note.

Type
Short Communications
Information
Journal of Applied Probability , Volume 6 , Issue 3 , December 1969 , pp. 708 - 710
Copyright
Copyright © Applied Probability Trust 

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References

Kingman, J. F. C. (1966) On the algebra of queues. J. Appl. Prob. 3, 285–326.CrossRefGoogle Scholar
Prabhu, N. U. (1965) Queues and Inventories. J. Wiley and Sons. Inc., New York.Google Scholar